30562 lines
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30562 lines
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<o:Description>Before calling swe_calc(), call swe_set_topo(). position. swe_sol_eclipse_when_glob( tjd...) Lunar eclipses: swe_lun_eclipse_when(tjd...) Swe_calc() returns true positions for these points.</o:Description>
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Grid 6"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Grid 7"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Grid 8"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 1"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 2"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 3"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 4"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 5"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 6"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 7"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table List 8"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table 3D effects 1"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table 3D effects 2"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table 3D effects 3"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Contemporary"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Elegant"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Professional"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Subtle 1"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Subtle 2"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Web 1"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Web 2"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Web 3"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Balloon Text"/>
|
||
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
|
||
Name="Table Theme"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
|
||
<w:LsdException Locked="false" Priority="1" Name="No Spacing"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
|
||
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
|
||
<w:LsdException Locked="false" Priority="34" QFormat="true"
|
||
Name="List Paragraph"/>
|
||
<w:LsdException Locked="false" Priority="29" Name="Quote"/>
|
||
<w:LsdException Locked="false" Priority="30" Name="Intense Quote"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="19" Name="Subtle Emphasis"/>
|
||
<w:LsdException Locked="false" Priority="21" Name="Intense Emphasis"/>
|
||
<w:LsdException Locked="false" Priority="31" Name="Subtle Reference"/>
|
||
<w:LsdException Locked="false" Priority="32" Name="Intense Reference"/>
|
||
<w:LsdException Locked="false" Priority="33" Name="Book Title"/>
|
||
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
|
||
UnhideWhenUsed="true" Name="Bibliography"/>
|
||
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
|
||
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
|
||
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
|
||
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
|
||
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
|
||
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
|
||
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
|
||
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
|
||
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
|
||
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
|
||
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="Grid Table 1 Light Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="Grid Table 6 Colorful Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="Grid Table 7 Colorful Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
|
||
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
|
||
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="List Table 6 Colorful Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="List Table 7 Colorful Accent 1"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="List Table 6 Colorful Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="List Table 7 Colorful Accent 2"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="List Table 6 Colorful Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="List Table 7 Colorful Accent 3"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="List Table 6 Colorful Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="List Table 7 Colorful Accent 4"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="51"
|
||
Name="List Table 6 Colorful Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="52"
|
||
Name="List Table 7 Colorful Accent 5"/>
|
||
<w:LsdException Locked="false" Priority="46"
|
||
Name="List Table 1 Light Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
|
||
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
|
||
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mso-font-signature:-2147483601 10 0 0 1 0;}
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|
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|
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|
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|
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|
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mso-font-signature:-2147482973 717745402 16 0 131072 0;}
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mso-font-signature:-2147482973 717745402 16 0 131072 0;}
|
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mso-font-signature:-2147482973 717745402 16 0 131072 0;}
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mso-font-signature:-2147482973 717745402 16 0 131072 0;}
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mso-font-signature:-2147482973 717745402 16 0 131072 0;}
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mso-font-signature:-2147483001 0 0 0 15 0;}
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mso-font-signature:-2147483001 0 0 0 15 0;}
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mso-generic-font-family:roman;
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mso-font-signature:2097155 0 0 0 1 0;}
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mso-generic-font-family:swiss;
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
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{font-family:"Verdana Pro Black";
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mso-generic-font-family:swiss;
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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mso-generic-font-family:swiss;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
|
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{font-family:"Verdana Pro Cond Black";
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mso-font-charset:0;
|
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mso-generic-font-family:swiss;
|
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
|
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@font-face
|
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{font-family:"Verdana Pro Cond Light";
|
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mso-font-charset:0;
|
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mso-generic-font-family:swiss;
|
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
|
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{font-family:"Verdana Pro Cond SemiBold";
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mso-generic-font-family:swiss;
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
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{font-family:"Verdana Pro Light";
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mso-generic-font-family:swiss;
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
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{font-family:"Verdana Pro SemiBold";
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mso-generic-font-family:swiss;
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mso-font-pitch:variable;
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mso-font-signature:-2147483001 67 0 0 159 0;}
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@font-face
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{font-family:Vijaya;
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mso-generic-font-family:roman;
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mso-font-signature:1048579 0 0 0 1 0;}
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
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mso-generic-font-family:roman;
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
|
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mso-generic-font-family:roman;
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
|
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{font-family:"Walbaum Display SemiBold";
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
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|
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
|
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{font-family:"Walbaum Text";
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mso-font-charset:0;
|
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mso-generic-font-family:roman;
|
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mso-font-pitch:variable;
|
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mso-font-signature:-2147483601 10 0 0 1 0;}
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@font-face
|
||
{font-family:"Yu Mincho";
|
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mso-font-charset:128;
|
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mso-generic-font-family:roman;
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|
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mso-font-signature:-2147482905 717749503 18 0 131231 0;}
|
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@font-face
|
||
{font-family:"Yu Mincho Demibold";
|
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mso-font-charset:128;
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mso-generic-font-family:roman;
|
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mso-font-pitch:variable;
|
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mso-font-signature:-2147482905 717749503 18 0 131231 0;}
|
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@font-face
|
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{font-family:"Yu Mincho Light";
|
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|
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mso-generic-font-family:roman;
|
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|
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mso-font-signature:-2147482905 717749503 18 0 131231 0;}
|
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@font-face
|
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{font-family:"\@MS Mincho";
|
||
panose-1:2 2 6 9 4 2 5 8 3 4;
|
||
mso-font-charset:128;
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mso-generic-font-family:modern;
|
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mso-font-pitch:fixed;
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mso-font-signature:-536870145 1791491579 134217746 0 131231 0;}
|
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/* Style Definitions */
|
||
p.MsoNormal, li.MsoNormal, div.MsoNormal
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{mso-style-unhide:no;
|
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mso-style-parent:"";
|
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margin-top:0cm;
|
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margin-right:0cm;
|
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margin-bottom:3.0pt;
|
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margin-left:0cm;
|
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text-align:justify;
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mso-pagination:none;
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layout-grid-mode:char;
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text-autospace:ideograph-numeric;
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font-size:10.0pt;
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mso-bidi-font-size:11.0pt;
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font-family:"Segoe UI",sans-serif;
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mso-fareast-font-family:"Times New Roman";
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mso-ansi-language:EN-US;
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mso-fareast-language:AR-SA;}
|
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h1
|
||
{mso-style-unhide:no;
|
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mso-style-qformat:yes;
|
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mso-style-parent:"<22>berschrift 2";
|
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mso-style-next:Standard;
|
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margin-top:12.0pt;
|
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margin-right:0cm;
|
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margin-bottom:12.0pt;
|
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margin-left:1.0cm;
|
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text-indent:-1.0cm;
|
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mso-pagination:none;
|
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page-break-after:avoid;
|
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mso-list:l0 level1 lfo3;
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layout-grid-mode:char;
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text-autospace:ideograph-numeric;
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border:none;
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mso-border-bottom-alt:solid windowtext 1.5pt;
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padding:0cm;
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mso-padding-alt:0cm 0cm 4.0pt 0cm;
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font-size:14.0pt;
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font-family:"Segoe UI",sans-serif;
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mso-bidi-font-family:"Times New Roman";
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color:#4472C4;
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mso-font-kerning:0pt;
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mso-ansi-language:EN-US;
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mso-fareast-language:AR-SA;
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font-weight:normal;}
|
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h2
|
||
{mso-style-unhide:no;
|
||
mso-style-qformat:yes;
|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:0cm;
|
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margin-bottom:12.0pt;
|
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margin-left:19.85pt;
|
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text-align:justify;
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mso-list:l0 level2 lfo3;
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|
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|
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layout-grid-mode:char;
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text-autospace:ideograph-numeric;
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border:none;
|
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mso-border-bottom-alt:solid windowtext 1.5pt;
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padding:0cm;
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mso-padding-alt:0cm 0cm 1.0pt 0cm;
|
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font-size:13.0pt;
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mso-bidi-font-size:14.0pt;
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font-family:"Segoe UI",sans-serif;
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mso-bidi-font-family:"Times New Roman";
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color:#4472C4;
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mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-weight:normal;
|
||
mso-bidi-font-weight:bold;}
|
||
h3
|
||
{mso-style-unhide:no;
|
||
mso-style-qformat:yes;
|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:14.45pt;
|
||
margin-bottom:12.0pt;
|
||
margin-left:39.7pt;
|
||
text-indent:0cm;
|
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mso-pagination:none;
|
||
page-break-after:avoid;
|
||
mso-outline-level:3;
|
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mso-list:l0 level3 lfo3;
|
||
mso-hyphenate:none;
|
||
tab-stops:18.0pt;
|
||
layout-grid-mode:char;
|
||
text-autospace:ideograph-numeric;
|
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border:none;
|
||
mso-border-bottom-alt:solid windowtext 1.0pt;
|
||
padding:0cm;
|
||
mso-padding-alt:0cm 0cm 1.0pt 0cm;
|
||
font-size:12.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-bidi-font-family:"Times New Roman";
|
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color:#4472C4;
|
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mso-ansi-language:EN-US;
|
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mso-fareast-language:AR-SA;
|
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font-weight:normal;
|
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mso-bidi-font-weight:bold;}
|
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h4
|
||
{mso-style-unhide:no;
|
||
mso-style-qformat:yes;
|
||
mso-style-next:Standard;
|
||
margin-top:6.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:6.0pt;
|
||
margin-left:2.0cm;
|
||
text-indent:0cm;
|
||
mso-pagination:widow-orphan;
|
||
page-break-after:avoid;
|
||
mso-outline-level:4;
|
||
mso-list:l0 level4 lfo3;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-bidi-font-size:12.0pt;
|
||
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|
||
mso-bidi-font-family:"Times New Roman";
|
||
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|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-weight:normal;}
|
||
h5
|
||
{mso-style-unhide:no;
|
||
mso-style-next:Standard;
|
||
margin-top:6.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:144.0pt;
|
||
text-align:justify;
|
||
text-indent:0cm;
|
||
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|
||
mso-outline-level:5;
|
||
mso-list:l0 level5 lfo3;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-bidi-font-family:"Times New Roman";
|
||
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|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-weight:normal;}
|
||
h6
|
||
{mso-style-unhide:no;
|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:180.0pt;
|
||
text-align:justify;
|
||
text-indent:0cm;
|
||
mso-pagination:none;
|
||
mso-outline-level:6;
|
||
mso-list:l0 level6 lfo3;
|
||
mso-hyphenate:none;
|
||
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|
||
layout-grid-mode:char;
|
||
text-autospace:ideograph-numeric;
|
||
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|
||
mso-bidi-font-size:11.0pt;
|
||
font-family:"Times New Roman",serif;
|
||
color:blue;
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-weight:normal;}
|
||
p.MsoHeading7, li.MsoHeading7, div.MsoHeading7
|
||
{mso-style-unhide:no;
|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:216.0pt;
|
||
text-align:justify;
|
||
text-indent:0cm;
|
||
mso-pagination:none;
|
||
mso-outline-level:7;
|
||
mso-list:l0 level7 lfo3;
|
||
mso-hyphenate:none;
|
||
tab-stops:64.8pt;
|
||
layout-grid-mode:char;
|
||
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|
||
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|
||
mso-bidi-font-size:11.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";
|
||
color:blue;
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoHeading8, li.MsoHeading8, div.MsoHeading8
|
||
{mso-style-unhide:no;
|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:252.0pt;
|
||
text-align:justify;
|
||
text-indent:0cm;
|
||
mso-pagination:none;
|
||
mso-outline-level:8;
|
||
mso-list:l0 level8 lfo3;
|
||
mso-hyphenate:none;
|
||
tab-stops:72.0pt;
|
||
layout-grid-mode:char;
|
||
text-autospace:ideograph-numeric;
|
||
font-size:10.0pt;
|
||
mso-bidi-font-size:11.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-style:italic;}
|
||
p.MsoHeading9, li.MsoHeading9, div.MsoHeading9
|
||
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|
||
mso-style-next:Standard;
|
||
margin-top:12.0pt;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:288.0pt;
|
||
text-align:justify;
|
||
text-indent:0cm;
|
||
mso-pagination:none;
|
||
mso-outline-level:9;
|
||
mso-list:l0 level9 lfo3;
|
||
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|
||
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|
||
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|
||
text-autospace:ideograph-numeric;
|
||
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|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
font-weight:bold;
|
||
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|
||
p.MsoIndex1, li.MsoIndex1, div.MsoIndex1
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:10.0pt;
|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
mso-pagination:none;
|
||
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|
||
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|
||
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|
||
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|
||
font-family:"Times New Roman",serif;
|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex2, li.MsoIndex2, div.MsoIndex2
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:20.0pt;
|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
mso-pagination:none;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex3, li.MsoIndex3, div.MsoIndex3
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
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|
||
margin-bottom:3.0pt;
|
||
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|
||
text-align:justify;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex4, li.MsoIndex4, div.MsoIndex4
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
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|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
font-family:"Times New Roman",serif;
|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex5, li.MsoIndex5, div.MsoIndex5
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:50.0pt;
|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex6, li.MsoIndex6, div.MsoIndex6
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:60.0pt;
|
||
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|
||
text-indent:-10.0pt;
|
||
mso-pagination:none;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex7, li.MsoIndex7, div.MsoIndex7
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
margin-top:0cm;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:70.0pt;
|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex8, li.MsoIndex8, div.MsoIndex8
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
margin-top:0cm;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:80.0pt;
|
||
text-align:justify;
|
||
text-indent:-10.0pt;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoIndex9, li.MsoIndex9, div.MsoIndex9
|
||
{mso-style-noshow:yes;
|
||
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|
||
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|
||
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
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|
||
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|
||
text-indent:-10.0pt;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoToc1, li.MsoToc1, div.MsoToc1
|
||
{mso-style-priority:39;
|
||
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|
||
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|
||
margin-top:0cm;
|
||
margin-right:0cm;
|
||
margin-bottom:2.0pt;
|
||
margin-left:0cm;
|
||
text-align:center;
|
||
mso-pagination:none;
|
||
mso-hyphenate:none;
|
||
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|
||
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|
||
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|
||
mso-bidi-font-size:11.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
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|
||
mso-bidi-font-family:"Times New Roman";
|
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color:#4472C4;
|
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mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;
|
||
mso-bidi-font-weight:bold;}
|
||
p.MsoToc2, li.MsoToc2, div.MsoToc2
|
||
{mso-style-priority:39;
|
||
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|
||
mso-style-next:Standard;
|
||
margin-top:0cm;
|
||
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|
||
margin-bottom:2.0pt;
|
||
margin-left:9.9pt;
|
||
text-align:justify;
|
||
mso-pagination:none;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
||
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|
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color:#4472C4;
|
||
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|
||
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|
||
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|
||
p.MsoToc3, li.MsoToc3, div.MsoToc3
|
||
{mso-style-priority:39;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
mso-pagination:none;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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|
||
mso-no-proof:yes;}
|
||
p.MsoToc4, li.MsoToc4, div.MsoToc4
|
||
{mso-style-priority:39;
|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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color:navy;
|
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|
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|
||
p.MsoToc5, li.MsoToc5, div.MsoToc5
|
||
{mso-style-priority:39;
|
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|
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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||
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|
||
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|
||
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|
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|
||
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|
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|
||
p.MsoToc6, li.MsoToc6, div.MsoToc6
|
||
{mso-style-priority:39;
|
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|
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|
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
||
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|
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color:navy;
|
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|
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|
||
p.MsoToc7, li.MsoToc7, div.MsoToc7
|
||
{mso-style-priority:39;
|
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|
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|
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|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
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|
||
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|
||
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|
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|
||
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|
||
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mso-fareast-font-family:"Times New Roman";
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mso-ansi-language:EN-US;
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|
||
p.MsoToc8, li.MsoToc8, div.MsoToc8
|
||
{mso-style-priority:39;
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|
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|
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margin-top:0cm;
|
||
margin-right:0cm;
|
||
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|
||
margin-left:70.0pt;
|
||
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|
||
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|
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|
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|
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mso-fareast-font-family:"Times New Roman";
|
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mso-ansi-language:EN-US;
|
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|
||
p.MsoToc9, li.MsoToc9, div.MsoToc9
|
||
{mso-style-priority:39;
|
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|
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|
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margin-top:0cm;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:80.0pt;
|
||
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|
||
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|
||
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|
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|
||
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|
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font-family:"Times New Roman",serif;
|
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mso-fareast-font-family:"Times New Roman";
|
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mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoFootnoteText, li.MsoFootnoteText, div.MsoFootnoteText
|
||
{mso-style-noshow:yes;
|
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mso-style-unhide:no;
|
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margin-top:0cm;
|
||
margin-right:0cm;
|
||
margin-bottom:3.0pt;
|
||
margin-left:0cm;
|
||
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|
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|
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|
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|
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font-family:"Segoe UI",sans-serif;
|
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mso-fareast-font-family:"Times New Roman";
|
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mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoCommentText, li.MsoCommentText, div.MsoCommentText
|
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{mso-style-noshow:yes;
|
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mso-style-unhide:no;
|
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margin-top:0cm;
|
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|
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margin-bottom:3.0pt;
|
||
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|
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|
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|
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mso-fareast-font-family:"Times New Roman";
|
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mso-ansi-language:EN-US;
|
||
mso-fareast-language:AR-SA;}
|
||
p.MsoHeader, li.MsoHeader, div.MsoHeader
|
||
{mso-style-noshow:yes;
|
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mso-style-unhide:no;
|
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margin-top:0cm;
|
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|
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margin-bottom:3.0pt;
|
||
margin-left:0cm;
|
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text-align:justify;
|
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mso-pagination:none;
|
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mso-hyphenate:none;
|
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tab-stops:center 216.0pt right 432.0pt;
|
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text-autospace:ideograph-numeric;
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mso-fareast-font-family:"Times New Roman";
|
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mso-ansi-language:EN-US;
|
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mso-fareast-language:AR-SA;}
|
||
p.MsoFooter, li.MsoFooter, div.MsoFooter
|
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{mso-style-noshow:yes;
|
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mso-style-unhide:no;
|
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margin-top:0cm;
|
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margin-right:0cm;
|
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margin-bottom:3.0pt;
|
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margin-left:0cm;
|
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text-align:justify;
|
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|
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|
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|
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font-family:"Segoe UI",sans-serif;
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p.MsoSubtitle, li.MsoSubtitle, div.MsoSubtitle
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p.MsoBodyText2, li.MsoBodyText2, div.MsoBodyText2
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p
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{mso-style-noshow:yes;
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pre
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span.MsoBookTitle
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span.WW8Num4z0
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{mso-list-id:5;
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-list-template-ids:6;
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-list-template-ids:-1180420116;
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@list l5:level1
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{mso-level-number-format:bullet;
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-list-template-ids:9;
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mso-level-text:\F0B7;
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mso-list-template-ids:11;
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@list l8:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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@list l9
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{mso-list-id:12;
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mso-list-type:simple;
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mso-list-template-ids:12;
|
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mso-list-name:WW8Num21;}
|
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@list l9:level1
|
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{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l10
|
||
{mso-list-id:13;
|
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mso-list-type:simple;
|
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mso-list-template-ids:13;
|
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mso-list-name:WW8Num24;}
|
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@list l10:level1
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l11
|
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{mso-list-id:14;
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mso-list-type:simple;
|
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mso-list-template-ids:14;
|
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mso-list-name:WW8Num25;}
|
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@list l11:level1
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l12
|
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{mso-list-id:15;
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mso-list-type:simple;
|
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mso-list-template-ids:15;
|
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mso-list-name:WW8Num26;}
|
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@list l12:level1
|
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l13
|
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{mso-list-id:16;
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mso-list-type:simple;
|
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mso-list-template-ids:16;
|
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mso-list-name:WW8Num27;}
|
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@list l13:level1
|
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l14
|
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{mso-list-id:17;
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mso-list-type:simple;
|
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mso-list-template-ids:17;
|
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mso-list-name:WW8Num28;}
|
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@list l14:level1
|
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{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l15
|
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{mso-list-id:18;
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mso-list-type:simple;
|
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mso-list-template-ids:18;
|
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mso-list-name:WW8Num29;}
|
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@list l15:level1
|
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{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l16
|
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{mso-list-id:19;
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mso-list-type:simple;
|
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mso-list-template-ids:19;
|
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mso-list-name:WW8Num30;}
|
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@list l16:level1
|
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{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l17
|
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{mso-list-id:20;
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mso-list-type:simple;
|
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mso-list-template-ids:20;
|
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mso-list-name:WW8Num31;}
|
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@list l17:level1
|
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{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
|
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l18
|
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{mso-list-id:21;
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mso-list-type:simple;
|
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mso-list-template-ids:21;
|
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mso-list-name:WW8Num32;}
|
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@list l18:level1
|
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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margin-left:0cm;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l19
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{mso-list-id:22;
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mso-list-type:simple;
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mso-list-template-ids:22;
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mso-list-name:WW8Num33;}
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@list l19:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l20
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{mso-list-id:23;
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mso-list-type:simple;
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mso-list-template-ids:23;
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mso-list-name:WW8Num34;}
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@list l20:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l21
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{mso-list-id:24;
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mso-list-type:simple;
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mso-list-template-ids:24;
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mso-list-name:WW8Num41;}
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@list l21:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l22
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{mso-list-id:25;
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mso-list-type:simple;
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mso-list-template-ids:25;
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mso-list-name:WW8Num45;}
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@list l22:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l23
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{mso-list-id:26;
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mso-list-type:simple;
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mso-list-template-ids:26;
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mso-list-name:WW8Num46;}
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@list l23:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l24
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{mso-list-id:27;
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mso-list-type:simple;
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mso-list-template-ids:27;
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mso-list-name:WW8Num48;}
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@list l24:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l25
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{mso-list-id:28;
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mso-list-type:simple;
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mso-list-template-ids:28;
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mso-list-name:WW8Num56;}
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@list l25:level1
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
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mso-level-tab-stop:18.0pt;
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mso-level-number-position:left;
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mso-ascii-font-family:Symbol;
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mso-hansi-font-family:Symbol;
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mso-bidi-font-family:"Times New Roman";}
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@list l26
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{mso-list-id:34356597;
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mso-list-template-ids:-727831850 536870927 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
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@list l26:level1
|
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{mso-level-tab-stop:none;
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mso-level-number-position:left;
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margin-left:108.0pt;
|
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text-indent:-18.0pt;}
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@list l26:level2
|
||
{mso-level-number-format:bullet;
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mso-level-text:o;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:144.0pt;
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text-indent:-18.0pt;
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font-family:"Courier New";}
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@list l26:level3
|
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{mso-level-number-format:bullet;
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mso-level-text:\F0A7;
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:180.0pt;
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font-family:Wingdings;}
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@list l26:level4
|
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{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:216.0pt;
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l26:level5
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:o;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:252.0pt;
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text-indent:-18.0pt;
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font-family:"Courier New";}
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@list l26:level6
|
||
{mso-level-number-format:bullet;
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mso-level-text:\F0A7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:288.0pt;
|
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text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l26:level7
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:324.0pt;
|
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l26:level8
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:o;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:360.0pt;
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text-indent:-18.0pt;
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font-family:"Courier New";}
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@list l26:level9
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0A7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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margin-left:396.0pt;
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text-indent:-18.0pt;
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font-family:Wingdings;}
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@list l27
|
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{mso-list-id:143739522;
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mso-list-template-ids:1423222636 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
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@list l27:level1
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l27:level2
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
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mso-level-number-position:left;
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text-indent:-18.0pt;
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font-family:"Courier New";}
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@list l27:level3
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0A7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l27:level4
|
||
{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l27:level5
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
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text-indent:-18.0pt;
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font-family:"Courier New";}
|
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@list l27:level6
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
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text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l27:level7
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l27:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
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text-indent:-18.0pt;
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font-family:"Courier New";}
|
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@list l27:level9
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
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mso-level-number-position:left;
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text-indent:-18.0pt;
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font-family:Wingdings;}
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@list l28
|
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{mso-list-id:172111639;
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mso-list-template-ids:-648799250 536870913 536870913 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
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@list l28:level1
|
||
{mso-level-number-format:bullet;
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
||
margin-left:54.0pt;
|
||
text-indent:-18.0pt;
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font-family:Symbol;}
|
||
@list l28:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:90.0pt;
|
||
text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l28:level3
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
||
margin-left:126.0pt;
|
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text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l28:level4
|
||
{mso-level-number-format:bullet;
|
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mso-level-text:\F0B7;
|
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mso-level-tab-stop:none;
|
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mso-level-number-position:left;
|
||
margin-left:162.0pt;
|
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text-indent:-18.0pt;
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font-family:Symbol;}
|
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@list l28:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:198.0pt;
|
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text-indent:-18.0pt;
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font-family:"Courier New";}
|
||
@list l28:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:234.0pt;
|
||
text-indent:-18.0pt;
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font-family:Wingdings;}
|
||
@list l28:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:270.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l28:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:306.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l28:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:342.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l29
|
||
{mso-list-id:218592014;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:1869794132 -494244720 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l29:level1
|
||
{mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
mso-ansi-font-weight:bold;
|
||
mso-bidi-font-weight:bold;}
|
||
@list l29:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l29:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l29:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l29:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l29:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l29:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l29:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l29:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l30
|
||
{mso-list-id:570889181;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:1740530830 536870929 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l30:level1
|
||
{mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l30:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l30:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l30:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l31
|
||
{mso-list-id:679626811;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:-2032006272 -1095462022 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l31:level1
|
||
{mso-level-style-link:"Kein Leerraum";
|
||
mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l31:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l31:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l31:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l32
|
||
{mso-list-id:738526063;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:52744518 536870913 536870913 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l32:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:54.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l32:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:90.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l32:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:126.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l32:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:162.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l32:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:198.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l32:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:234.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l32:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:270.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l32:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:306.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l32:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:342.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l33
|
||
{mso-list-id:788553390;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:-1890309382 312623772 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l33:level1
|
||
{mso-level-start-at:5;
|
||
mso-level-number-format:bullet;
|
||
mso-level-text:<3A>;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:54.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";}
|
||
@list l33:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:90.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l33:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:126.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l33:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:162.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l33:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:198.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l33:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:234.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l33:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:270.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l33:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:306.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l33:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:342.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l34
|
||
{mso-list-id:817377648;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:-1122835736 -1970643310 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l34:level1
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-style-link:"list lettered";
|
||
mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:50.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:86.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:122.2pt;
|
||
text-indent:-9.0pt;}
|
||
@list l34:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:158.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:194.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:230.2pt;
|
||
text-indent:-9.0pt;}
|
||
@list l34:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:266.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:302.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l34:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:338.2pt;
|
||
text-indent:-9.0pt;}
|
||
@list l35
|
||
{mso-list-id:835875479;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:-658361138 505174366 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l35:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-style-link:Listenabsatz;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:108.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;
|
||
color:windowtext;}
|
||
@list l35:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:144.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l35:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:180.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l35:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:216.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l35:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:252.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l35:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:288.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l35:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:324.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l35:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:360.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l35:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:396.0pt;
|
||
text-indent:-18.0pt;
|
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font-family:Wingdings;}
|
||
@list l36
|
||
{mso-list-id:850948240;
|
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mso-list-type:hybrid;
|
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mso-list-template-ids:594449452 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l36:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:108.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l36:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:144.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l36:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:180.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l36:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:216.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l36:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:252.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l36:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:288.0pt;
|
||
text-indent:-18.0pt;
|
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font-family:Wingdings;}
|
||
@list l36:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:324.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l36:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:360.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l36:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:396.0pt;
|
||
text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l37
|
||
{mso-list-id:954748617;
|
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mso-list-type:hybrid;
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mso-list-template-ids:334420920 -456247874 -337458228 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l37:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:54.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l37:level2
|
||
{mso-level-start-at:4;
|
||
mso-level-number-format:bullet;
|
||
mso-level-text:-;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:90.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";}
|
||
@list l37:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:126.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l37:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:162.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l37:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:198.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l37:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:234.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l37:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:270.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l37:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:306.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l37:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:342.0pt;
|
||
text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l38
|
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{mso-list-id:1000279430;
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mso-list-type:hybrid;
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mso-list-template-ids:-746707164 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l38:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:108.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l38:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:144.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l38:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:180.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l38:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:216.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l38:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:252.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l38:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:288.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l38:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:324.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l38:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:360.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l38:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:396.0pt;
|
||
text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l39
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{mso-list-id:1214271604;
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|
||
@list l39:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:108.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l39:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:144.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l39:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:180.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l39:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:216.0pt;
|
||
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|
||
font-family:Symbol;}
|
||
@list l39:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:252.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l39:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:288.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l39:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:324.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l39:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:360.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l39:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:396.0pt;
|
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text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l40
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{mso-list-id:1358970096;
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mso-list-template-ids:693956868 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l40:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l40:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
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text-indent:-18.0pt;
|
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font-family:"Courier New";}
|
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@list l40:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l40:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l40:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l40:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l40:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l40:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l40:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
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font-family:Wingdings;}
|
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@list l41
|
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mso-list-type:hybrid;
|
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mso-list-template-ids:1824799922 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l41:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l41:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l41:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l41:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l41:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l41:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l41:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l41:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l41:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l42
|
||
{mso-list-id:1545095756;
|
||
mso-list-type:hybrid;
|
||
mso-list-template-ids:-1055605160 -1012127172 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l42:level1
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:32.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:68.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:104.2pt;
|
||
text-indent:-9.0pt;}
|
||
@list l42:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:140.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:176.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:212.2pt;
|
||
text-indent:-9.0pt;}
|
||
@list l42:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:248.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:284.2pt;
|
||
text-indent:-18.0pt;}
|
||
@list l42:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
margin-left:320.2pt;
|
||
text-indent:-9.0pt;}
|
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@list l43
|
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{mso-list-id:1554855140;
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mso-list-type:hybrid;
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mso-list-template-ids:-1584737144 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
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@list l43:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l43:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
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font-family:"Courier New";}
|
||
@list l43:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l43:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l43:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l43:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l43:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l43:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l43:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
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font-family:Wingdings;}
|
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@list l44
|
||
{mso-list-id:1610578113;
|
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mso-list-type:hybrid;
|
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mso-list-template-ids:350541778 901648412 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l44:level1
|
||
{mso-level-style-link:"list numbered";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:25.1pt;
|
||
text-indent:-18.0pt;}
|
||
@list l44:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:54.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l44:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:90.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l44:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:126.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l44:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:162.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l44:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:198.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l44:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:234.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l44:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:270.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l44:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:306.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l45
|
||
{mso-list-id:1664822352;
|
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mso-list-type:hybrid;
|
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mso-list-template-ids:-2049119074 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l45:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l45:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l45:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l45:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l45:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l45:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l45:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l45:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l45:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
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|
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font-family:Wingdings;}
|
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@list l46
|
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{mso-list-id:1715150667;
|
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|
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mso-list-template-ids:2013583364 536870913 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
|
||
@list l46:level1
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:108.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l46:level2
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:144.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l46:level3
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:180.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l46:level4
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:216.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l46:level5
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:252.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l46:level6
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:288.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Wingdings;}
|
||
@list l46:level7
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0B7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:324.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:Symbol;}
|
||
@list l46:level8
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:o;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:360.0pt;
|
||
text-indent:-18.0pt;
|
||
font-family:"Courier New";}
|
||
@list l46:level9
|
||
{mso-level-number-format:bullet;
|
||
mso-level-text:\F0A7;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
margin-left:396.0pt;
|
||
text-indent:-18.0pt;
|
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font-family:Wingdings;}
|
||
@list l47
|
||
{mso-list-id:1731952597;
|
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mso-list-type:hybrid;
|
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mso-list-template-ids:1510488726 75952422 536870937 536870939 536870927 536870937 536870939 536870927 536870937 536870939;}
|
||
@list l47:level1
|
||
{mso-level-style-link:List1;
|
||
mso-level-text:"%1\)";
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;
|
||
font-variant:normal !important;
|
||
color:black;
|
||
mso-text-animation:none;
|
||
mso-hide:none;
|
||
text-transform:none;
|
||
position:relative;
|
||
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|
||
mso-text-raise:0pt;
|
||
letter-spacing:0pt;
|
||
mso-font-kerning:0pt;
|
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mso-style-textoutline-type:none;
|
||
mso-style-textoutline-outlinestyle-dpiwidth:0pt;
|
||
mso-style-textoutline-outlinestyle-linecap:round;
|
||
mso-style-textoutline-outlinestyle-join:bevel;
|
||
mso-style-textoutline-outlinestyle-pctmiterlimit:0%;
|
||
mso-style-textoutline-outlinestyle-dash:solid;
|
||
mso-style-textoutline-outlinestyle-align:center;
|
||
mso-style-textoutline-outlinestyle-compound:simple;
|
||
mso-effects-shadow-color:black;
|
||
mso-effects-shadow-alpha:100.0%;
|
||
mso-effects-shadow-dpiradius:0pt;
|
||
mso-effects-shadow-dpidistance:0pt;
|
||
mso-effects-shadow-angledirection:0;
|
||
mso-effects-shadow-align:none;
|
||
mso-effects-shadow-pctsx:0%;
|
||
mso-effects-shadow-pctsy:0%;
|
||
mso-effects-shadow-anglekx:0;
|
||
mso-effects-shadow-angleky:0;
|
||
font-emphasize:none;
|
||
mso-ansi-font-weight:normal;
|
||
mso-bidi-font-weight:normal;
|
||
mso-ansi-font-style:normal;
|
||
mso-bidi-font-style:normal;
|
||
mso-no-proof:no;
|
||
text-decoration:none;
|
||
text-underline:none;
|
||
text-decoration:none;
|
||
text-line-through:none;
|
||
vertical-align:baseline;}
|
||
@list l47:level2
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l47:level3
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l47:level4
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l47:level5
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l47:level6
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l47:level7
|
||
{mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l47:level8
|
||
{mso-level-number-format:alpha-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:left;
|
||
text-indent:-18.0pt;}
|
||
@list l47:level9
|
||
{mso-level-number-format:roman-lower;
|
||
mso-level-tab-stop:none;
|
||
mso-level-number-position:right;
|
||
text-indent:-9.0pt;}
|
||
@list l48
|
||
{mso-list-id:1900624548;
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mso-list-type:hybrid;
|
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mso-list-template-ids:-1224036592 536870927 536870915 536870917 536870913 536870915 536870917 536870913 536870915 536870917;}
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||
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|
||
fAEAACwuAQAAAA==
|
||
">
|
||
<v:imagedata src="swisseph-Dateien/image001.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img width=239 height=239
|
||
src="swisseph-Dateien/image002.png" v:shapes="Picture_x0020_7"><![endif]></span><span
|
||
lang=EN-US style='font-size:100.0pt;letter-spacing:.25pt;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=center style='text-align:center'><span
|
||
class=MsoBookTitle><span lang=EN-US style='font-size:48.0pt'><o:p> </o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=center style='text-align:center'><span
|
||
class=MsoBookTitle><b style='mso-bidi-font-weight:normal'><span lang=EN-US
|
||
style='font-size:36.0pt;mso-bidi-font-size:11.0pt;color:#2F5496'>Computer
|
||
ephemeris for developers of astrological software</span></b></span><b><span
|
||
lang=EN-US style='font-size:100.0pt;mso-bidi-font-size:20.0pt;color:#2F5496;
|
||
letter-spacing:.25pt;mso-bidi-font-style:italic'><o:p></o:p></span></b></p>
|
||
|
||
</div>
|
||
|
||
<b><span lang=EN-US style='font-size:100.0pt;mso-bidi-font-size:20.0pt;
|
||
font-family:"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";
|
||
color:#2F5496;letter-spacing:.25pt;mso-ansi-language:EN-US;mso-fareast-language:
|
||
AR-SA;mso-bidi-language:AR-SA;mso-bidi-font-style:italic'><br clear=all
|
||
style='page-break-before:always;mso-break-type:section-break'>
|
||
</span></b>
|
||
|
||
<div class=WordSection2>
|
||
|
||
<p class=contents><a name=contents><span lang=EN-US>Contents</span></a></p>
|
||
|
||
<span style='mso-bookmark:contents'></span>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><!--[if supportFields]><span
|
||
lang=EN-US><span style='mso-element:field-begin'></span><span
|
||
style='mso-spacerun:yes'><3E></span>TOC \o "1-3" \h \z <span
|
||
style='mso-element:field-separator'></span></span><![endif]--><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488748"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>1.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Introduction<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488748 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700340038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488749">1.1.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Licensing<span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488749 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700340039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488750"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>2.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Description
|
||
of the ephemerides<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488750 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488751">2.1.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Planetary and lunar ephemerides<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488751 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488752">2.1.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Three
|
||
ephemerides<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488752 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488753">2.1.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Swiss Ephemeris Compared with Astronomical Almanac and JPL Horizons<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488753 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488754">2.1.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
details of coordinate transformation<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488754 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488755">2.1.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Swiss Ephemeris compression mechanism<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488755 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488756">2.1.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
extension of DE406-based ephemerides to 10.800 years<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488756 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488757">2.1.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Solar
|
||
Ephemeris in the remote past<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488757 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488758">2.2.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Lunar and Planetary Nodes and
|
||
Apsides<span style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488758 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488759">2.2.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Mean
|
||
Lunar Node and Mean Lunar Apogee (Lilith, Black Moon in astrology)<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488759 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700350039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488760">2.2.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
True Node<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488760 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488761">2.2.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Osculating Apogee (astrological True Lilith or True Dark Moon)<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488761 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488762">2.2.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Interpolated or Natural Apogee and Perigee (astrological Lilith and Priapus)<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488762 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488763">2.2.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Planetary
|
||
Nodes and Apsides<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:
|
||
screen;text-decoration:none;text-underline:none'><span style='mso-tab-count:
|
||
1 dotted'>. </span></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-begin'></span></span><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'> PAGEREF
|
||
_Toc58488763 \h </span><span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488764">2.3.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Asteroids<span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488764 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488765">2.3.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Asteroid
|
||
ephemeris files<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:
|
||
screen;text-decoration:none;text-underline:none'><span style='mso-tab-count:
|
||
1 dotted'>. </span></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-begin'></span></span><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'> PAGEREF
|
||
_Toc58488765 \h </span><span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488766">2.3.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>How
|
||
the asteroids were computed<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488766 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488767">2.3.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Ceres,
|
||
Pallas, Juno, Vesta<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488767 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488768">2.3.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Chiron<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488768 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488769">2.3.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Pholus<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488769 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700360039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488770">2.3.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Asteroid
|
||
99942 Apophis<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488770 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488771">2.3.7.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Ceres
|
||
- an application program for asteroid astrology<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488771 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488772">2.4.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Planetary Centers of Body (COB)
|
||
and Planetary Moons<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488772 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488773">2.5.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Comets and Interstellar Objects<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488773 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488774">2.6.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Fixed stars and Galactic Center<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488774 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488775">2.7.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Hypothetical bodies<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488775 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488776">2.7.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Uranian
|
||
planets (Hamburg planets: Cupido, Hades, Zeus, Kronos, Apollon, Admetos,
|
||
Vulkanus, Poseidon)<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488776 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488777">2.7.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Transpluto
|
||
(Isis)<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488777 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488778">2.7.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Harrington<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488778 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488779">2.7.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Nibiru<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488779 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700370039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488780">2.7.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Vulcan<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488780 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488781">2.7.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Selena/White
|
||
Moon<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488781 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488782">2.7.7.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Dr.
|
||
Waldemath<92>s Black Moon<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488782 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488783">2.7.8.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Planets X of Leverrier, Adams, Lowell and Pickering<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488783 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488784">2.8.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Sidereal Ephemerides for Astrology<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488784 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488785">2.8.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
problem of defining the zodiac<span style='mso-bidi-font-size:9.0pt;display:
|
||
none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488785 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488786">2.8.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Babylonian tradition and the Fagan/Bradley ayanamsha<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488786 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488787">2.8.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Hipparchan tradition<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488787 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488788">2.8.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Suryasiddhanta
|
||
and Aryabhata<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488788 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488789">2.8.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Spica/Citra tradition and the Lahiri ayanamsha<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488789 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700380039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488790">2.8.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Krishnamurti
|
||
ayanamshas<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488790 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488791">2.8.7.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
sidereal zodiac and the Galactic Center<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488791 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488792">2.8.8.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
sidereal zodiac and the Galactic Equator<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488792 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488793">2.8.9.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Other
|
||
ayanamshas<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488793 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488794">2.8.10.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Conclusions<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488794 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488795">2.8.11.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Ayanamshas
|
||
with different precession rates<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488795 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488796">2.8.12.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>On
|
||
which ecliptic is the ayanamsha measured?<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488796 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488797">2.8.13.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>More
|
||
benefits from our new sidereal algorithms: standard equinoxes and
|
||
precession-corrected transits<span style='mso-bidi-font-size:9.0pt;display:
|
||
none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488797 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488798"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>3.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Apparent
|
||
versus true planetary positions<span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488798 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488799"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>4.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Geocentric,
|
||
topocentric, heliocentric, barycentric, and planetocentric positions<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488799 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003700390039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488800"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>5.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Heliacal
|
||
Events, Eclipses, Occultations, and Other Planetary Phenomena<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488800 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488801">5.1.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Heliacal Events of the Moon,
|
||
Planets and Stars<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488801 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488802">5.1.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Introduction<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488802 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488803">5.1.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Aspect
|
||
determining visibility<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488803 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488804">5.1.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Functions
|
||
to determine the heliacal events<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488804 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488805">5.1.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Future
|
||
developments<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488805 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488806">5.1.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>References<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488806 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488807">5.2.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Eclipses, occultations, risings,
|
||
settings, and other planetary phenomena<span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488807 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488808"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>6.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Sidereal
|
||
Time, Ascendant, MC, Houses, Vertex<span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488808 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488809">6.1.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Sidereal Time<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488809 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800300039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488810">6.2.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Astrological House Systems<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488810 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488811">6.2.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Placidus<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488811 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488812">6.2.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Koch/GOH<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488812 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488813">6.2.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Regiomontanus<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488813 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488814">6.2.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Campanus<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488814 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488815">6.2.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Equal
|
||
Systems<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488815 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488816">6.2.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Porphyry
|
||
Houses and Related House Systems<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488816 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488817">6.2.7.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Axial
|
||
rotation systems<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:
|
||
screen;text-decoration:none;text-underline:none'><span style='mso-tab-count:
|
||
1 dotted'>. </span></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-begin'></span></span><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'> PAGEREF
|
||
_Toc58488817 \h </span><span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488818">6.2.8.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>The
|
||
Morinus system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488818 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488819">6.2.9.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Horizontal
|
||
system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488819 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800310039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488820">6.2.10.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>The
|
||
Polich-Page (<28>topocentric<69>) system<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488820 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488821">6.2.11.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Alcabitus
|
||
system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488821 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488822">6.2.12.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Gauquelin
|
||
sectors<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488822 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488823">6.2.13.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Krusinski/Pisa/Goelzer
|
||
system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488823 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488824">6.2.14.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>APC
|
||
house system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488824 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488825">6.2.15.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0> </span></span>Sunshine
|
||
house system<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488825 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488826">6.3.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Vertex, Antivertex, East Point and
|
||
Equatorial Ascendant etc.<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488826 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488827">6.4.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>House cusps beyond the polar
|
||
circle<span style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488827 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488828">6.4.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Implementation
|
||
in other calculation modules:<span style='mso-bidi-font-size:9.0pt;display:
|
||
none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488828 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488829">6.5.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>House position of a planet<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488829 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800320039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488830">6.6.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Gauquelin sector position of a
|
||
planet<span style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488830 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488831">6.7.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Improvement of the Placidus house
|
||
calculation in SE 2.09<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488831 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488832"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>7.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span><span
|
||
style='mso-bidi-font-family:"Segoe UI"'>Δ</span>T (Delta T)<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488832 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488833"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>8.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Programming
|
||
Environment<span style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488833 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:20.15pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488834"><span style='mso-style-style3d-lightrigtype:
|
||
13;mso-style-style3d-lightrigdirection:2;mso-style-style3d-lightrigrotation-anglatitude:
|
||
0;mso-style-style3d-lightrigrotation-anglongitude:0;mso-style-style3d-lightrigrotation-angrevolution:
|
||
0'>9.</span><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;
|
||
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;
|
||
mso-bidi-theme-font:minor-bidi;color:windowtext;mso-ansi-language:DE;
|
||
mso-fareast-language:ZH-CN;mso-bidi-font-weight:normal;text-decoration:none;
|
||
text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span>Swiss
|
||
Ephemeris Functions<span style='mso-bidi-font-size:11.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488834 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488835">9.1.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Swiss Ephemeris API<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488835 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488836">9.1.1.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Calculation
|
||
of planets and stars<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488836 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488837">9.1.2.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Date
|
||
and time conversion<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488837 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488838">9.1.3.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Initialization,
|
||
setup, and closing functions<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488838 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488839">9.1.4.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>House
|
||
calculation<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488839 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800330039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488840">9.1.5.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Auxiliary
|
||
functions<span style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488840 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3 style='tab-stops:60.0pt right dotted 523.25pt'><span
|
||
class=MsoHyperlink><span lang=EN-US><a href="#_Toc58488841">9.1.6.<span
|
||
lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
text-decoration:none;text-underline:none'><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span></span>Other
|
||
functions that may be useful<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488841 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:40.0pt right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488842">9.2.<span lang=DE style='font-size:
|
||
11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
|
||
mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span></span>Placalc API<span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488842 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc1 style='text-align:justify;tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488843">Appendix<span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488843 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488844">A. The gravity deflection for a
|
||
planet passing behind the Sun<span style='mso-bidi-font-size:11.0pt;display:
|
||
none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488844 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488845">B. A list of asteroids<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488845 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488846">C. How to Compare the Swiss Ephemeris
|
||
with Ephemerides of the JPL Horizons System<span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>.. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488846 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488847">Test 1: Astrometric Positions ICRF/J2000<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488847 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488848">Test 2: Inertial Apparent Positions, RA and DE, in ICRF<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488848 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488849">Test 3: Apparent Positions, True Equinox of Date, RA, DE,
|
||
Ecliptic Longitude and Latitude<span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488849 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800340039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488850">Test 4: Heliocentric Apparent Positions, Ecliptic
|
||
Longitude and Latitude<span style='mso-bidi-font-size:9.0pt;display:none;
|
||
mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488850 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488851">Test 5: Ephemerides before 1962<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488851 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350031000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488852">Test 6: Jupiter versus Jupiter Barycentre<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488852 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350032000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488853">Test 7: Jupiter<65>s Center of Body<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488853 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350033000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488854">Test 8: Geocentric Position of a Planetary Moon<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488854 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350034000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488855">Test 9: Planetocentric Position of a Planetary Moon<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488855 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350035000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488856">Test 10: Topocentric Position of a Planet<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488856 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350036000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488857">D. How to compare the Swiss Ephemeris
|
||
with Ephemerides of the Astronomical Almanac (apparent positions)<span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488857 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350037000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488858">Test 7: Astronomical Almanac online<span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488858 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350038000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc3><span class=MsoHyperlink><span lang=EN-US><a
|
||
href="#_Toc58488859">Test 8: Astronomical Almanac printed<span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-tab-count:1 dotted'>. </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488859 \h </span><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:9.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:9.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800350039000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
9.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoToc2 style='tab-stops:right dotted 522.75pt'><span
|
||
class=MsoHyperlink><span lang=EN-US style='mso-bidi-font-family:"Times New Roman";
|
||
mso-no-proof:yes'><a href="#_Toc58488860">E. How to compare the Swiss Ephemeris
|
||
Lahiri Ayanamsha with Values from <i style='mso-bidi-font-style:normal'>Indian
|
||
Astronomical Ephemeris</i> (IAE)<span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-tab-count:1 dotted'> </span></span><!--[if supportFields]><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-begin'></span></span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'> PAGEREF _Toc58488860 \h </span><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'><span style='mso-element:field-separator'></span></span><![endif]--><span
|
||
style='mso-bidi-font-size:11.0pt;display:none;mso-hide:screen;text-decoration:
|
||
none;text-underline:none'>1</span><span style='mso-bidi-font-size:11.0pt;
|
||
display:none;mso-hide:screen;text-decoration:none;text-underline:none'><!--[if gte mso 9]><xml>
|
||
<w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000D0000005F0054006F006300350038003400380038003800360030000000</w:data>
|
||
</xml><![endif]--></span><!--[if supportFields]><span style='mso-bidi-font-size:
|
||
11.0pt;display:none;mso-hide:screen;text-decoration:none;text-underline:none'><span
|
||
style='mso-element:field-end'></span></span><![endif]--></a></span></span><span
|
||
style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-ascii-theme-font:
|
||
minor-latin;mso-fareast-font-family:DengXian;mso-fareast-theme-font:minor-fareast;
|
||
mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Arial;mso-bidi-theme-font:
|
||
minor-bidi;color:windowtext;mso-ansi-language:DE;mso-fareast-language:ZH-CN;
|
||
mso-bidi-font-weight:normal;mso-no-proof:yes'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left'><!--[if supportFields]><span
|
||
lang=EN-US><span style='mso-element:field-end'></span></span><![endif]--></p>
|
||
|
||
</div>
|
||
|
||
<span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:11.0pt;font-family:
|
||
"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";mso-ansi-language:
|
||
EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA'><br clear=all
|
||
style='page-break-before:always;mso-break-type:section-break'>
|
||
</span>
|
||
|
||
<div class=WordSection3>
|
||
|
||
<p class=MsoNormal align=center style='text-align:center'><span lang=EN-US
|
||
style='font-size:16.0pt'>SWISS EPHEMERIS - computer ephemeris for developers of
|
||
astrological software<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'><3E> 1997 - 2019 by<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>Astrodienst AG<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>Dammstr. 23<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>Postfach (Station)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>CH-8702 Zollikon /
|
||
Z<FC>rich, Switzerland<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>Tel. +41-44-392 18 18<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Fax +41-44-391 75 74</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Email of developers: <a
|
||
href="mailto:alois@astro.com"><span style='mso-bidi-font-size:11.0pt'>alois@astro.com</span></a>
|
||
and <a href="mailto:dieter@astro.com"><span style='mso-bidi-font-size:11.0pt'>dieter@astro.com</span></a></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Authors: Dieter Koch and Dr. Alois Treindl</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Editing history:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>14-sep-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Appendix A by Alois</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15-sep-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>split docu, swephprg.doc now separate
|
||
(programming interface)</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>16-sep-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: absolute precision of JPL,
|
||
position and speed transformations</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24-sep-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: main asteroids</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27-sep-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: restructured for better HTML
|
||
conversion, added public function list</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>8-oct-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapter 4 (houses) added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>28-nov-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapter 5 (delta t) added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>20-jan-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapter 3 (more than...) added,
|
||
Chapter 4 (houses) enlarged</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>14-jul-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: more about the precision of our
|
||
asteroids</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21-jul-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: houses in PLACALC and ASTROLOG</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27-jul-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: True node Chapter improved</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2-sep-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: updated asteroid Chapter </span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29-nov-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: added info on Public License and
|
||
source code availability</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4-dec-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: updated asteroid file information</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-dec-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: Section 2.1.5 added: extended time
|
||
range to 10.800 years</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-dec-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: paragraphs on Chiron and Pholus
|
||
ephemerides updated</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jan-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: paragraph on eclipses</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>19-apr-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: paragraph on eclipses and
|
||
planetary phenomena</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21-jun-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapter 2.27 on sidereal
|
||
ephemerides</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:19'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27-jul-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapter 2.27 on sidereal
|
||
ephemerides completed</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:20'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15-feb-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: many things for Version 1.52</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:21'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-sep-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: a few additions for version 1.61</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:22'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24-jul-2001</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: a few additions for version 1.62</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:23'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5-jan-2002</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: house calculation added to swetest
|
||
for version 1.63</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:24'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>26-feb-2002</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Gauquelin sectors for version
|
||
1.64</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:25'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jun-2003</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: code revisions for compatibility
|
||
with 64-bit compilers, version 1.65</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:26'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-jul-2003</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Morinus houses for Version 1.66</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:27'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jul-2004</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: documentation of Delta T
|
||
algorithms implemented with version 1.64</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:28'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>7-feb-2005</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: added note about mean lunar
|
||
elements, section 2.2.1</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:29'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22-feb-2006</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: added documentation for version
|
||
1.70, see section 2.1.2.1-3</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:30'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-jul-2007</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: updated documentation of
|
||
Krusinski-Pisa house system.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:31'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>28-nov-2007</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: documentation of new Delta T
|
||
calculation for version 1.72, see section 7</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:32'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-jun-2008</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: license change to dual license,
|
||
GNU GPL or Professional License</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:33'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>31-mar-2009</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: heliacal events</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:34'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>26-feb-2010</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Alois: manual update, deleted references
|
||
to CDROM</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:35'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>25-jan-2011</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>Dieter: Delta T
|
||
updated, v. 1.77.<o:p></o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:36'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2-aug-2012</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: new precession, v. 1.78.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:37'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>23-apr-2013</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: new ayanamshas</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:38'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-feb-2014</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: many additions for v. 2.00</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:39'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>18-mar-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: documentation of APC house system
|
||
and Pushya ayanamsha</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:40'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21-oct-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: small correction in documentation
|
||
of Lahiri ayanamsha</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:41'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3-feb-2016</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: documentation of house systems
|
||
updated (equal, Porphyry, Pullen, Sripati)</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:42'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22-apr-2016</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: documentation of ayanamsha
|
||
revised </span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:43'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-jan-2017</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: new Delta T</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:44'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29-nov-2017</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: update for comparison SwissEph -
|
||
JPL Horizons using SE2.07; Ch. 2.1.6 added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:45'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4-jan-2018</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: <20>Vedic<69>/Sheoran ayanamsha added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:46'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>13-jun-2019</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: small corrections for version 2.08</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:47'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-sep-2019</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Simon Hren, documentation reformatted, merged
|
||
with a recent unpublished update by Dieter</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:48'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6-jan-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>A few corrections by Simon Hren and
|
||
updates by Dieter</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:49'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24-jun-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Chapters on ayanamsha improved;
|
||
appendix E on Swiss Ephemeris versus IAE, IENA, RP</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:50'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24-jun-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: Appendix C: added Test 2a
|
||
concerning inertial apparent positions with JPL Horizons </span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:51'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27-jun-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: small corrections in chapter 7 on
|
||
Delta T</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:52'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29-jun-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: small changes in Appendix E</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:53'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1-dec-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: several Additions in Appendix E,
|
||
concerning the centers of body of the planets,</span></p>
|
||
<p class=MsoNormal><span lang=EN-US>planetary moons, comets and 99942 Apophis</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:54'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>9-dec-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Dieter: <20>AD<41> replaced by <20>CE<43> and <20>BC<42>
|
||
replaced by <20>CE<43>.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:55;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Swiss Ephemeris release history:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.00</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>30-sept-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.01</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>9-oct-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>simplified houses() and sidtime()
|
||
functions, Vertex added.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.02</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>16-oct-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>houses() changed again</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.03</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>28-oct-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.04</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>8-dec-1997</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.10</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>9-jan-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>bug fix, pushed to all licensees</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.11</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jan-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.20</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21-jan-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: topocentric planets and house
|
||
positions </span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.21</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>28-jan-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Delphi declarations and sample for Delphi
|
||
1.0</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.22</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2-feb-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>asteroids moved to subdirectory.
|
||
Swe_calc() finds them there.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.23</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-feb-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>two minor bug fixes.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.24</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>7-mar-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>documentation for Borland C++ Builder
|
||
added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.25</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4-june-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>sample for Borland Delphi-2 added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.26</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29-nov-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>source added, Placalc API added</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.30</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-dec-1998</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: Time range extended to 10.800 years</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.31</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jan-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: Eclipses</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.40</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>19-apr-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: planetary phenomena</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.50</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27-jul-1999</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: sidereal ephemerides</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.52</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15-feb-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>several NEW features, minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:19'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.60</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15-feb-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>major release with many new features and
|
||
some minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:20'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.61</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-sep-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor release, additions to
|
||
se_rise_trans(), swe_houses(), fictitious planets</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:21'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.62</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>23-jul-2001</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor release, fictitious Earth
|
||
satellites, asteroid numbers > 55535 possible</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:22'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.63</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5-jan-2002</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor release, house calculation added to
|
||
swetest.c and swetest.exe</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:23'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.64</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>7-apr-2002</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: occultations of planets, minor bug
|
||
fixes, new Delta T algorithms</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:24'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.65</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12-jun-2003</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor release, small code renovations for
|
||
64-bit compilation</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:25'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.66</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-jul-2003</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: Morinus houses</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:26'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.67</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>31-mar-2005</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>minor release: Delta-T updated, minor bug
|
||
fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:27'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.70</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2-mar-2006</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>IAU resolutions up to 2005 implemented;
|
||
"interpolated" lunar apsides</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:28'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.72</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>28-nov-2007</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Delta T calculation according to
|
||
Morrison/Stephenson 2004</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:29'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.74</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>17-jun-2008</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>license model changed to dual license,
|
||
GNU GPL or Professional License</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:30'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.76</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>31-mar-2009</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: Heliacal events</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:31'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.77</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>25-jan-2011</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Delta T calculation updated acc. to Espenak/Meeus
|
||
2006, new fixed stars file</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:32'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.78</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2-aug-2012</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>precession calculation updated acc. to
|
||
Vondr<64>k et alii 2012</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:33'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.79</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>23-apr-2013</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>new ayanamshas, improved precision of
|
||
eclipse functions, minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:34'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>1.80</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3-sep-2013</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>security update and bugfixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:35'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.00</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-feb-2014</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris now based on JPL
|
||
ephemeris DE431</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:36'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.01</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>18-mar-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>bug fixes for version 2.00</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:37'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.02</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11-aug-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>new functions swe_deltat_ex() and swe_get_ayanamsa_ex();
|
||
bug fixes.</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:38'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.03</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>16-oct-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris thread safe; minor bug
|
||
fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:39'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.04</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21-oct-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>V. 2.03 had DLL with calling convention
|
||
__cdecl; we return to _stdcall </span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:40'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.05</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22-apr-2015</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>new house methods, new ayanamshas, minor
|
||
bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:41'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.06</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-jan-2017</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>new Delta T, minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:42'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.07</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-jan-2018</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>better performance of swe_fixstar() and
|
||
swe_rise_trans()</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:43'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.08</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>13-jun-2019</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>update of Delta T and minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:44'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.09</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22-jul-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>Improved Placidus houses, sidereal
|
||
ephemerides, planetary magnitudes; minor bug fixes</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:45;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>2.10</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10-dec-2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>NEW: planetary moons</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488748"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Introduction</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Swiss Ephemeris</span></b><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt'> </span><span lang=EN-US>is a
|
||
function package of astronomical calculations that serves the needs of
|
||
astrologers, archeoastronomers, and, depending on purpose, also the needs of
|
||
astronomers. It includes long-term ephemerides for the Sun, the Moon, the
|
||
planets, more than 300.000 asteroids, historically relevant fixed stars and
|
||
some <20>hypothetical<61> objects.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The precision of the Swiss Ephemeris is at
|
||
least as good as that of the Astronomical Almanac, which follows current
|
||
standards of ephemeris calculation. Swiss Ephemeris will, as we hope, be able
|
||
to keep abreast to the scientific advances in ephemeris computation for the
|
||
coming decades.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris package consists of
|
||
source code in C, a DLL, a collection of ephemeris files and a few sample
|
||
programs which demonstrate the use of the DLL and the Swiss Ephemeris graphical
|
||
label. The ephemeris files contain compressed astronomical ephemerides.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Full C source code is included with the
|
||
Swiss Ephemeris, so that non-Windows programmers can create a linkable or
|
||
shared library in their environment and use it with their applications.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488749"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>1.1.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Licensing</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris is <span
|
||
style='color:red'>not</span> a product for end users. It is a toolset for
|
||
programmers to build into their astrological software.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris is made available by its
|
||
authors under a dual licensing system. The software developer, who uses any
|
||
part of Swiss Ephemeris in his or her software, must choose between one of the
|
||
two license models, which are:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>a) GNU public license version 2 or later:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><span style='mso-spacerun:yes'><3E></span>b)
|
||
Swiss Ephemeris Professional License.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>The choice must
|
||
be made before the software developer distributes software containing parts of
|
||
Swiss Ephemeris to others, and before any public service using the developed
|
||
software is activated.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the developer choses the GNU GPL
|
||
software license, he or she must fulfill the conditions of that license, which
|
||
includes the obligation to place his or her whole software project under the
|
||
GNU GPL or a compatible license. See
|
||
http://www.gnu.org/licenses/old-licenses/gpl-2.0.html</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the developer choses the Swiss Ephemeris
|
||
Professional license, he must follow the instructions as found in
|
||
http://www.astro.com/swisseph/ and purchase the Swiss Ephemeris Professional
|
||
Edition from Astrodienst and sign the corresponding license contract.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris Professional Edition
|
||
can be purchased from Astrodienst for a one-time fixed fee for each commercial
|
||
programming project. The license is just a legal document. All actual software
|
||
and data are found in the public download area and are to be downloaded from
|
||
there.</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Professional license</span></b><span
|
||
lang=EN-US>: The license fee for the first license is Swiss Francs (CHF) 750.-,
|
||
and CHF 400.- for each additional license by the same licensee. An unlimited
|
||
license is available for CHF 1550.-.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488750"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Description of the ephemerides</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488751"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.1.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Planetary and lunar ephemerides</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488752"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Three ephemerides</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris package allows
|
||
planetary and lunar computations from any of the following three astronomical
|
||
ephemerides:</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Swiss Ephemeris</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The core part of Swiss Ephemeris is a
|
||
compression of the JPL-Ephemeris DE431, which covers roughly the time range 13.000
|
||
BCE to 17.000 CE. Using a sophisticated mechanism, we succeeded in reducing
|
||
JPL's 2.8 GB storage to only 99 MB. The compressed version agrees with the JPL
|
||
Ephemeris to 1 milli-arcsecond (0.001<94>). Since the inherent uncertainty of the
|
||
JPL ephemeris for most of its time range is a lot greater, the Swiss Ephemeris
|
||
should be completely satisfying even for computations demanding very high
|
||
accuracy.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Before 2014, the Swiss Ephemeris was based
|
||
on JPL Ephemeris DE406. Its 200 MB were compressed to 18 MB. The time range of
|
||
the DE406 was 3000 BCE to 3000 CE or 6000 years. We had extended this time
|
||
range to 10.800 years, from 2 Jan 5401 BCE to 31 Dec 5399 CE. The details of
|
||
this extension are described below in section 2.1.5. To make sure that you work
|
||
with current data, please check the date of the ephemeris files. They must be
|
||
2014 or later.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Each Swiss Ephemeris file covers a period
|
||
of 600 years; there are 50 planetary files, 50 Moon files for the whole time
|
||
range of almost 30.000 years and 18 main-asteroid files for the time range of
|
||
10.800 years.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The file names are as follows:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><b><span
|
||
lang=EN-US>Planetary file<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>Moon file<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Main asteroid file<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>Time range<o:p></o:p></span></b></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm132.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom132.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>11 Aug 13000 BCE <20>
|
||
12602 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm126.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom126.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12601 BCE <20> 12002 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm120.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom120.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12001 BCE <20> 11402 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm114.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom114.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>11401 BCE <20> 10802 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm108.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom108.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>10801 BCE <20> 10202 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm102.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom102.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>10201 BCE <20> 9602 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm96.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom96.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>9601 BCE <20> 9002 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm90.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom90.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>9001 BCE <20> 8402 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm84.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom84.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>8401 BCE <20> 7802 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm78.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom78.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>7801 BCE <20> 7202 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm72.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom72.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>7201 BCE <20> 6602 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm66.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom66.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>6601 BCE <20> 6002 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>Seplm60.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Semom60.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>6001 BCE <20> 5402 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm54.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom54.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm54.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>5401
|
||
BCE <20> 4802 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm48.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom48.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm48.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>4801
|
||
BCE <20> 4202 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm42.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom42.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm42.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>4201
|
||
BCE <20> 3602 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm36.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom36.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm36.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>3601
|
||
BCE <20> 3002 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm30.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom30.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm30.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>3001
|
||
BCE <20> 2402 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm24.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom24.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm24.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>2401
|
||
BCE <20> 1802 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm18.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom18.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm18.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>1801
|
||
BCE <20> 1202 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm12.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom12.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm12.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>1201
|
||
BCE <20> 602 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>seplm06.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semom06.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seasm06.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>601
|
||
BCE <20> 2 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_00.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_00.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_00.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>1
|
||
BCE <20> 599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_06.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_06.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_06.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>600
|
||
CE <20> 1199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_12.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_12.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_12.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>1200
|
||
CE <20> 1799 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_18.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_18.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_18.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>1800
|
||
CE <20> 2399 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_24.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_24.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_24.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>2400
|
||
CE <20> 2999 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_30.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_30.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_30.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>3000
|
||
CE <20> 3599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_36.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_36.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_36.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>3600
|
||
CE <20> 4199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_42.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_42.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_42.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>4200
|
||
CE <20> 4799 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_48.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_48.se1<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>seas_48.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>4800
|
||
CE <20> 5399 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_54.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_54.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>5400 CE <20> 5999 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_60.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_60.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>6000 CE <20> 6599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_66.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_66.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>6600 CE <20> 7199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_72.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_72.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>7200 CE <20> 7799 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_78.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_78.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>7800 CE <20> 8399 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_84.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_84.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>8400 CE <20> 8999 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_90.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_90.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>9000 CE <20> 9599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_96.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_96.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>9600 CE <20> 10199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_102.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_102.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>10200 CE <20> 10799 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_108.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_108.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>10800 CE <20> 11399 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_114.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_114.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>11400 CE <20> 11999 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_120.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_120.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12000 CE <20> 12599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_126.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_126.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12600 CE <20> 13199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_132.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_132.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>13200 CE <20> 13799 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_138.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_138.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>13800 CE <20> 14399 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_144.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_144.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>14400 CE <20> 14999 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_150.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_150.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>15000 CE <20> 15599 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_156.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_156.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>15600 CE <20> 16199 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt 191.4pt 304.8pt'><span lang=EN-US>sepl_162.se1<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>semo_162.se1<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>16200 CE <20> 7 Jan
|
||
16800 CE</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>All Swiss
|
||
Ephemeris files have the file suffix .se1. A planetary file is about 500 kb, a
|
||
lunar file 1300 kb. Swiss Ephemeris files are available for download from
|
||
Astrodienst's web server.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>The time range of the Swiss Ephemeris</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Versions until 1.80, which were based on
|
||
JPL Ephemeris DE406 and some extension created by Astrodienst, work for the
|
||
following time range:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;tab-stops:70.9pt 212.65pt'><span
|
||
lang=EN-US>Start date<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>2 Jan 5401 BCE
|
||
(-5400) Jul.<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>= JD -251291.5</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 212.65pt'><span lang=EN-US>End date<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>31 Dec 5399 CE (Greg. Cal.)<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>= JD 3693368.5</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>Versions since
|
||
2.00, which are based on JPL Ephemeris DE431, work for the following time
|
||
range:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;tab-stops:70.9pt 212.65pt'><span
|
||
lang=EN-US>Start date<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>11 Aug
|
||
13000 BCE (-12999) Jul.<span style='mso-tab-count:1'><3E> </span>= JD -3026604.5</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 212.65pt'><span lang=EN-US>End date<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>7 Jan 16800 CE Greg.<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span style='mso-tab-count:1'> </span>=
|
||
JD 7857139.5</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>Please note that
|
||
versions prior to 2.00 are not able to correctly handle the JPL ephemeris
|
||
DE431.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>A note on year numbering</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are two numbering systems for years
|
||
before the year 1 CE. The historical numbering system (indicated with BCE) has
|
||
no year zero. Year 1 BCE is followed directly by year 1 CE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The astronomical year numbering system does
|
||
have a year zero; years before the common era are indicated by negative year
|
||
numbers. The sequence is year -1, year 0, year 1 CE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The historical year 1 BCE corresponds to
|
||
astronomical year 0,</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>the historical year 2 BCE corresponds to
|
||
astronomical year -1, etc.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In this and other documents related to the
|
||
Swiss Ephemeris we use both systems of year numbering. When we write a negative
|
||
year number, it is astronomical style; when we write BCE, it is historical
|
||
style.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Moshier Ephemeris</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is a semi-analytical approximation of
|
||
the JPL planetary and lunar ephemerides DE404, developed by Steve Moshier. Its
|
||
deviation from JPL is below 1 arc second with the planets and a few arc seconds
|
||
with the Moon. No data files are required for this ephemeris, as all data are
|
||
linked into the program code already.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This may be sufficient accuracy for most
|
||
purposes, since the Moon moves 1 arc second in 2 time seconds and the Sun 2.5
|
||
arc seconds in one minute.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The advantage of the Moshier mode of the
|
||
Swiss Ephemeris is that it needs no disk storage. Its disadvantage, besides the
|
||
limited precision, is reduced speed: it is about 10 times slower than JPL mode
|
||
and the compressed JPL mode (described above).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Moshier Ephemeris covers the interval
|
||
from 3000 BCE to 3000 CE. However, Moshier notes that <20>the adjustment for the
|
||
inner planets is strictly valid only from 1350 B.C. to 3000 A.D., but may be
|
||
used to 3000 B.C. with some loss of precision<6F>. And: <20>The Moon's position is
|
||
calculated by a modified version of the lunar theory of Chapront-Touze' and
|
||
Chapront. This has a precision of 0.5 arc second relative to DE404 for all
|
||
dates between 1369 B.C. and 3000 A.D.<2E> (Moshier,
|
||
http://www.moshier.net/aadoc.html).</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The full JPL Ephemeris</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is the full precision state-of-the-art
|
||
ephemeris. It provides the highest precision and is the basis of the
|
||
Astronomical Almanac. Time range:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;tab-stops:2.0cm 7.0cm'><span
|
||
lang=EN-US>Start date<span style='mso-tab-count:1'><3E><><A0><A0> </span>9 Dec 13002 BCE
|
||
(-13001) Jul.<span style='mso-tab-count:1'><3E><><A0> </span>= JD -3027215.5</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 7.0cm'><span lang=EN-US>End date<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span>11 Jan 17000 CE Greg.<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>= JD 7930192.5</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>JPL is the Jet
|
||
Propulsion Laboratory of NASA in Pasadena, CA, USA (see http://www.jpl.nasa.gov
|
||
). Since many years this institute, which is in charge of the planetary
|
||
missions of NASA, has been the source of the highest precision planetary
|
||
ephemerides. The currently newest version of JPL ephemeris is the DE430/DE431.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are several versions of the JPL
|
||
Ephemeris. The version is indicated by the DE-number. A higher number indicates
|
||
a more recent version. SWISSEPH should be able to read any JPL file from DE200
|
||
upwards.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Accuracy of JPL ephemerides DE403/404
|
||
(1996) and DE405/406 (1998)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>According to a paper (see below) by
|
||
Standish and others on DE403 (of which DE406 is only a slight refinement), the
|
||
accuracy of this ephemeris can be partly estimated from its difference from
|
||
DE200:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With the inner planets, Standish shows that
|
||
within the period 1600 <20> 2160 there is a maximum difference of 0.1 <20> 0.2<94> which
|
||
is mainly due to a mean motion error of DE200. This means that the absolute
|
||
precision of DE406 is estimated significantly better than 0.1<94> over that
|
||
period. However, for the period 1980 <20> 2000 the deviations between DE200 and
|
||
DE406 are below 0.01<94> for all planets, and for this period the JPL integration
|
||
has been fit to measurements by radar and laser interferometry, which are
|
||
extremely precise.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With the outer planets, Standish's diagrams
|
||
show that there are large differences of several <20> around 1600, and he says
|
||
that these deviations are due to the inherent uncertainty of extrapolating the
|
||
orbits beyond the period of accurate observational data. The uncertainty of
|
||
Pluto exceeds 1<> before 1910 and after 2010, and increases rapidly in more
|
||
remote past or future.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With the Moon, there is an increasing
|
||
difference of 0.9<94>/cty2 between 1750 and 2169. It is mainly caused by errors in
|
||
LE200 (Lunar Ephemeris).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The differences between DE200 and DE403
|
||
(DE406) can be summarized as follows:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;margin-right:0cm;margin-bottom:
|
||
3.0pt;margin-left:35.45pt;tab-stops:106.35pt 219.75pt'><span lang=EN-US>1980 <20>
|
||
2000<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>all planets<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>< 0.01<94>,</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:106.35pt 219.75pt'><span
|
||
lang=EN-US>1600 <20> 1980<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Sun <20> Jupiter<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>a few 0.1<94>,</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:106.35pt 219.75pt'><span
|
||
lang=EN-US>1900 <20> 1980<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Saturn <20>
|
||
Neptune<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>a few 0.1<94>,</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:106.35pt 219.75pt'><span
|
||
lang=EN-US>1600 <20> 1900<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Saturn <20>
|
||
Neptune<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>a few <20>,</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:106.35pt 219.75pt'><span
|
||
lang=EN-US>1750 <20> 2169<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Moon<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>a few <20>.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>(see: E.M.
|
||
Standish, X.X. Newhall, J.G. Williams, and W.M. Folkner, JPL Planetary and
|
||
Lunar Ephemerides, DE403/LE403, JPL Interoffice Memorandum IOM 314.10-127, May
|
||
22, 1995, pp. 7f.)</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Comparison of JPL ephemerides DE406
|
||
(1998) with DE431 (2013)</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences DE431-DE406 for 3000 BCE to
|
||
3000 CE:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;margin-right:0cm;margin-bottom:
|
||
3.0pt;margin-left:35.45pt;tab-stops:148.85pt'><span lang=EN-US>Moon<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>< 7" (TT),
|
||
< 2" (UT)</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Sun, Mercury, Venus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span><
|
||
0.4 "</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Mars<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
2"</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Jupiter<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
6"</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Saturn<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
0.1"</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Uranus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
28"</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Neptune<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
53"</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:35.45pt;tab-stops:148.85pt'><span
|
||
lang=EN-US>Pluto<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
129"</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Moon, position (DE431) <20> position (DE406)
|
||
in TT and UT</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Delta T adjusted to tidal acceleration of
|
||
lunar ephemeris)</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:35.45pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dL(TT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dL(UT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dB(TT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dB(UT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2999</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6.33"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.30"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.05"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5.91"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.62"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.85"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.32"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3.39"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.21"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.59"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.20"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1.74"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.49"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.06"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1.06"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.50"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.30"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.12"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.63"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.40"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.28"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.09"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.13"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.99"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.11"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.05"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.08"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.99"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.03"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.05"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.12"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.38"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.08"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.06"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.08"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.15"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.03"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.06"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.06"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.10"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.10"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.09"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.09"</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US style='color:white;mso-color-alt:windowtext'>Sun</span><span
|
||
lang=EN-US>, position (DE431) <20> position (DE406) in TT and UT</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:35.45pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dL(TT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dL(UT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2999</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.21"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.34"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.11"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.33"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.09"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.26"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.04"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.22"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.06"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.14"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.02"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.11"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.02"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.06"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.04"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01"</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Pluto, position (DE431) <20> position (DE406)
|
||
in TT</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:35.45pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>dL(TT)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2999</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>66.31"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>82.93"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>100.17"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>115.19"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>126.50"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>127.46"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>115.31"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>92.43"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>63.06"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>31.17"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-28.38"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-53.38"</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris is based on the latest
|
||
JPL file, and reproduces the full JPL precision with better than 1/1000 of an
|
||
arc second, while requiring only a tenth storage. Therefore for most
|
||
applications it makes little sense to get the full JPL file. Precision
|
||
comparison can be done at the Astrodienst web server. The Swiss Ephemeris test
|
||
page http://www.astro.com/swisseph/swetest.htm allows to compute planetary
|
||
positions for any date using the full JPL ephemerides DE200, DE406, DE421,
|
||
DE431, or the compressed Swiss Ephemeris or the Moshier ephemeris.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488753"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Swiss Ephemeris Compared
|
||
with Astronomical Almanac and JPL Horizons</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Swiss Ephemeris and the Astronomical
|
||
Almanac</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The original JPL ephemeris provides barycentric
|
||
equatorial Cartesian positions relative to the equinox 2000/ICRS. Moshier
|
||
provides heliocentric positions. The conversions to apparent geocentric
|
||
ecliptical positions were done using the algorithms and constants of the
|
||
Astronomical Almanac as described in the <20>Explanatory Supplement to the
|
||
Astronomical Almanac<61>. Using the DE200 data file, it is possible to reproduce
|
||
the positions given by the Astronomical Almanac 1984, 1995, 1996, and 1997 (on
|
||
p. B37-38 in all editions) to the last digit. Editions of other years have not
|
||
been checked. DE200 was used by Astronomical Almanac from 1984 to 2002. The
|
||
sample positions given the mentioned editions of Astronomical Almanac can also
|
||
be reproduced using a recent version of the Swiss Ephemeris and a recent JPL
|
||
ephemeris. The number of digits given in AA do not allow to see a difference.
|
||
The Swiss Ephemeris has used DE405/DE406 since its beginning in 1997.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>From 2003 to 2015, the Astronomical Almanac
|
||
has been using JPL ephemeris DE405, and since Astronomical Almanac 2006 all
|
||
relevant resolutions of the International Astronomical Union (IAU) have been
|
||
implemented. Versions 1.70 and higher of the Swiss Ephemeris also follow these
|
||
resolutions and reproduce the sample calculation given by AA2006 (p. B61-B63),
|
||
AA2011 and AA2013 (both p. B68-B70) to the last digit, i.e. to better than
|
||
0.001 arc second. (To avoid confusion when checking AA2006, it may be useful to
|
||
know that the JD given on page B62 does not have enough digits in order to
|
||
produce the correct final result. With later AA2011 and AA2013, there is no
|
||
such problem.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris uses JPL Ephemeris
|
||
DE431 since version 2.0 (2014). The Astronomical Almanac uses JPL Ephemeris
|
||
DE430 since 2016. The Swiss Ephemeris and the Astronomical Almanac still
|
||
perfectly agree.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Detailed instructions how to compare
|
||
planetary positions as given by the Swiss Ephemeris with those of Astronomical
|
||
Almanac are given in Appendix D at the end of this documentation.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Swiss Ephemeris and JPL
|
||
Horizons System of NASA</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris, from version 1.70 on,
|
||
reproduces astrometric planetary positions of the JPL Horizons System
|
||
precisely. However, there have been small differences of about 52 mas
|
||
(milli-arcseconds) with apparent positions. The same deviations also occur if
|
||
Horizons is compared with the example calculations given in the Astronomical
|
||
Almanac.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Horizons uses an entirely different
|
||
approach and a different reference system. It follows IERS Conventions 1996 (p.
|
||
22), i.e. it uses the old precession models IAU 1976 (Lieske) and nutation IAU
|
||
1980 (Wahr) and corrects the resulting positions by adding daily-measured
|
||
celestial pole offsets (delta_psi and delta_epsilon) to nutation.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On the other hand, the Astronomical Almanac
|
||
and the Swiss Ephemeris follow IERS Conventions 2003 and 2010, but do not take
|
||
into account daily celestial pole offsets.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>While Horizons<6E> approach is more accurate
|
||
in that it takes into account very small and unpredictable motions of the
|
||
celestial pole (free core nutation), the resulting positions are not relative to
|
||
the same reference frame as Astronomical Almanac and the Swiss Ephemeris, and
|
||
they are not in agreement with the recent IERS Conventions 2003 and 2010. Some
|
||
component of so-called frame bias is lost in Horizons positions. This causes a
|
||
more or less constant offset of 52 mas in right ascension or 42 mas in ecliptic
|
||
longitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='letter-spacing:-.1pt'>Swiss
|
||
Ephemeris versions 2.00 and higher contain code to reproduce positions of
|
||
Horizons with a precision of about 1</span><span lang=EN-US> <span
|
||
style='letter-spacing:-.1pt'>mas for 1799 CE <20> today. From version 2.07 on,
|
||
Horizons can be reproduced with a similar precision for its whole time range.</span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For best agreement with Horizons, current
|
||
data files with Earth orientation parameters (EOP) must be downloaded from the
|
||
IERS website and put into the ephemeris path. If they are not available, the
|
||
Swiss Ephemeris uses an approximation which reproduces Horizons still with an
|
||
accuracy of about 2 mas between 1962 and present.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>It must be noted that correct values for
|
||
delta_psi and delta_epsilon are only available between 1962 and present. For
|
||
all calculations before that, Horizons uses the first values of the EOP data,
|
||
and for all calculations in the future, it uses the last values of the existing
|
||
data are used. The resulting positions are not really correct, but the
|
||
ephemeris is at least continuous.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>More information on this and technical
|
||
details are found in the programmer<65>s documentation and in the source code,
|
||
file swephlib.h.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>IERS Conventions 1996, 2003, and 2010 can
|
||
be read or downloaded from here:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>http://www.iers.org/IERS/EN/DataProducts/Conventions/conventions.html</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Detailed instructions how to compare
|
||
planetary positions as given by the Swiss Ephemeris with those of JPL are given
|
||
in Appendix C at the end of this documentation.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Many thanks to Jon Giorgini, developer of
|
||
the Horizons System, for explaining us the methods used at JPL.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Differences between Swiss
|
||
Ephemeris 1.70 and older versions</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With version 1.70, the standard algorithms
|
||
recommended by the IAU resolutions up to 2005 were implemented. The following
|
||
calculations have been added or changed with Swiss Ephemeris version 1.70:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>"Frame Bias"
|
||
transformation from ICRS to J2000;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Nutation IAU 2000B (could be
|
||
switched to 2000A by the user);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Precession model P03
|
||
(Capitaine/Wallace/Chapront 2003), including improvements in ecliptic obliquity
|
||
and sidereal time that were achieved by this model.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The differences between the old and new
|
||
planetary positions in ecliptic longitude (arc seconds) are:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>New
|
||
<20> Old<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.00108</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1995</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.02448</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1980</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.05868</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1970</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.10224</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1950</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.15768</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.30852</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1800</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.58428</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1799</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.04644</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1700</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.07524</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.12636</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.25344</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.53316</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-0.85824</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-1.40796</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-3.33684</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-10.64808</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-32.68944</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>-49.15188</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>The discontinuity
|
||
of the curve between 1800 and 1799 is explained by the fact that old versions
|
||
of the Swiss Ephemeris used different precession models for different time
|
||
ranges: the model IAU 1976 by Lieske for 1800-2200, and the precession model by
|
||
Williams 1994 outside that time range.</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Note</span></b><span lang=EN-US>:
|
||
Precession model P03 is said to be accurate to 0.00005 arc second for CE
|
||
1000-3000.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The differences between version 1.70 and
|
||
older versions for the future are as follows:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00108</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2010</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01620</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2050</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.14004</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.29448</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2200</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.61452</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2201</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.05940</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.27252</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.48708</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.47592</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10;mso-yfti-lastrow:yes;page-break-inside:avoid'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.40032</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>The discontinuity
|
||
in 2200 has the same explanation as the one in 1800.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Jyotish / sidereal ephemerides</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ephemeris changes by a constant value
|
||
of about +0.3 arc second. This is because all our ayanamshas have the start
|
||
epoch 1900, for which epoch precession was corrected by the same amount.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Fictitious planets / bodies from the
|
||
orbital elements file seorbel.txt</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are changes of several 0.1 arcsec,
|
||
depending on the epoch of the orbital elements and the correction of precession
|
||
as can be seen in the tables above.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>The differences for ecliptic obliquity in
|
||
arc seconds (new - old) are:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.71468</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.25244</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.63612</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.31788</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.06336</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.04212</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02016</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1800</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.01296</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1700</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.04032</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1600</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.06696</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.09432</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.22716</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.51444</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1.07064</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2.62908</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6.68016</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15.73272</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>33.54480</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:19;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>44.22924</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<b><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:11.0pt;
|
||
font-family:"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA'><br
|
||
clear=all style='page-break-before:always'>
|
||
</span></b>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>The differences for sidereal time in
|
||
seconds (new - old) are:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2.544</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.461</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.122</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.126</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.019</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.001</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.019</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.126</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.122</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-500</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.594</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.461</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5.029</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-12.355</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-25.330</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-46.175</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5400</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-57.273</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Differences between Swiss
|
||
Ephemeris 1.78 and 1.77</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Former versions of the Swiss Ephemeris had
|
||
used the precession model by Capitaine, Wallace, and Chapront of 2003 for the
|
||
time range -5500 until 9500 and the precession model Laskar 1986 for epochs
|
||
outside this time range. (Since planetary ephemerides are restricted to -5400
|
||
to +5400, Laskar precession is only relevant for calculations of fixed stars.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Version 1.78 calculates precession and
|
||
ecliptic obliquity according to Vondr<64>k, Capitaine, and Wallace, <20>New
|
||
precession expressions, valid for long time intervals<6C>, A&A 534, A22
|
||
(2011), which is good for +- 200 millennia.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This change has almost no ramifications for
|
||
historical epochs. Planetary positions and the obliquity of the ecliptic change
|
||
by less than an arc minute in 5400 BCE. However, for research concerning the
|
||
prehistoric cave paintings (Lascaux, Altamira, etc., some of which may
|
||
represent celestial constellations), fixed star positions are required for 15.000
|
||
BCE or even earlier (the Chauvet cave was painted in 33.000 BCE). Such
|
||
calculations are now possible using the Swiss Ephemeris version 1.78 or higher.
|
||
However, the Sun, Moon, and the planets remain restricted to the time range
|
||
5400 BCE to 5400 CE.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences (in arc sec) in precession
|
||
(v. 1.78 <20> v. 1.77, test star was Aldebaran)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Only differences between -5500 and +9500
|
||
are differences Vondr<64>k <20> P03. Those outside this time range are actually
|
||
differences Vondr<64>k <20> Laskar 1986.</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-20000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-26716"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-15000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2691"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-10000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-256"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3.95352"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-9.77940"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-7.00524"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3.40524"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.23732"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.33948"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.05400"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1800</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00108"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00036"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00000"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00036"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2200</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.00072"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.03528"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.59904"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2.90160"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:19'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>77"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:20'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>228"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:21'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>19000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2839"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:22;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>20000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5218"</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences (in arc sec) in ecliptic
|
||
obliquity:</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-20000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11074.43664"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-15000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3321.50652"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-10000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>632.60532"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-33.42636"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.01008"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00972"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00000"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.01008"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.05868"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-72.91980"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-772.91712"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12;mso-yfti-lastrow:yes'>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>20000</span></p>
|
||
</td>
|
||
<td style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3521.23488<94></span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Differences between Swiss
|
||
Ephemeris 2.00 and 1.80</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>These differences are explained by the fact
|
||
that the Swiss Ephemeris is now based on JPL Ephemeris DE431, whereas before
|
||
release 2.00 it was based on DE406. The differences are listed above in Ch. 2.1.1.3,
|
||
see paragraph on <20>Comparison of JPL ephemerides DE406 (1998) with DE431
|
||
(2013)<29>.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Differences between Swiss
|
||
Ephemeris 2.05.01 and 2.06</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris 2.06 has a new Delta T
|
||
algorithm based on:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison, L.V.,
|
||
and Hohenkerk, C.Y., "Measurement of the Earth's Rotation: 720 BCE to CE
|
||
2015", Royal Society Proceedings A, 7 Dec 2016,</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>http://rspa.royalsocietypublishing.org/lookup/doi/10.1098/rspa.2016.0404</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris uses it for
|
||
calculations before 1948.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Differences resulting from this update are
|
||
shown in Chapter 7 on Delta T.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488754"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The details of coordinate
|
||
transformation</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The following conversions are applied to
|
||
the coordinates after reading the raw positions from the ephemeris files:</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Correction
|
||
for light-time</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Since the planet's light needs time to
|
||
reach the Earth, it is never seen where it actually is, but where it was some
|
||
time before. Light-time amounts to a few minutes with the inner planets and a
|
||
few hours with distant planets like Uranus, Neptune and Pluto. For the Moon,
|
||
the light-time correction is about one second. With planets, light-time
|
||
correction may be of the order of 20<32> in position, with the Moon 0.5<94></span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Conversion
|
||
from the solar system barycenter to the geocenter</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Original JPL data are referred to the
|
||
center of the gravity of the solar system. Apparent planetary positions are
|
||
referred to an imaginary observer in the center of the Earth.</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Light
|
||
deflection by the gravity of the Sun<o:p></o:p></span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the gravitational fields of the Sun and
|
||
the planets light rays are bent. However, within the solar system only the Sun has
|
||
enough mass to deflect light significantly. Gravity deflection is greatest for
|
||
distant planets and stars, but never greater than 1.8<94>. When a planet
|
||
disappears behind the Sun, the Explanatory Supplement recommends to set the
|
||
deflection = 0. To avoid discontinuities, we chose a different procedure. See
|
||
Appendix A.</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'><3E>Annual<61>
|
||
aberration of light</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The velocity of light is finite, and
|
||
therefore the apparent direction of a moving body from a moving observer is
|
||
never the same as it would be if both the planet and the observer stood still.
|
||
For comparison: if you run through the rain, the rain seems to come from ahead
|
||
even though it actually comes from above. Aberration may reach 20<32>.</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Frame
|
||
Bias (ICRS to J2000)</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>JPL ephemerides since DE403/DE404 are
|
||
referred to the International Celestial Reference System, a time-independent,
|
||
non-rotating reference system which was introduced by the IAU in 1997. The
|
||
planetary positions and speed vectors are rotated to the J2000 system. This
|
||
transformation makes a difference of only about 0.0068 arc seconds in right
|
||
ascension. (Implemented from Swiss Ephemeris 1.70 on)</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif;
|
||
font-weight:normal'>Precession</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Precession is the motion of the vernal
|
||
equinox on the ecliptic. It results from the gravitational pull of the Sun, the
|
||
Moon, and the planets on the equatorial bulge of the Earth. Original JPL data
|
||
are referred to the mean equinox of the year 2000. Apparent planetary positions
|
||
are referred to the equinox of date. (From Swiss Ephemeris 1.78 on, we use the
|
||
precession model Vondr<64>k/Capitaine/Wallace 2011.)</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Nutation
|
||
(true equinox of date)</span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A short-period oscillation of the vernal
|
||
equinox. It results from the Moon<6F>s gravity which acts on the equatorial bulge
|
||
of the Earth. The period of nutation is identical to the period of a cycle of
|
||
the lunar node, i.e. 18.6 years. The difference between the true vernal point
|
||
and the mean one is always below 17<31>. (From Swiss Ephemeris 2.00, we use the
|
||
nutation model IAU 2006. Since 1.70, we used nutation model IAU 2000. Older
|
||
versions used the nutation model IAU 1980 (Wahr).)</span></p>
|
||
|
||
<p class=MsoSubtitle><strong><span lang=EN-US style='font-family:"Segoe UI",sans-serif'>Transformation
|
||
from equatorial to ecliptic coordinates<o:p></o:p></span></strong></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For <span class=italic>precise speed</span>
|
||
of the planets and the Moon, we had to make a special effort, because the <span
|
||
class=italic>Explanatory Supplement</span> does not give algorithms that apply
|
||
the above-mentioned transformations to speed. Since this is not a trivial job,
|
||
the easiest way would have been to compute three positions in a small interval
|
||
and determine the speed from the derivation of the parabola going through them.
|
||
However, double float calculation does not guarantee a precision better than
|
||
0.1<94>/day. Depending on the time difference between the positions, speed is
|
||
either good near station or during fast motion. Derivation from more positions
|
||
and higher order polynomials would not help either.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Therefore we worked out a way to apply
|
||
directly all the transformations to the barycentric speeds that can be derived
|
||
from JPL or Swiss Ephemeris. The precision of daily motion is now better than
|
||
0.002<94> for all planets, and the computation is even a lot faster than it would
|
||
have been from three positions. A position with speed takes in average only
|
||
1.66 times longer than one without speed, if a JPL or a Swiss Ephemeris
|
||
position is computed. With Moshier, however, a computation with speed takes 2.5
|
||
times longer.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488755"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Swiss Ephemeris compression
|
||
mechanism</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The idea behind our mechanism of ephemeris
|
||
compression was developed by Dr. Peter Kammeyer of the U.S. Naval Observatory
|
||
in 1987.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is how it works: The ephemerides of
|
||
the Moon and the inner planets require by far the greatest part of the storage.
|
||
A more sophisticated mechanism is required for these than for the outer
|
||
planets. Instead of the positions we store the differences between JPL and the
|
||
mean orbits of the analytical theory VSOP87. These differences are a lot
|
||
smaller than the position values, wherefore they require less storage. They are
|
||
stored in Chebyshew polynomials covering a period of an anomalistic cycle each.
|
||
(By the way, this is the reason, why the Swiss Ephemeris does not cover the
|
||
time range of the full JPL ephemeris. The first ephemeris file begins on the
|
||
date on which the last of the inner planets (including Mars) passes its first
|
||
perihelion after the start date of the JPL ephemeris.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With the outer planets from Jupiter through
|
||
Pluto we use a simpler mechanism. We rotate the positions provided by the JPL
|
||
ephemeris to the mean plane of the planet. This has the advantage that only two
|
||
coordinates have high values, whereas the third one becomes very small. The
|
||
data are stored in Chebyshew polynomials that cover a period of 4000 days each.
|
||
(This is the reason, why Swiss Ephemeris stops before the end date of the JPL
|
||
ephemeris.)</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488756"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The extension of DE406-based
|
||
ephemerides to 10.800 years</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This Chapter is only relevant to those who
|
||
use pre-2014, DE406-based ephemeris files of the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The JPL ephemeris DE406 covers the time
|
||
range from 3000 BCE to 3000 CE. While this is an excellent range covering all
|
||
precisely known historical events, there are some types of ancient astrology
|
||
and archeoastronomical research which would require a longer time range.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In December 1998 we have made an effort to
|
||
extend the time range using our own numerical integration. The exact physical
|
||
model used by Standish et. al. for the numerical integration of the DE406
|
||
ephemeris is not fully documented (at least we do not understand some details),
|
||
so that we cannot use the same integration program as had been used at JPL for
|
||
the creation of the original ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The previous JPL ephemeris DE200, however,
|
||
has been reproduced by Steve Moshier over a very long-time range with his
|
||
numerical integrator, which was available to us. We used this software with
|
||
start vectors taken at the end points of the DE406 time range. To test our numerical
|
||
integrator, we ran it upwards from 3000 BCE to 600 BCE for a period of 2400
|
||
years and compared its results with the DE406 ephemeris itself. The agreement
|
||
is excellent for all planets except the Moon (see table below). The lunar orbit
|
||
creates a problem because the physical model for the Moon's libration and the
|
||
effect of the tides on lunar motion is quite different in the DE406 from the
|
||
model in the DE200. We varied the tidal coupling parameter (love number) and
|
||
the longitudinal libration phase at the start epoch until we found the best
|
||
agreement over a 2400-year test range between our integration and the JPL data.
|
||
We could reproduce the Moon's motion over a 2400-time range with a maximum
|
||
error of 12 arcseconds. For most of this time range the agreement is better
|
||
than 5 arcsec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With these modified parameters we ran the
|
||
integration backward in time from 3000 BCE to 5400 BCE. It is reasonable to
|
||
assume that the integration errors in the backward integration are not
|
||
significantly different from the integration errors in the upward integration.</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Planet<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>max. error<br>
|
||
arcsec<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>avg. error<br>
|
||
arcsec<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Mercury </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1.67</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.61</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Venus </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.14</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.03</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Earth </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1.00</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.42</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Mars</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.21</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.06</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Jupiter </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.85</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.38</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Saturn </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.59</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.24</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Uranus </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.20</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.09</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Neptune</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.12</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.06</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Pluto</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.12</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.04</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Moon</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>12.2</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>2.53</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Sun bary. </span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>6.3</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.39</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US style='letter-spacing:
|
||
-.1pt'>The same procedure was applied at the upper end of the DE406 range, to
|
||
cover an extension period from 3000 CE to 5400 CE. The maximum integration
|
||
errors as determined in the test run 3000 CE down to 600 CE are given in the
|
||
table below.<o:p></o:p></span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Planet<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>max. error<br>
|
||
arcsec<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>avg. error<br>
|
||
arcsec<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Mercury</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>2.01</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.69</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Venus</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.06</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.02</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Earth</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.33</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.14</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Mars</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>1.69</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.82</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Jupiter</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.09</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.05</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Saturn</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.05</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.02</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Uranus</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.16</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.07</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Neptune</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.06</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.03</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Pluto</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.11</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.04</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Moon</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>8.89</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>3.43</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>Sun bary.</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.61</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:2.0pt;text-align:right'><span
|
||
lang=EN-US>0.05</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Deviations in heliocentric longitude from
|
||
new JPL ephemeris DE431 (2013), time range 5400 BCE to 3000 BCE</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Moon (geocentric)<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
40<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Earth, Mercury, Venus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span><
|
||
1.4<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Mars<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
4<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Jupiter<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
9<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Saturn<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
1.2<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Uranus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
36<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Neptune<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
76<94></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:134.7pt'><span
|
||
lang=EN-US>Pluto<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><
|
||
120<94></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488757"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.1.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Solar Ephemeris in the remote
|
||
past</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Since SE 2.00 and the introduction of JPL
|
||
ephemerid DE431, there has been a small inaccuracy with solar ephemerides in
|
||
the remote past. In 10.000 BCE, the ecliptic latitude of the Sun seems to
|
||
oscillate between -36 and +36 arcsec. In reality, the solar latitude should be
|
||
below 1 arcsec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This phenomenon is caused by the precession
|
||
theory Vondrak 2011 (A&A 534, A22 (2011)), whose precision is limited. On
|
||
p. 2 the paper states:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>The goal of the present study is to find
|
||
relatively simple expressions for all precession parameters (listed, e.g., by
|
||
Hilton et al. 2006), the primary ones being the orientation parameters of the
|
||
secularly-moving ecliptic and equator poles with respect to a fixed celestial
|
||
frame. We require that the accuracy of these expressions is comparable to the
|
||
IAU 2006 model near the epoch J2000.0, while lower accuracy is allowed outside
|
||
the interval <20>1000 years, gradually increasing up to several arcminutes at the
|
||
extreme epochs <20>200 millennia.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This means that this theory is probably the
|
||
best one available for current centuries but not necessarily perfect for the
|
||
remote past.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The problem could be avoided if we used the
|
||
precession theory Laskar 1986 or Owen 1990. However, precession Vondrak 2011 is
|
||
better for recent centuries. This seems more relevant to us.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488758"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.2.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Lunar and Planetary Nodes and Apsides</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488759"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.2.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Mean Lunar Node and Mean Lunar
|
||
Apogee (Lilith, Black Moon in astrology)</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>JPL ephemerides do not include a mean lunar
|
||
node or mean lunar apsis (perigee/apogee). We therefore have to derive them
|
||
from different sources.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Our mean node and mean apogee are computed
|
||
from Moshier's lunar routine, which is an adjustment of the ELP2000-85 lunar
|
||
theory to the JPL ephemeris on the interval from 3000 BCE to 3000 CE. Its
|
||
deviation from the mean node of ELP2000-85 is 0 for J2000 and remains below 20
|
||
arc seconds for the whole period. With the apogee, the deviation reaches 3 arc
|
||
minutes at 3000 BCE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In order to cover the whole time range of
|
||
DE431, we had to add some corrections to Moshier<65>s mean node and apsis, which
|
||
we derived from the true node and apsis that result from the DE431 lunar
|
||
ephemeris. Estimated precision is 1 arcsec, relative to DE431.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Notes for astrologers</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Astrological Lilith or the Dark Moon is either
|
||
the apogee (<28>aphelion<6F>) of the lunar orbital ellipse or, according to some, its
|
||
empty focal point. As seen from the geocenter, this makes no difference. Both
|
||
of them are located in exactly the same direction. But the definition makes a
|
||
difference for topocentric ephemerides.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The opposite point, the lunar perigee or
|
||
orbital point closest to the Earth, is also known as Priapus. However, if
|
||
Lilith is understood as the second focal point, an opposite point makes no
|
||
sense, of course.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Originally, the term <20>Dark Moon<6F> stood for
|
||
a hypothetical second body that was believed to move around the Earth. There
|
||
are still ephemerides circulating for such a body, but modern celestial
|
||
mechanics clearly exclude the possibility of such an object. Later the term <20>Dark
|
||
Moon<94> was used for the lunar apogee.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris apogee differs from the
|
||
ephemeris given by Jo<4A>lle de Gravelaine in her book <20>Lilith, der schwarze Mond<6E>
|
||
(Astrodata 1990). The difference reaches several arc minutes. The mean apogee
|
||
(or perigee) moves along the mean lunar orbit which has an inclination of 5
|
||
degrees. Therefore it has to be projected on the ecliptic. With de Gravelaine's
|
||
ephemeris, this was not taken into account. As a result of this projection, we
|
||
also provide an ecliptic latitude of the apogee, which will be of importance if
|
||
declinations are used.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There may be still another problem. The
|
||
'first' focal point does not coincide with the geocenter but with the
|
||
barycenter of the Earth-Moon-system. The difference is about 4700 km. If one
|
||
took this into account, it would result in a monthly oscillation of the Black Moon.
|
||
If one defines the Black Moon as the apogee, this oscillation would be about
|
||
+/- 40 arc minutes. If one defines it as the second focus, the effect is a lot
|
||
greater: +/- 6 degrees. However, we have neglected this effect.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>[added by Alois 7-feb-2005, arising out of
|
||
a discussion with Juan Revilla] The concept of 'mean lunar orbit' means that
|
||
short term. e.g. monthly, fluctuations must not be taken into account. In the
|
||
temporal average, the EMB coincides with the geocenter. Therefore, when mean
|
||
elements are computed, it is correct only to consider the geocenter, not the Earth-Moon
|
||
Barycenter.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Computing topocentric positions of mean
|
||
elements is also meaningless and should not be done.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488760"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.2.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The True Node</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The 'true' lunar node is usually considered
|
||
the osculating node element of the momentary lunar orbit. I.e., the axis of the
|
||
lunar nodes is the intersection line of the momentary orbital plane of the Moon
|
||
and the plane of the ecliptic. Or in other words, the nodes are the
|
||
intersections of the two great circles representing the momentary apparent
|
||
orbit of the Moon and the ecliptic.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The nodes are considered important because
|
||
they are connected with eclipses. They are the meeting points of the Sun and the
|
||
Moon. From this point of view, a more correct definition might be: The axis of
|
||
the lunar nodes is the intersection line of the momentary orbital plane of the Moon
|
||
and the momentary orbital plane of the Sun.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This makes a difference, although a small
|
||
one. Because of the monthly motion of the Earth around the Earth-Moon barycenter,
|
||
the Sun is not exactly on the ecliptic but has a latitude, which, however, is
|
||
always below an arc second. Therefore the momentary plane of the Sun's motion
|
||
is not identical with the ecliptic. For the true node, this would result in a
|
||
difference in longitude of several arc seconds. However, Swiss Ephemeris
|
||
computes the traditional version.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The advantage of the 'true' nodes against
|
||
the mean ones is that when the Moon is in exact conjunction with them, it has
|
||
indeed a zero latitude. This is not so with the mean nodes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the strict sense of the word, even the
|
||
<94>true<94> nodes are true only twice a month, viz. at the times when the Moon crosses
|
||
the ecliptic. Positions given for the times in between those two points are
|
||
based on the idea that celestial orbits can be approximated by elliptical
|
||
elements or great circles. The monthly oscillation of the node is explained by
|
||
the strong perturbation of the lunar orbit by the Sun. A different approach for
|
||
the <20>true<75> node that would make sense, would be to interpolate between the true
|
||
node passages. The monthly oscillation of the node would be suppressed, and the
|
||
maximum deviation from the conventional <20>true<75> node would be about 20 arc
|
||
minutes.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Precision of the true node</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The true node can be computed from all of
|
||
our three ephemerides. If you want a precision of the order of at least one arc
|
||
second, you have to choose either the JPL or the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Maximum differences</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:9.0cm'><span lang=EN-US>JPL-derived node <20>
|
||
Swiss-Ephemeris-derived node<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>~
|
||
0.1 arc second</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:9.0cm'><span lang=EN-US>JPL-derived node <20>
|
||
Moshier-derived node<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>~
|
||
70 arc seconds</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(PLACALC was not better either. Its error
|
||
was often > 1 arc minute.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Distance of the true lunar node:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The distance of the true node is calculated
|
||
on the basis of the osculating ellipse of date.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Small discontinuities in ephemeris of
|
||
true node and apogee based on compressed file</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If our compressed lunar ephemeris files
|
||
semo*.se1 are used, then small discontinuities occur every 27.55 days at the
|
||
segment boundaries of the compressed lunar orbit. The errors are small, but can
|
||
be inconvenient if a smooth function is required for the osculating node and
|
||
apogee. This problem does not occur if an original JPL ephemeris or the Moshier
|
||
ephemeris is used.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488761"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.2.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Osculating Apogee
|
||
(astrological True Lilith or True Dark Moon)</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The position of 'true Lilith' is given in
|
||
the New International Ephemerides (NIE, Editions St. Michel) and in Francis
|
||
Santoni 'Ephemerides de la lune noire vraie 1910-2010' (Editions St. Michel,
|
||
1993). Both Ephemerides coincide precisely.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The relation of this point to the mean
|
||
apogee is not exactly of the same kind as the relation between the true node
|
||
and the mean node. Like the 'true' node, it can be considered as an osculating
|
||
orbital element of the lunar motion. But there is an important difference: The
|
||
apogee contains the concept of the ellipse, whereas the node can be defined
|
||
without thinking of an ellipse. As has been shown above, the node can be derived
|
||
from orbital planes or great circles, which is not possible with the apogee.
|
||
Now ellipses are good as a description of planetary orbits because planetary
|
||
orbits are close to a two-body problem. But they are not good for the lunar
|
||
orbit which is strongly perturbed by the gravity of the Sun (three-body
|
||
problem). <span class=italic>The lunar orbit is far from being an ellipse!</span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The osculating apogee is 'true' twice a
|
||
month: when it is in exact conjunction with the Moon, the Moon is most distant
|
||
from the Earth; and when it is in exact opposition to the Moon, the Moon is
|
||
closest to the Earth. The motion in between those two points, is an oscillation
|
||
with the period of a month. This oscillation is largely an artifact caused by
|
||
the reduction of the Moon<6F>s orbit to a two-body problem. The amplitude of the
|
||
oscillation of the <span class=italic>osculating</span> apogee around the mean
|
||
apogee is +/- 30 degrees, while the <span class=italic>actual</span> apogee's
|
||
deviation from the mean one never exceeds 5 degrees.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is a small difference between the
|
||
NIE's 'true Lilith' and our osculating apogee, which results from an inaccuracy
|
||
in NIE. The error reaches 20 arc minutes. According to Santoni, the point was
|
||
calculated using 'les 58 premiers termes correctifs au perig<69>e moyen' published
|
||
by Chapront and Chapront-Touz<75>. And he adds: <20>Nous constatons que m<>me en
|
||
utilisant ces 58 termes correctifs, l'erreur peut atteindre 0,5d!<21> (p. 13) We
|
||
avoid this error, computing the orbital elements from the position and the
|
||
speed vectors of the Moon. (By the way, there is also an error of +/- 1 arc minute
|
||
in NIE's true node. The reason is probably the same.)</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Precision</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The osculating apogee can be computed from
|
||
any one of the three ephemerides. If a precision of at least one arc second is
|
||
required, one has to choose either the JPL or the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Maximum differences</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:9.0cm'><span lang=EN-US>JPL-derived apogee
|
||
<96> Swiss-Ephemeris-derived apogee<span style='mso-tab-count:1'><3E><><A0> </span>~ 0.9
|
||
arc second</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:9.0cm'><span lang=EN-US>JPL-derived apogee
|
||
<96> Moshier-derived apogee<span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>~
|
||
360 arc seconds<span style='mso-tab-count:1'><3E> </span>= 6 arc minutes!</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>There have been
|
||
several other attempts to solve the problem of a 'true' apogee. They are not
|
||
included in the SWISSEPH package. All of them work with a correction table.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>They are listed in Santoni's 'Ephemerides
|
||
de la lune noire vraie' mentioned above. With all of them, a value is added to
|
||
the mean apogee depending on the angular distance of the Sun from the mean
|
||
apogee. There is something to this idea. The actual apogees that take place
|
||
once a month differ from the mean apogee by never more than 5 degrees and seem
|
||
to move along a regular curve that is a function of the elongation of the mean
|
||
apogee.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, this curve does not have exactly
|
||
the shape of a sine, as is assumed by all of those correction tables. And most
|
||
of them have an amplitude of more than 10 degrees, which is a lot too high. The
|
||
most realistic solution so far was the one proposed by Henry Gouchon in
|
||
<94>Dictionnaire Astrologique<75>, Paris 1992, which is based on an amplitude of 5
|
||
degrees.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In <20>Meridian<61> 1/95, Dieter Koch has
|
||
published another table that pays regard to the fact that the motion does not
|
||
precisely have the shape of a sine. (Unfortunately, <20>Meridian<61> confused the
|
||
labels of the columns of the apogee and the perigee.)</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Small discontinuities in ephemeris of
|
||
true node and apogee based on compressed file</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>See remarks in Chapter 2.2.2 on The True
|
||
Node.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488762"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.2.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Interpolated or Natural
|
||
Apogee and Perigee (astrological Lilith and Priapus)</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As has been said above, the osculating
|
||
lunar apogee (so-called <20>true Lilith<74>) is a mathematical construct which
|
||
assumes that the motion of the Moon is a two-body problem. This solution is
|
||
obviously too simplistic. Although Kepler ellipses are a good means to describe
|
||
planetary orbits, they fail with the orbit of the Moon, which is strongly
|
||
perturbed by the gravitational pull of the Sun. This solar perturbation results
|
||
in gigantic monthly oscillations in the ephemeris of the osculating apsides
|
||
(the amplitude is 30 degrees). These oscillations have to be considered an <span
|
||
class=italic>artifact</span> of the insufficient model, they do not really show
|
||
a motion of the apsides.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A more sensible solution seems to be an
|
||
interpolation between the real passages of the Moon through its apogees and
|
||
perigees. It turns out that the motions of the lunar perigee and apogee form
|
||
curves of different quality and the two points are usually not in opposition to
|
||
each other. They are more or less opposite points only at times when the Sun is
|
||
in conjunction with one of them or at an angle of 90<39> from them. The amplitude
|
||
of their oscillation about the mean position is 5 degrees for the apogee and 25
|
||
degrees for the perigee.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This solution has been called the "<span
|
||
class=italic>interpolated</span>" or "realistic" apogee and
|
||
perigee by Dieter Koch in his publications. Juan Revilla prefers to call them
|
||
the "<span class=italic>natural</span>" apogee and perigee. Today,
|
||
Dieter Koch would prefer the designation "natural". The designation
|
||
"interpolated" is a bit misleading, because it associates something
|
||
that astrologers used to do every day in old days, when they still used to work
|
||
with printed ephemerides and house tables.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Note on implementation (from Swiss
|
||
Ephemeris Version 1.70 on)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Conventional interpolation algorithms do
|
||
not work well in the case of the lunar apsides. The supporting points are too
|
||
far away from each other in order to provide a good interpolation, the error
|
||
estimation is greater than 1 degree for the perigee. Therefore, Dieter chose a
|
||
different solution. He derived an "interpolation method" from the
|
||
analytical lunar theory which we have in the form of Moshier's lunar ephemeris.
|
||
This "interpolation method" has not only the advantage that it
|
||
probably makes more sense, but also that the curve and its derivation are both
|
||
continuous.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Literature (in German):</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>Dieter Koch, "Was ist Lilith und welche
|
||
Ephemeride ist richtig", Meridian 1/95<o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>Dieter Koch and Bernhard Rindgen, "Lilith und
|
||
Priapus", Frankfurt/Main, 2000.<o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>(http://www.vdhb.de/Lilith_und_Priapus/lilith_und_priapus.html)<o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Juan Revilla, "The
|
||
Astronomical Variants of the Lunar Apogee - Black Moon".</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.expreso.co.cr/centaurs/blackMoon/barycentric.html</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488763"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.2.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Planetary Nodes and Apsides</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Differences between the Swiss Ephemeris and
|
||
other ephemerides of the osculation nodes and apsides are probably due to
|
||
different planetary ephemerides being used for their calculation. Small
|
||
differences in the planetary ephemerides lead to greater differences in nodes
|
||
and apsides.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Definitions of the nodes</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Methods described in small font are not
|
||
supported by the Swiss Ephemeris software.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The lunar nodes are defined by the
|
||
intersection axis of the lunar orbital plane with the plane of the ecliptic. At
|
||
the lunar nodes, the Moon crosses the plane of the ecliptic and its ecliptic
|
||
latitude changes sign. There are similar nodes for the planets, but their
|
||
definition is more complicated. Planetary nodes can be defined in the following
|
||
ways:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>They can be understood as an
|
||
axis defined by the intersection line of two orbital planes. E.g., the nodes of
|
||
Mars are defined by the intersection line of the orbital plane of Mars with the
|
||
plane of the ecliptic (or the orbital plane of the Earth).</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Note</span></b><span lang=EN-US>:
|
||
However, as Michael Erlewine points out in his elaborate web page on this topic<br>
|
||
(http://thenewage.com/resources/articles/interface.html), planetary nodes could
|
||
be defined for any couple of planets. E.g. there is also an intersection line
|
||
for the two orbital planes of Mars and Saturn. Such non-ecliptic nodes have not
|
||
been implemented in the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Because such lines are, in principle,
|
||
infinite, the heliocentric and the geocentric positions of the planetary nodes
|
||
will be the same. There are astrologers that use such heliocentric planetary
|
||
nodes in geocentric charts.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ascending and the descending node will,
|
||
in this case, be in precise opposition.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>There is a second definition
|
||
that leads to different geocentric ephemerides. The planetary nodes can be
|
||
understood, not as an infinite axis, but as the two points at which a planetary
|
||
orbit intersects with the ecliptic plane.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the lunar nodes and heliocentric
|
||
planetary nodes, this definition makes no difference from the definition 1).
|
||
However, it does make a difference for geocentric planetary nodes, where, the
|
||
nodal points on the planets orbit are transformed to the geocenter. The two
|
||
points will not be in opposition anymore, or they will roughly be so with the
|
||
outer planets. The advantage of these nodes is that when a planet is in
|
||
conjunction with its node, then its ecliptic latitude will be zero. This is not
|
||
true when a planet is in geocentric conjunction with its heliocentric node.
|
||
(And neither is it always true for inner the planets, for Mercury and Venus.)</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Note</span></b><span lang=EN-US>: There
|
||
is another possibility, not implemented in the Swiss ephemeris: E.g., instead
|
||
of considering the points of the Mars orbit that are located in the ecliptic
|
||
plane, one might consider the points of the Earth<74>s orbit that are located in
|
||
the orbital plane of Mars. If one takes these points geocentrically, the ascending
|
||
and the descending node will always form an approximate square. This
|
||
possibility has not been implemented in the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Third, the planetary nodes
|
||
could be defined as the intersection points of the plane defined by their
|
||
momentary geocentric position and motion with the plane of the ecliptic. Here
|
||
again, the ecliptic latitude would change sign at the moment when the planet
|
||
were in conjunction with one of its nodes. This possibility has not been
|
||
implemented in the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Possible definitions for apsides and
|
||
focal points</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The lunar apsides - the lunar apogee and
|
||
lunar perigee - have already been discussed further above. Similar points exist
|
||
for the planets, as well, and they have been considered by astrologers. Also,
|
||
as with the lunar apsides, there is a similar disagreement:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One may consider either the planetary <span
|
||
class=italic>apsides</span>, i.e. the two points on a planetary orbit that are
|
||
closest to the Sun and most distant from the Sun, resp. The former point is
|
||
called the <20><span class=italic>perihelion</span><3E> and the latter one the <20><span
|
||
class=italic>aphelion</span><3E>. For a geocentric chart, these points could be
|
||
transformed from the heliocenter to the geocenter.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, Bernard Fitzwalter and Raymond
|
||
Henry prefer to use the second focal points of the planetary orbits. And they
|
||
call them the <20>black stars<72> or the <20>black Suns of the planets<74>. The
|
||
heliocentric positions of these points are identical to the heliocentric
|
||
positions of the aphelia, but geocentric positions are not identical, because
|
||
the focal points are much closer to the Sun than the aphelia. Most of them are
|
||
even inside the Earth orbit.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris supports both points of
|
||
view.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Special case: the Earth</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Earth is a special case. Instead of the
|
||
motion of the Earth herself, the heliocentric motion of the Earth-Moon-Barycenter
|
||
(EMB) is used to determine the osculating perihelion.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is no node of the Earth orbit itself.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is an axis around which the Earth's
|
||
orbital plane slowly rotates due to planetary precession. The position points
|
||
of this axis are not calculated by the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Special case: the Sun</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In addition to the Earth (EMB) apsides, our
|
||
software computes so-to-say "apsides" of the solar orbit around the Earth,
|
||
i.e. points on the orbit of the Sun where it is closest to and where it is farthest
|
||
from the Earth. These points form an opposition and are used by some
|
||
astrologers, e.g. by the Dutch astrologer George Bode or the Swiss astrologer
|
||
Liduina Schmed. The <20>perigee<65>, located at about 13 Capricorn, is called the
|
||
"Black Sun", the other one, in Cancer, is called the <20>Diamond<6E>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>So, for a complete set of apsides, one
|
||
might want to calculate them for the Sun and the Earth and all other planets.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Mean and osculating positions</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are serious problems about the
|
||
ephemerides of planetary nodes and apsides. There are mean ones and osculating
|
||
ones. Both are well-defined points in astronomy, but this does not necessarily
|
||
mean that these definitions make sense for astrology. Mean points, on the one
|
||
hand, are not true, i.e. if a planet is in precise conjunction with its mean
|
||
node, this does not mean it be crossing the ecliptic plane exactly that moment.
|
||
Osculating points, on the other hand, are based on the idealization of the
|
||
planetary motions as two-body problems, where the gravity of the Sun and a single
|
||
planet is considered and all other influences neglected. There are no planetary
|
||
nodes or apsides, at least today, that really deserve the label <20>true<75>.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Mean positions</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mean nodes and apsides can be computed for
|
||
the Moon, the Earth and the planets Mercury <20> Neptune. They are taken from the
|
||
planetary theory VSOP87. Mean points <b>cannot</b> be calculated for Pluto and
|
||
the asteroids, because there is no planetary theory for them.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Although the Nasa has published mean
|
||
elements for the planets Mercury <20> Pluto based on the JPL ephemeris DE200, we
|
||
do not use them (so far), because their validity is limited to a 250 year
|
||
period, because only linear rates are given, and because they are not based on
|
||
a planetary theory.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(http://ssd.jpl.nasa.gov/elem_planets.html,
|
||
<94>mean orbit solutions from a 250 yr. least squares fit of the DE 200 planetary
|
||
ephemeris to a Keplerian orbit where each element is allowed to vary linearly
|
||
with time<6D>)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The differences between the DE200 and the
|
||
VSOP87 mean elements are considerable, though:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><o:p> </o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Node<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Perihelion<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><o:p> </o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Mercury</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3<></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4<></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Venus</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3<></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>107<30></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Earth</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>35<33></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Mars</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>74<37></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4<></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Jupiter</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>330<33></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1850<35></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Saturn</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>178<37></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1530<33></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Uranus</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>806<30></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6540<34></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Neptune</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>225<32></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11600<30></span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>(>3
|
||
deg!)</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Osculating nodes and apsides</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Nodes and apsides can also be derived from
|
||
the osculating orbital elements of a body, the parameters that define an ideal
|
||
unperturbed elliptic (two-body) orbit for a given time. Celestial bodies would
|
||
follow such orbits <span class=italic>if perturbations were to cease suddenly
|
||
or if there were only two bodies (the Sun and the planet) involved in the
|
||
motion and the motion were an ideal ellipse</span>. This ideal assumption makes
|
||
it obvious that it would be misleading to call such nodes or apsides
|
||
"true". It is more appropriate to call them "osculating".
|
||
Osculating nodes and apsides are "true" only at the precise moments,
|
||
when the body passes through them, but for the times in between, they are a
|
||
mere mathematical construct, nothing to do with the nature of an orbit.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We tried to solve the problem by <span
|
||
class=italic>interpolating</span> between actual passages of the planets
|
||
through their nodes and apsides. However, this method works only well with
|
||
Mercury. With all other planets, the supporting points are too far apart as to
|
||
allow a sensible interpolation.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is another problem about heliocentric
|
||
ellipses. E.g. Neptune's orbit has often two perihelia and two aphelia (i. e.
|
||
minima and maxima in heliocentric distance) within one revolution. As a result,
|
||
there is a wild oscillation of the osculating or "true" perihelion
|
||
(and aphelion), which is not due to a transformation of the orbital ellipse but
|
||
rather due to the deviation of the heliocentric orbit from an elliptic shape.
|
||
Neptune<92>s orbit cannot be adequately represented by a heliocentric ellipse.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In actuality, Neptune<6E>s orbit is not
|
||
heliocentric at all. The double perihelia and aphelia are an effect of the
|
||
motion of the Sun about the solar system barycenter. This motion is a lot
|
||
faster than the motion of Neptune, and Neptune cannot react to such fast
|
||
displacements of the Sun. As a result, Neptune seems to move around the
|
||
barycenter (or a mean Sun) rather than around the real Sun. In fact, Neptune's
|
||
orbit around the barycenter is therefore closer to an ellipse than his orbit
|
||
around the Sun. The same is also true, though less obvious, for Saturn, Uranus
|
||
and Pluto, but not for Jupiter and the inner planets.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This fundamental problem about osculating
|
||
ellipses of planetary orbits does of course not only affect the apsides but
|
||
also the nodes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As a solution, it seems reasonable to
|
||
compute the osculating elements of slow planets from their barycentric motions
|
||
rather than from their heliocentric motions. This procedure makes sense
|
||
especially for Neptune, but also for all planets beyond Jupiter. It comes
|
||
closer to the mean apsides and nodes for planets that have such points defined.
|
||
For Pluto and all trans-Saturnian asteroids, this solution may be used as a
|
||
substitute for "mean" nodes and apsides. Note, however, that there
|
||
are considerable differences between barycentric osculating and mean nodes and
|
||
apsides for Saturn, Uranus, and Neptune. (A few degrees! But heliocentric ones
|
||
are worse.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Anyway, neither the heliocentric nor the
|
||
barycentric ellipse is a perfect representation of the nature of a planetary
|
||
orbit. So, astrologers should not expect anything very reliable here either!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The best choice of method will probably be:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>For Mercury <20> Neptune: mean
|
||
nodes and apsides.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>For asteroids that belong to
|
||
the inner asteroid belt: osculating nodes/apsides from a heliocentric ellipse.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>For Pluto and transjovian
|
||
asteroids: osculating nodes/apsides from a barycentric ellipse.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>The modes of the Swiss Ephemeris function
|
||
swe_nod_aps()</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The function </span><span class=functions><span
|
||
lang=EN-US>swe_nod_aps()</span></span><span lang=EN-US> can be run in the
|
||
following modes:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Mean positions are given for
|
||
nodes and apsides of Sun, Moon, Earth, and the planets up to Neptune.
|
||
Osculating positions are given with Pluto and all asteroids. This is the
|
||
default mode.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Osculating positions are
|
||
returned for nodes and apsides of all planets.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Same as 2), but for planets and
|
||
asteroids beyond Jupiter, a barycentric ellipse is used.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Same as 1), but for Pluto and
|
||
asteroids beyond Jupiter, a barycentric ellipse is used.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the reasons given above, method 4)
|
||
seems to make best sense.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In all of these modes, the second focal
|
||
point of the ellipse can be computed instead of the aphelion.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488764"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.3.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Asteroids</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488765"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Asteroid ephemeris files</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The standard distribution of SWISSEPH
|
||
includes the main asteroids Ceres, Pallas, Juno, Vesta, as well as 2060 Chiron,
|
||
and 5145 Pholus. To compute them, one must have the main-asteroid ephemeris
|
||
files in the ephemeris directory.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The names of these files are of the
|
||
following form:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt'><span class=sourcecode><span
|
||
lang=EN-US>seas_18.se1<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span></span></span><span
|
||
lang=EN-US>main asteroids for 600 years from 1800 - 2400</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The size of such a file is about 200 kb.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>All other asteroids are available in
|
||
separate files. The names of additional asteroid files look like:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:92.15pt'><span class=sourcecode><span
|
||
lang=EN-US>se00433.se1</span></span><span lang=EN-US><span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>the file of asteroid no. 433 (= Eros)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>These files cover the period 3000 BCE -
|
||
3000 CE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A short version for the years 1500 <20> 2100 CE
|
||
has the file name with an 's' imbedded, se00433s.se1.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The numerical integration of the all
|
||
numbered asteroids is an ongoing effort. In December 1998, 8000 asteroids were
|
||
numbered, and their orbits computed by the developers of Swiss Ephemeris. In
|
||
January 2001, the list of numbered asteroids reached 20957, in January 2014
|
||
more than 380.000, and it is still growing very fast.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Any asteroid can be called either with the
|
||
JPL, the Swiss, or the Moshier ephemeris flag, and the results will be slightly
|
||
different. The reason is that the solar position (which is needed for
|
||
geocentric positions) will be taken from the ephemeris that has been specified.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Availability of asteroid files</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>all short files (over 200000)
|
||
are available for free download at our ftp server ftp.astro.ch/pub/swisseph.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The purpose of providing this large number
|
||
of files for download is that the user can pick those few asteroids he/she is
|
||
interested in.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>for all named asteroids also a
|
||
long (6000 years) file is available in the download area.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488766"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>How the asteroids were computed</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To generate our asteroid ephemerides, we
|
||
have modified the numerical integrator of Steve Moshier, which was capable to
|
||
rebuild the DE200 JPL ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Orbital elements, with a few exceptions,
|
||
were taken from the asteroid database computed by E. Bowell, Lowell
|
||
Observatory, Flagstaff, Arizona (astorb.dat). After the introduction of the JPL
|
||
database mpcorb.dat, we still keep working with the Lowell data because Lowell
|
||
elements are given with one more digit, which can be relevant for long-term
|
||
integrations.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For a few close-Sun-approaching asteroids
|
||
like 1566 Icarus, we use the elements of JPL<50>s DASTCOM database. Here, the
|
||
Bowell elements are not good for long term integration because they do not
|
||
account for relativity.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Our asteroid ephemerides take into account
|
||
the gravitational perturbations of all planets, including the major asteroids
|
||
Ceres, Pallas, and Vesta and also the Moon.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The mutual perturbations of Ceres, Pallas,
|
||
and Vesta were included by iterative integration. The first run was done
|
||
without mutual perturbations, the second one with the perturbing forces from
|
||
the positions computed in the first run.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The precision of our integrator is very
|
||
high. A test integration of the orbit of Mars with start date 2000 has shown a
|
||
difference of only 0.0007 arc second from DE200 for the year 1600. We also
|
||
compared our asteroid ephemerides with data from JPL<50>s on-line ephemeris system
|
||
<93>Horizons<94> which provides asteroid positions from 1600 on. Taking into account
|
||
that Horizons does not consider the mutual perturbations of the major asteroids
|
||
Ceres, Pallas and Vesta, the difference is never greater than a few 0.1 arcsec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(However, the Swisseph asteroid ephemerides
|
||
do consider those perturbations, which makes a difference of 10 arcsec for
|
||
Ceres and 80 arcsec for Pallas. This means that our asteroid ephemerides are
|
||
even better than the ones that JPL offers on the web.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The accuracy limits are therefore not set
|
||
by the algorithms of our program but by the inherent uncertainties in the orbital
|
||
elements of the asteroids from which our integrator has to start.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources of errors are:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Only some of the minor planets
|
||
are known to better than an arc second for recent decades. (See also information
|
||
below on Ceres, Chiron, and Pholus.)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Bowells elements do not
|
||
consider relativistic effects, which leads to significant errors with long-term
|
||
integrations of a few close-Sun-approaching orbits (except 1566, 2212, 3200,
|
||
5786, and 16960, for which we use JPL elements that do take into account
|
||
relativity).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The orbits of some asteroids are extremely
|
||
sensitive to perturbations by major planets. E.g. 1862 Apollo becomes chaotic
|
||
before the year 1870 CE when he passes Venus within a distance which is only
|
||
one and a half the distance from the Moon to the Earth. In this moment, the
|
||
small uncertainty of the initial elements provided by the Bowell database
|
||
grows, so to speak, <20>into infinity<74>, so that it is impossible to determine the
|
||
precise orbit prior to that date. Our integrator is able to detect such
|
||
happenings and end the ephemeris generation to prevent our users working with
|
||
meaningless data.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488767"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Ceres, Pallas, Juno, Vesta</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The orbital elements of the four main
|
||
asteroids Ceres, Pallas, Juno, and Vesta are known very precisely, because
|
||
these planets have been discovered almost 200 years ago and observed very often
|
||
since. On the other hand, their orbits are not as well-determined as the ones
|
||
of the main planets. We estimate that the precision of the main asteroid
|
||
ephemerides is better than 1 arc second for the whole 20th century. The
|
||
deviations from the Astronomical Almanac positions can reach 0.5<94> (AA 1985 <20>
|
||
1997). But the tables in AA are based on older computations, whereas we used
|
||
recent orbital elements. (s. AA 1997, page L14)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>MPC elements have a precision of five digits
|
||
with mean anomaly, perihelion, node, and inclination and seven digits with
|
||
eccentricity and semi-axis. For the four main asteroids, this implies an
|
||
uncertainty of a few arc seconds in 1600 CE and a few arc minutes in 3000 BCE.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488768"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Chiron</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Positions of Chiron can be well computed
|
||
for the time between 700 CE and 4650 CE. As a result of close encounters with
|
||
Saturn in Sept. 720 CE and in 4606 CE we cannot trace its orbit beyond this
|
||
time range. Small uncertainties in today's orbital elements have chaotic
|
||
effects before the year 700.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Do not rely on earlier Chiron ephemerides
|
||
supplying a Chiron for Cesar's, Jesus', or Buddha's birth chart. They are
|
||
meaningless.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488769"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Pholus</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Pholus is a minor planet with orbital
|
||
characteristics that are similar to Chiron's. It was discovered in 1992.
|
||
Pholus' orbital elements are not yet as well-established as Chiron's. Our
|
||
ephemeris is reliable from 1500 CE through now. Outside the 20th century it
|
||
will probably have to be corrected by several arc minutes during the coming
|
||
years.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488770"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Asteroid 99942 Apophis</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>99942 Apophis is a near-Earth asteroid
|
||
which sometime in the future impact Earth. The ephemeris of this object is
|
||
particularly uncertain after 13 April 2029 when it will have a very close
|
||
encounter with the earth. Our ephemeris was created from data from JPL
|
||
Horizons.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Horizons<6E>s ephemeris of Apophis after 2029
|
||
varies considerable depending on the start date and step width one uses in the
|
||
Horizons web interface. (If you don<6F>t believe it, please try it out!) However,
|
||
as pointed out by Jon Giorgini in a Mail to Dieter Koch of 1 April 2020, this
|
||
variation is smaller than the uncertainty of the orbit.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We will have to update our ephemeris of
|
||
Apophis after his close encounter with Earth in April 2029 in order to make it
|
||
accurate at least until the year 2036. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488771"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.3.7.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Ceres - an application program
|
||
for asteroid astrology</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Dieter Koch has written the application
|
||
program <strong><span style='font-family:"Segoe UI",sans-serif'>Ceres</span></strong>
|
||
which allows to compute all kinds of lists for asteroid astrology. E.g. you can
|
||
generate a list of all your natal asteroids ordered by position in the zodiac.
|
||
But the program does much more:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>natal positions,
|
||
synastries/transits, composite charts, progressions, primary directions etc.;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>geocentric, heliocentric,
|
||
topocentric, house horoscopes;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>lists sorted by position in
|
||
zodiac, by asteroid name, by declination etc.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The program is found in the Swiss Ephermeris
|
||
download area in the folder <20>programs<6D>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488772"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.4.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Planetary Centers of Body (COB) and Planetary Moons</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Although nobody ever finds it worth
|
||
mentioning and hardly anybody is aware of it, all hitherto ephemerides and
|
||
astrology softwares provide only the <b>barycenter</b> of the Jupiter system,
|
||
i.e. the center of mass of Jupiter together with all his moons, not the center
|
||
of Jupiter<65>s body or the real planet. And the same holds for all the other
|
||
planets that have moons, except the earth. We call the center of the real planets
|
||
the <b style='mso-bidi-font-weight:normal'>centers of body (COB)</b><span
|
||
style='mso-bidi-font-weight:bold'>. <o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-bidi-font-weight:bold'>The
|
||
difference between the barycenters and the COBs are small. The maximum
|
||
geocentric angular distances are</span><span lang=EN-US> as follows:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Mars
|
||
<span style='mso-tab-count:1'><3E> </span>(0.2 m, irrelevant to us)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Jupiter <span
|
||
style='mso-tab-count:1'><3E> </span>0.075<span style='mso-spacerun:yes'><3E>
|
||
</span>arcsec <span style='mso-tab-count:1'> </span>(jd 2468233.5)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Saturn <span
|
||
style='mso-tab-count:2'><3E><> </span>0.053<span style='mso-spacerun:yes'><3E>
|
||
</span>arcsec <span style='mso-tab-count:1'> </span>(jd 2463601.5)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Uranus <span
|
||
style='mso-tab-count:2'><3E><><A0> </span>0.0032 arcsec <span style='mso-tab-count:
|
||
1'> </span>(jd 2446650.5)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Neptune <span style='mso-tab-count:
|
||
2'><3E><><A0><A0> </span>0.0036 arcsec <span style='mso-tab-count:1'> </span>(jd
|
||
2449131.5)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'>Pluto
|
||
<span style='mso-tab-count:1'><3E> </span>0.088<span style='mso-spacerun:yes'><3E>
|
||
</span>arcsec <span style='mso-tab-count:1'> </span>(jd 2437372.5)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>(from one-day-step
|
||
calculations over 150 years)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris versions 2.10 and higher
|
||
can provide positions of the <b style='mso-bidi-font-weight:normal'>centers of
|
||
body of the planets</b> as well as some <b style='mso-bidi-font-weight:normal'>planetary
|
||
moons</b>, thanks to a joint effort by Walter Pullen and Dieter Koch. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ephemerides were downloaded from JPL
|
||
Horizons and then compressed using the Astrodienst software <i
|
||
style='mso-bidi-font-style:normal'>chopt</i>, the same software that is also
|
||
used to generate asteroid ephemeris files.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Currently, not all planetary moons are
|
||
available to Swiss Ephemeris users.</span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US>Software developers who want to
|
||
implement COB have to know that the performance of this calculation is not as
|
||
good as with the barycenters. Moreover, the time range is currently limited to
|
||
the years 1900 to 2047.<o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488773"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.5.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Comets and Interstellar Objects</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris provides ephemerides of
|
||
a few selected comets under the following pseudo-MPC numbers:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999032s.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0> </span>999032
|
||
Churyumov-Ger<span style='mso-spacerun:yes'><3E><><A0><A0> </span>= Comet
|
||
67P/Churyumov-Gerasimenko <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999043s.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0> </span>999043
|
||
Neowise<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>= Comet C/2020 F3
|
||
(NEOWISE) <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999044.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0><A0> </span>999044
|
||
Halley<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>= Comet 1P/Halley<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999046.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0><A0> </span>999046
|
||
Hale-Bopp<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span>= Comet Hale-Bopp
|
||
(C/1995 O1)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999047.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0><A0> </span>999047
|
||
West<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>= Comet West (C/1975
|
||
V1-A)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
|
||
layout-grid-mode:both;text-autospace:ideograph-numeric ideograph-other'><span
|
||
class=sourcecode><span lang=EN-US style='mso-fareast-language:ZH-CN'>s999045.se1</span></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:"Courier New";
|
||
mso-fareast-language:ZH-CN'><span style='mso-tab-count:1'><3E><><A0><A0> </span>999045
|
||
Oumuamua<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>= 1I/'Oumuamua (A/2017
|
||
U1)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ephemerides of these objects were
|
||
downloaded from JPL Horizons and compressed in the format of Swiss Ephemeris
|
||
data files.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488774"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.6.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Fixed stars and Galactic Center</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A database of fixed stars is included with
|
||
Swiss Ephemeris. It contains about 800 stars, which can be computed with the </span><span
|
||
class=functions><span lang=EN-US>swe_fixstar()</span></span><span lang=EN-US>
|
||
function. The precision is about 0.001<94>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This database was originally based on the
|
||
star catalogue of Steve Moshier. It was improved in 1999 by Valentin Abramov,
|
||
Tartu, Estonia. He reordered the stars by constellation, added some stars, many
|
||
names and alternative spellings of names.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In Feb. 2006 (Version 1.70) the fixed stars
|
||
file was updated with data from the SIMBAD database.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(http://simbad.u-strasbg.fr/Simbad)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In Jan. 2011 (Version 1.77) a new fixed
|
||
stars file </span><span class=FileName><span lang=DA>sefstars.txt </span></span><span
|
||
lang=EN-US>was created from the SIMBAD database with a data format that is
|
||
compatible with the SIMBAD database. The file continues to be updated every few
|
||
years.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488775"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.7.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Hypothetical bodies</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We include some astrological factors in the
|
||
ephemeris which have no astronomical basis <20> they have never been observed
|
||
physically. As the purpose of the Swiss Ephemeris is astrology, we decided to
|
||
drop our scientific view in this area and to be of service to those astrologers
|
||
who use these <20>hypothetical<61> planets and factors. Of course neither of our
|
||
scientific sources, JPL or Steve Moshier, have anything to do with this part of
|
||
the Swiss Ephemeris.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488776"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Uranian planets (Hamburg planets:
|
||
Cupido, Hades, Zeus, Kronos, Apollon, Admetos, Vulkanus, Poseidon)</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There have been discussions whether these
|
||
factors are to be called 'planets' or 'Transneptunian points'. However, their
|
||
inventors, the German astrologers Witte and Sieggr<67>n, considered them to be
|
||
planets. And moreover they behave like planets in as far as they circle around
|
||
the Sun and obey its gravity.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On the other hand, if one looks at their
|
||
orbital elements, it is obvious that these orbits are highly unrealistic. Some
|
||
of them are perfect circles <20> something that does not exist in physical
|
||
reality. The inclination of the orbits is zero, which is very improbable as
|
||
well. The revised elements published by James Neely in Matrix Journal VII
|
||
(1980) show small eccentricities for the four Witte planets, but they are still
|
||
smaller than the eccentricity of Venus which has an almost circular orbit. This
|
||
is again very improbable.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are even more problems. An ephemeris
|
||
computed with such elements describes an unperturbed motion, i.e. it takes into
|
||
account only the Sun's gravity, not the gravitational influences of the other
|
||
planets. This may result in an error of a degree within the 20th century, and
|
||
greater errors for earlier centuries.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Also, note that none of the real
|
||
transneptunian objects that have been discovered since 1992 can be identified
|
||
with any of the Uranian planets.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>SWISSEPH uses James Neely's revised orbital
|
||
elements, because they agree better with the original position tables of Witte
|
||
and Sieggr<67>n.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The hypothetical planets can again be
|
||
called with any of the three ephemeris flags. The solar position needed for
|
||
geocentric positions will then be taken from the ephemeris specified.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488777"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Transpluto (Isis)</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This hypothetical planet was postulated
|
||
1946 by the French astronomer M.E. Sevin because of otherwise unexplainable
|
||
gravitational perturbations in the orbits of Uranus and Neptune.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, this theory has been superseded by
|
||
other attempts during the following decades, which proceeded from better
|
||
observational data. They resulted in bodies and orbits completely different
|
||
from what astrologers know as 'Isis-Transpluto'. More recent studies have shown
|
||
that the perturbation residuals in the orbits of Uranus and Neptune are too
|
||
small to allow postulation of a new planet. They can, to a great extent, be
|
||
explained by observational errors or by systematic errors in sky maps.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In telescope observations, no hint could be
|
||
discovered that this planet actually existed. Rumors that claim the opposite
|
||
are wrong. Moreover, all of the transneptunian bodies that have been discovered
|
||
since 1992 are very different from Isis-Transpluto.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Even if Sevin's computation were correct,
|
||
it could only provide a rough position. To rely on arc minutes would be
|
||
illusory. Neptune was more than a degree away from its theoretical position
|
||
predicted by Leverrier and Adams.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, Transpluto's position is computed
|
||
from a simple Kepler ellipse, disregarding the perturbations by other planets'
|
||
gravities. Moreover, Sevin gives no orbital inclination.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Though Sevin gives no inclination for his
|
||
Transpluto, you will realize that there is a small ecliptic latitude in
|
||
positions computed by SWISSEPH. This mainly results from the fact that its
|
||
orbital elements are referred to epoch 5.10.1772 whereas the ecliptic changes
|
||
position with time.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The elements used by SWISSEPH are taken
|
||
from <20>Die Sterne<6E> 3/1952, p. 70. The article does not say which equinox they
|
||
are referred to. Therefore, we fitted it to the Astron ephemeris which
|
||
apparently uses the equinox of 1945 (which, however, is rather unusual!).</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488778"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Harrington</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is another attempt to predict Planet
|
||
X's orbit and position from perturbations in the orbits of Uranus and Neptune.
|
||
It was published in The Astronomical Journal 96(4), October 1988, p. 1476ff.
|
||
Its precision is meant to be of the order of +/- 30 degrees. According to
|
||
Harrington there is also the possibility that it is actually located in the
|
||
opposite constellation, i.e. Taurus instead of Scorpio. The planet has a mean
|
||
solar distance of about 100 AU and a period of about 1000 years.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488779"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Nibiru</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A highly speculative planet derived from
|
||
the theory of Zecharia Sitchin, who is an expert in ancient Mesopotamian
|
||
history and a <20>paleoastronomer<65>. The elements have been supplied by Christian
|
||
Woeltge, Hannover. This planet is interesting because of its bizarre orbit. It
|
||
moves in clockwise direction and has a period of 3600 years. Its orbit is
|
||
extremely eccentric. It has its perihelion within the asteroid belt, whereas
|
||
its aphelion lies at about 12 times the mean distance of Pluto. In spite of its
|
||
retrograde motion, it seems to move counterclockwise in recent centuries. The
|
||
reason is that it is so slow that it does not even compensate the precession of
|
||
the equinoxes.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488780"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Vulcan</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is a <20>hypothetical<61> planet inside the
|
||
orbit of Mercury (not identical to the <20>Uranian<61> planet Vulkanus). Orbital
|
||
elements according to L.H. Weston. Note that the speed of this <20>planet<65> does
|
||
not agree with the Kepler laws. It is too fast by 10 degrees per year.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488781"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Selena/White Moon</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is a <20>hypothetical<61> second Moon of the
|
||
Earth (or a third one, after the <20>Black Moon<6F>) of obscure provenance. Many
|
||
Russian astrologers use it. Its distance from the Earth is more than 20 times the
|
||
distance of the Moon and it moves about the Earth in 7 years. Its orbit is a
|
||
perfect, unperturbed circle. Of course, the physical existence of such a body
|
||
is not possible. The gravities of Sun, Earth, and Moon would strongly influence
|
||
its orbit.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488782"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.7.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Dr. Waldemath<74>s Black Moon</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is another hypothetical second Moon of
|
||
the Earth, postulated by a Dr. Waldemath in the Monthly Wheather Review 1/1898.
|
||
Its distance from the Earth is 2.67 times the distance of the Moon, its daily
|
||
motion about 3 degrees. The orbital elements have been derived from Waldemath<74>s
|
||
original data. There are significant differences from elements used in earlier
|
||
versions of Solar Fire, due to different interpretations of the values given by
|
||
Waldemath. After a discussion between Graham Dawson and Dieter Koch it has been
|
||
agreed that the new solution is more likely to be correct. The new ephemeris
|
||
does not agree with Delphine Jay<61>s ephemeris either, which is obviously
|
||
inconsistent with Waldemath<74>s data.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This body has never been confirmed. With its
|
||
700-km diameter and an apparent diameter of 2.5 arc min, this should have been
|
||
possible very soon after Waldemath<74>s publication.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488783"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.7.8.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Planets X of Leverrier,
|
||
Adams, Lowell and Pickering</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>These are the hypothetical planets that
|
||
have led to the discovery of Neptune and Pluto or at least have been brought
|
||
into connection with them. Their enormous deviations from true Neptune and
|
||
Pluto may be interesting for astrologers who work with hypothetical bodies.
|
||
E.g. Leverrier and Adams are good only around the 1840ies, the discovery epoch
|
||
of Neptune. To check this, call the program </span><span class=FileName><span
|
||
lang=DA>swetest</span></span><span lang=EN-US> as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>$ swetest -p8 -dU
|
||
-b1.1.1770 -n8 -s7305 -hel -fPTLBR -head<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(i.e.: compute planet 8 (Neptune) - planet
|
||
'U' (Leverrier), from 1.1.1770, 8 times, in 7305-day-steps, heliocentrically.
|
||
You can do this from the Internet web page <a
|
||
href="https://www.astro.com/swisseph/swetest.htm"><span style='font-size:11.0pt'>swetest.htm</span></a>.
|
||
The output will be:)</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'><span lang=EN-US
|
||
style='font-size:10.0pt;mso-bidi-font-size:11.0pt;font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
|
||
AR-SA;mso-bidi-language:AR-SA'><br clear=all style='mso-special-character:
|
||
line-break;page-break-before:always'>
|
||
</span>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><o:p> </o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><o:p> </o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>difference
|
||
in<br>
|
||
longitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>difference
|
||
in<br>
|
||
latitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>difference
|
||
in<br>
|
||
solar distance<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>01.01.1770</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-18<31>0'52.3811</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0<>55'0.0332</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-6.610753489</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>01.01.1790</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-8<>42'9.1113</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1<>42'55.7192</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4.257690148</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>02.01.1810</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3<>49'45.2014</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1<>35'12.0858</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2.488363869</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>02.01.1830</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1<>38'2.8076</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0<>35'57.0580</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2.112570665</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>02.01.1850</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1<>44'23.0943</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0<>43'38.5357</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3.340858070</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>02.01.1870</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>9<>17'34.4981</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1<>39'24.1004</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5.513270186</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>02.01.1890</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21<32>20'56.6250</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1<>38'43.1479</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-7.720578177</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>Nep-Lev</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>03.01.1910</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>36<33>27'56.1314</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0<>41'59.4866</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-9.265417529</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US style='color:
|
||
white;mso-color-alt:windowtext'>One can see that the error is </span><span
|
||
lang=EN-US>in the range of 2 degrees between 1830 and 1850 and grows very fast
|
||
beyond that period.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488784"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>2.8.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Sidereal Ephemerides for Astrology</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488785"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The problem of defining the
|
||
zodiac</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p style='margin-top:0cm;margin-right:0cm;margin-bottom:3.0pt;margin-left:0cm'><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:"Segoe UI",sans-serif;
|
||
mso-ansi-language:EN-US'>Western astrology mostly uses the </span><em><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:major-fareast;
|
||
mso-ansi-language:EN-US'>tropical</span></em><span lang=EN-US style='font-size:
|
||
10.0pt;font-family:"Segoe UI",sans-serif;mso-ansi-language:EN-US'> zodiac, in
|
||
which 0<> Aries is fixed at the vernal point. The vernal point is the point
|
||
where the Sun is located at the spring equinox. By contrast, </span><em><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:major-fareast;
|
||
mso-ansi-language:EN-US'>sidereal</span></em><span lang=EN-US style='font-size:
|
||
10.0pt;font-family:"Segoe UI",sans-serif;mso-ansi-language:EN-US'> astrology
|
||
uses a <i style='mso-bidi-font-style:normal'>sidereal</i> zodiac whose initial
|
||
point is defined relative to the fixed stars. Sidereal astrology has a western
|
||
as well as an eastern tradition.<o:p></o:p></span></p>
|
||
|
||
<p style='margin-top:0cm;margin-right:0cm;margin-bottom:3.0pt;margin-left:0cm'><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:"Segoe UI",sans-serif;
|
||
mso-ansi-language:EN-US'>Since the vernal point makes a slow motion relative to
|
||
the fixed stars, the so-called precession of the equinox (1<> in 71.6 years),
|
||
the tropical and the sidereal zodiacs slowly drift apart. About 1500 - 2000
|
||
years ago, both zodiacs almost perfectly agreed with each other. However, in
|
||
our time, the difference between them amounts to more than 20<32> and continues
|
||
increasing. <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>While the definition of the tropical zodiac
|
||
is very obvious and never questioned by astrologers, sidereal astrologers
|
||
unfortunately disagree about where exactly in the sky the initial point of the
|
||
sidereal zodiac should be located. There are numerous divergent ideas about it
|
||
and, consequently, a considerable number of different ayanamshas. New
|
||
ayanamshas are invented almost every year. Beginners in sidereal astrology are
|
||
confronted with the difficult problem of deciding which ayanamsha to use,
|
||
unless they choose to follow the recommendation of their teacher. Hindu
|
||
astrologers and their western disciples mostly use the so-called Lahiri ayanamsha,
|
||
whereas the western sidereal tradition mostly uses the Fagan/Bradley Ayanamsha.
|
||
</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Nowadays, sidereal ephemerides are derived
|
||
from tropical ephemerides by subtracting a certain difference value from the
|
||
tropical positions of the planets. This difference value is called </span><em><span
|
||
lang=EN-US style='font-family:"Segoe UI",sans-serif;mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>ayanamsha</span></em><span
|
||
lang=EN-US>. The Sanskrit term </span><em><span lang=EN-US style='font-family:
|
||
"Segoe UI",sans-serif;mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:
|
||
major-fareast'>ayanāṃśaḥ</span></em><span lang=EN-US> is
|
||
composed of the words </span><em><span lang=EN-US style='font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:major-fareast'>ayanam</span></em><span
|
||
lang=EN-US>, "course (of the Sun), half-year" and </span><em><span
|
||
lang=EN-US style='font-family:"Segoe UI",sans-serif;mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>aṃśaḥ</span></em><span
|
||
lang=EN-US>, "part", thus literally means "part of the
|
||
course". It refers to the distance of a solstice from the initial point of
|
||
the cardinal zodiac sign that is associated with it. This distance equals the
|
||
distance of the vernal point from the sidereal Aries point. (The correct
|
||
pronunciation of </span><em><span lang=EN-US style='font-family:"Segoe UI",sans-serif;
|
||
mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:major-fareast'>ayanāṃśaḥ</span></em><span
|
||
lang=EN-US> is with <20>sh<73>, although many write and pronounce it with an <20>s<93>.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Thus, sidereal planetary positions are
|
||
usually computed from tropical positions using the equation:</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:
|
||
major-fareast'>sidereal_position = tropical_position <20> ayanamsha(t)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>where </span><span class=italic><span
|
||
lang=EN-US style='mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:
|
||
major-fareast'>ayanamsha</span></span><span lang=EN-US> is the difference
|
||
between the two zodiacs at a given epoch. </span><span lang=EN-US
|
||
style='mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:major-fareast'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The value of the ayanamsha of date is
|
||
usually computed from the ayanamsha value at a particular start date and the
|
||
speed of the vernal point, the so-called </span><span class=italic><span
|
||
lang=EN-US style='mso-fareast-font-family:"DengXian Light";mso-fareast-theme-font:
|
||
major-fareast'>precession rate,</span></span><span lang=EN-US> in ecliptic
|
||
longitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The zero point of the sidereal zodiac is
|
||
therefore traditionally defined by the equation:</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt'><span class=sourcecode><span
|
||
lang=EN-US>sidereal_0_Aries = tropical_0_Aries + ayanamsha(t).<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As has been stated, the number of existing
|
||
ayanamshas is considerable.<span style='mso-spacerun:yes'><3E> </span>The Swiss
|
||
Ephemeris offers more than forty of them. At first glance, they all look
|
||
arbitrary in their definitions, and there is no striking evidence <20> from a mere
|
||
astronomical point of view <20> for anyone of them. However, a historical study
|
||
shows at least that many of them are related to each other and the basic
|
||
approaches are not so many.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488786"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Babylonian tradition and
|
||
the Fagan/Bradley ayanamsha</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There have been several attempts to
|
||
calculate the zero point of the Babylonian ecliptic from cuneiform lunar and
|
||
planetary tablets. Positions were given relative to some siderealy fixed
|
||
reference point. The main problem in fixing the zero point is the inaccuracy of
|
||
ancient observations. Around 1900 F.X. Kugler found that the Babylonian star
|
||
positions fell into three groups:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>Kugler ayanamshas:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm 5.0cm 212.65pt'><span lang=EN-US>9)<a
|
||
style='mso-footnote-id:ftn1' href="#_ftn1" name="_ftnref1" title=""><span
|
||
class=MsoFootnoteReference><span style='mso-special-character:footnote'><![if !supportFootnotes]><span
|
||
class=MsoFootnoteReference><span lang=EN-US style='font-size:10.0pt;mso-bidi-font-size:
|
||
11.0pt;font-family:"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a>
|
||
ayanamsha =<span style='mso-tab-count:1'><3E><><A0> </span>-5<>40<34>,<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>t0 = -100</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm 5.0cm 212.65pt'><span lang=EN-US>10) ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><> </span>-4<>16<31>,<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>t0 = -100<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>Spica
|
||
at 29 vi 26</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm 5.0cm 212.65pt'><span lang=EN-US>11) ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><> </span>-3<>25<32>,<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>t0 = -100</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>In 1958, Peter
|
||
Huber reviewed the topic in the light of new material and found:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>12) Huber ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>-4<>28<32> +/- 20<32>,<span
|
||
style='mso-tab-count:1'><3E><> </span>t0 = <20>100<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>Spica
|
||
at 29 vi 07<30>59<35></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The standard deviation was 1<>08<30>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(<b>Note</b>, this ayanamsha was corrected
|
||
with SE version 2.05. A wrong value of -4<>34<33> had been taken over from Mercier,
|
||
<93>Studies on the Transmission of Medieval Mathematical Astronomy<6D>, IIb, p. 49.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 1977 Raymond Mercier noted that the zero
|
||
point might have been defined as the ecliptic point that culminated
|
||
simultaneously with the star eta Piscium (Al Pherg). For this possibility, we
|
||
compute:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>13) Eta Piscium ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>-5<>04<30>46<34>,<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>t0 = <20>129<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>Spica
|
||
at 29 vi 21</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Around 1950, Cyril Fagan, the founder of
|
||
the modern western sidereal astrology, reintroduced the old Babylonian zodiac
|
||
into astrology, placing the fixed star Spica near 29<32>00 Virgo. As a result of
|
||
<93>rigorous statistical investigation<6F> (astrological!) of solar and lunar ingress
|
||
charts, Donald Bradley decided that the sidereal longitude of the vernal point
|
||
must be computed from Spica at 29 vi 06'05" disregarding its proper
|
||
motion. Fagan and Bradley defined their <20>synetic vernal point<6E> as:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>0) Fagan/Bradley ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>24<32>02<30>31.36<94><span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0> </span>for 1 Jan. 1950 with Spica at 29 vi 06'05" (without
|
||
aberration)</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>(For the
|
||
year <20>100, this ayanamsha places Spica at 29 vi 07<30>32<33>.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The difference between P. Huber<65>s zodiac
|
||
and the Fagan/Bradley ayanamsha is smaller than 1<>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>According to a text by Fagan (found on the
|
||
internet), Bradley <20>once opined in print prior to "New Tool" that it
|
||
made more sense to consider Aldebaran and Antares, at 15 degrees of their
|
||
respective signs, as prime fiducials than it did to use Spica at 29 Virgo<67>.
|
||
Such statements raise the question if the sidereal zodiac ought to be tied up
|
||
to one of those stars.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For this possibility, Swiss Ephemeris gives
|
||
an Aldebaran ayanamsha:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>14) Aldebaran-Antares ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>ayanamsha with Aldebaran at 15 ta 00<30>00<30>
|
||
and Antares at 15 sc 00<30>17<31> around the year <20>100.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The difference between this ayanamsha and
|
||
the Fagan/Bradley one is 1<>06<30>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 2010, the astronomy historian John P.
|
||
Britton made another investigation in cuneiform astronomical tablets and
|
||
corrected Huber<65>s by a 7 arc minutes.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>38) Britton ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>-3.2<B0> +- 0.09<B0><a style='mso-footnote-id:
|
||
ftn2' href="#_ftn2" name="_ftnref2" title=""><sup><span style='mso-special-character:
|
||
footnote'><![if !supportFootnotes]><sup><span lang=EN-US style='font-size:10.0pt;
|
||
mso-bidi-font-size:11.0pt;font-family:"Segoe UI",sans-serif;mso-fareast-font-family:
|
||
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:AR-SA;
|
||
mso-bidi-language:AR-SA'>[2]</span></sup><![endif]></span></sup></a>;<span
|
||
style='mso-tab-count:1'><3E> </span>t0 = 1 Jan. 0<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Spica
|
||
at 29 vi 14<31>58<35>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(For the year -100, this ayanamsha places
|
||
Spica at 29 vi 15<31>02<30>.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha deviates from the
|
||
Fagan/Bradley aynamsa by 7 arc min.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Raymond Mercier, <20>Studies in
|
||
the Medieval Conception of Precession<6F>, in 'Archives Internationales d'Histoire
|
||
des Sciences', (1976) 26:197-220 (part I), and (1977) 27:33-71 (part II);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Cyril Fagan and Brigadier R.C.
|
||
Firebrace, -Primer of Sidereal Astrology, Isabella, MO, USA 1971;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>P. Huber, <20><>ber den Nullpunkt der babylonischen
|
||
Ekliptik<93>, in: Centaurus 1958, 5, pp. 192-208;<o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>John P. Britton, "Studies
|
||
in Babylonian lunar theory: part III. The introduction of the uniform
|
||
zodiac", in Arch. Hist. Exact. Sci. (2010)64:617-663, p. 630.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>42) Vettius Valens ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ayanamsha used by Greek astrologers in late
|
||
antiquity does not have a clear-cut definition. However, from extant charts it
|
||
is known that the ayanamsha was about -3<> in the year 150 CE. The following ayanamsha
|
||
is derived from Vettius Valens<6E> (2nd century CE) lunar positions, according to:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>James H. Holden, <20>The Classical
|
||
Zodiac<94>, in: AFA Journal of Research, vol. 7, no. 2 1995, p. 12.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488787"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Hipparchan tradition</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Raymond Mercier has shown that all of the
|
||
ancient Greek and the medieval Arabic astronomical works located the zero point
|
||
of the ecliptic somewhere between 10 and 22 arc minutes east of the star zeta
|
||
Piscium. He is of the opinion that this definition goes back to the great Greek
|
||
astronomer Hipparchus.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier points out that according to
|
||
Hipparchus<92> star catalogue, the stars alpha Arietis, beta Arietis, zeta
|
||
Piscium, and Spica are in a very precise alignment on a great circle which goes
|
||
through that zero point near zeta Piscium. Moreover, this great circle was
|
||
identical with the horizon once a day at Hipparchus<75> geographical latitude of
|
||
36<B0>. In other words, the zero point rose at the same time when the three
|
||
mentioned stars in Aries and Pisces rose and when Spica set.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This would of course be a nice definition
|
||
for the zero point, but unfortunately the stars were not really in such precise
|
||
alignment. They were only assumed to be so.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier gives the following ayanamshas for
|
||
Hipparchus and Ptolemy (who used the same star catalogue as Hipparchus):</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>15) Hipparchus ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>-9<>20<32><span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>27 June <20>128 (jd 1674484)<span style='mso-tab-count:
|
||
1'><3E><><A0><A0> </span>zePsc 29pi33<33>49<34><span style='mso-tab-count:1'><3E><><A0> </span>Hipparchus</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(According to Mercier<65>s calculations, the
|
||
Hipparchan zero point should have been between 12 and 22 arc min east of zePsc,
|
||
but the Hipparchan ayanamsha, as given by Mercier, has actually the zero point
|
||
26<92> east of zePsc. This comes from the fact that Mercier refers to the
|
||
Hipparchan position of zeta Piscium, which was at least rounded to 10<31>, if
|
||
correct at all.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Using the information that Aries rose when
|
||
Spica set at a geographical latitude of 36 degrees, the precise ayanamsha would
|
||
be -8<>58<35>13<31> for 27 June <20>128 (jd 1674484) and zePsc would be found at 29pi12<31>,
|
||
which is too far from the place where it ought to be.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier also discusses the old Indian
|
||
precession models and zodiac point definitions. He notes that, in the S<>ryasiddh<64>nta,
|
||
the star zeta Piscium (in Sanskrit Revat<61>) has almost the same position as in
|
||
the Greek sidereal zodiac, i.e. 29<32>50<35> in Pisces. On the other hand, however,
|
||
Spica (in Sanskrit Citr<74>) is given the longitude 30<33> Virgo. Unfortunately,
|
||
these positions of Revat<61> and Citr<74>/Spica are incompatible; either Spica or
|
||
Revat<EE> must be considered wrong.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, if the precession model of the
|
||
S<FB>ryasidd<E2>nta is used to compute an ayanamsha for the date of Hipparchus, it
|
||
will turn out to be <20>9<96>14<31>01<30>, which is very close to the Hipparchan value. The
|
||
same calculation can be done with the <20>ryasidd<64>nta, and the ayanamsha for
|
||
Hipparchos<92> date will be <20>9<96>14<31>55<35>. For the Sidd<64>nta Shiromani the zero point
|
||
turns out to be Revat<61> itself. By the way, this is also the zero point chosen
|
||
by Copernicus! So, there is an astonishing agreement between Indian and Western
|
||
traditions!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The same zero point near the star Revat<61> is
|
||
also used by the so-called Ush<73>-Shash<73> ayanamsha. It differs from the
|
||
Hipparchan one by only 11 arc minutes.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>4) Usha-Shashi ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>18<31>39<33>39.46<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0> </span>1 Jan. 1900</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>zePsc
|
||
(Revat<61>) 29pi50<35> (today), 29pi45<34> (Hipparchus<75> epoch)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Greek-Arabic-Hindu ayanamsha was zero
|
||
around 560 CE. The tropical and the sidereal zero points were at exactly the
|
||
same place.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the year 556, under the Sassanian ruler
|
||
Khusrau An<41>shirw<72>n, the astronomers of Persia met to correct their astronomical
|
||
tables, the so-called Z<>j al-Sh<53>h. These tables are no longer extant, but they
|
||
were the basis of later Arabic tables, the ones of al-Khw<68>rizm<7A> and the Toledan
|
||
tables.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One of the most important cycles in Persian
|
||
astronomy/astrology was the synodic cycle of Jupiter, which started and ended
|
||
with the conjunctions of Jupiter with the Sun. This cycle happened to end in
|
||
the year 564, and the conjunction of Jupiter with the Sun took place only one
|
||
day after the spring equinox. And the spring equinox took place precisely 10
|
||
arcmin east of zePsc. This may be a mere coincidence from a present-day
|
||
astronomical point of view, but for scientists of those days this was obviously
|
||
the moment to redefine all astronomical data.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier also shows that in the precession
|
||
(trepidation) model used in that time and in other models used later by Arabic
|
||
astronomers, precession was considered to be a phenomenon connected with <20>the
|
||
movement of Jupiter, the calendar marker of the night sky, in its relation to
|
||
the Sun, the time keeper of the daily sky<6B>. Such theories were of course wrong,
|
||
from the point of view of modern knowledge, but they show how important that
|
||
date was considered to be.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After the Sassanian reform of astronomical
|
||
tables, we have a new definition of the Greek-Arabic-Hindu sidereal zodiac
|
||
(this is not explicitly stated by Mercier, however):</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>16) Sassanian ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:78.0pt 5.0cm 212.65pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>0<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>18
|
||
Mar 564,<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>7:53:23 UT (jd /ET
|
||
1927135.8747793)<span style='mso-tab-count:1'><3E><><A0> </span>Sassanian<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>zePsc 29pi49'59"</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The same zero point then reappears with a
|
||
precision of 1<> in the Toledan tables, the Khw<68>rizmian tables, the S<>rya
|
||
Siddh<E2>nta, and the Ush<73>-Shash<73> ayanamsha.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Raymond Mercier, <20>Studies in the
|
||
Medieval Conception of Precession<6F>, in Archives Internationales d'Histoire des
|
||
Sciences, (1976) 26:197-220 (part I), and (1977) 27:33-71 (part II)</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488788"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Suryasiddhanta and Aryabhata</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The explanations given above are mainly
|
||
derived from the article by Mercier. However, it is possible to derive ayanamshas
|
||
from ancient Indian works themselves.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The planetary theory of the main work of
|
||
ancient Indian astronomy, the Suryasiddhanta, uses the so-called Kaliyuga era as
|
||
its zero point, i.e. the 18th February 3102 BCE, 0:00 local time at Ujjain,
|
||
which is at geographic longitude of 75.7684565 east (Mahakala temple). This era
|
||
is henceforth called <20>K0s<30>. This is also the zero date for the planetary theory
|
||
of the ancient Indian astronomer Aryabhata, with the only difference that he
|
||
reckons from Sunrise of the same date instead of midnight. We call this
|
||
Aryabhatan Kaliyuga era <20>K0a<30>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Aryabhata mentioned that he was 23 years
|
||
old when exactly 3600 years had elapsed since the beginning of the Kaliyuga
|
||
era. If 3600 years with a year length as defined by the Aryabhata are counted
|
||
from K0a, we arrive at the 21st March, 499 CE, 6:56:55.57 UT. At this point of
|
||
time the mean Sun is assumed to have returned to the beginning of the sidereal
|
||
zodiac, and we can try to derive an ayanamsha from this information. There are
|
||
two possible solutions, though:</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>We can find the place of the mean Sun at that time using modern
|
||
astronomical algorithms and define this point as the beginning of the sidereal
|
||
zodiac.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Since Aryabhata believed that the zodiac began at the vernal point,
|
||
we can take the vernal point of this date as the zero point.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The same calculations can be done based on
|
||
K0s and the year length of the Suryasiddhanta. The resulting date of Kali 3600
|
||
is the same day but about half an hour later: 7:30:31.57 UT.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Algorithms for the mean Sun were taken
|
||
from: Simon et alii, <20>Numerical expressions for precession formulae and mean
|
||
elements for the Moon and the planets<74>, in: Astron. Astrophys. 282,663-683
|
||
(1994).</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>Suryasiddhanta/equinox ayanamshas with zero
|
||
year 499 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm'><span lang=EN-US>21) ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><> </span>0<span style='mso-tab-count:1'><3E><> </span>21
|
||
Mar 499,<span style='mso-tab-count:1'><3E> </span>7:30:31.57 UT = 12:33:36 LMT at
|
||
Ujjain, 75.7684565 E</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:3.0cm'><span lang=EN-US>Based on
|
||
Suryasiddhanta: ingress of mean Sun into Aries at point of mean equinox of
|
||
date.</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm'><span lang=EN-US>22) ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><> </span>-0.21463395</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:3.0cm'><span lang=EN-US>Based on
|
||
Suryasiddhanta again, but assuming ingress of mean Sun into Aries at true
|
||
position of mean Sun at the same epoch.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>Aryabhata/equinox ayanamshas with zero year
|
||
499 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm'><span lang=EN-US>23) ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><> </span>0<span style='mso-tab-count:1'><3E><> </span>21
|
||
Mar 499, 6:56:55.57 UT = 12 LMT, local noon at Ujjain, 75.7684565 E.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:3.0cm'><span lang=EN-US>Based on
|
||
Aryabhata, ingress of mean Sun into Aries at point of mean equinox of date.</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:3.0cm'><span lang=EN-US>24) ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><> </span>-0.23763238</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:3.0cm'><span lang=EN-US>Based on
|
||
Aryabhata again, but assuming ingress of mean Sun into Aries at true position
|
||
of mean Sun at the same epoch.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>According to Govindasvamin (850 n. Chr.),
|
||
Aryabhata and his disciples taught that the vernal point was at the beginning
|
||
of sidereal Aries in the year 522 CE (= Shaka 444). This tradition probably
|
||
goes back to an erroneous interpretation of Aryabhata's above-mentioned
|
||
statement that he was 23 years old when 3600 had elapsed after the beginning of
|
||
the Kaliyuga. For the sake of completeness, we therefore add the following ayanamsha:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>37) Aryabhata/equinox ayanamsha with zero
|
||
year 522 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 99.25pt 6.0cm'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>0<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>21.3.522,<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>5:46:44 UT</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 99.25pt 6.0cm'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Ayanamshas can also be derived from star
|
||
positions given in the Suryasiddhanta. E.g., it states that the star
|
||
Revati/zeta Piscium is at polar ecliptic longitude 359<35>50<35>. </span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>25) Ayanamsha having Revati/zeta Piscium at
|
||
polar longitude 359<35>50<35> in 499 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm'><span lang=EN-US>ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><><A0> </span>-0.79167046<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>21
|
||
Mar 499,<span style='mso-tab-count:1'><3E> </span>7:30:31.57 UT = noon at Ujjain,
|
||
75.7684565 E.</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Revati/zePsc
|
||
at polar ecliptic longitude 359<35>50<35></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>28) True Revati ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Revati/zePsc is always exactly at longitude
|
||
359<B0>50<92> (not polar!).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Note, this was incorrectly implemented in
|
||
SE 2.00 <20> SE 2.04. The Position of Revati was 0<>. Only from SE 2.05 on, this
|
||
ayanamsha is correct.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Unfortunately, other star positions given
|
||
in Suryasiddhanta are not compatible with the one of Revati. In particular the
|
||
star Spica/Citra, which is stated to be at 180<38> exactly, has been used to
|
||
create another bunch of ayanamshas (see next chapter). </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Siddhantas usually assume the star Pushya
|
||
(delta Cancri = Asellus Australis) at 106<30>. PVR Narasimha Rao believes this
|
||
star to be the best anchor point for a sidereal zodiac. In the Kalapurusha
|
||
theory, which assigns zodiac signs to parts of the human body, the sign of
|
||
Cancer is assigned to the heart, and according to Vedic spiritual literature,
|
||
the root of human existence is in the heart. Mr. Narasimha Rao therefore
|
||
proposed the following ayanamsha:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>29) True Pushya paksha ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Pushya/deCnC is always exactly at longitude
|
||
106<B0>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Surya-Siddhanta: A Text Book of
|
||
Hindu Astronomy by Ebenezer Burgess, ed. Phanindralal Gangooly (1989/1997) with
|
||
a 45-page commentary by P. C. Sengupta (1935).</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>D. Pingree, "Precession
|
||
and Trepidation in Indian Astronomy", in JHA iii (1972), pp. 28f.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488789"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Spica/Citra tradition and
|
||
the Lahiri ayanamsha</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal style='tab-stops:63.8pt 5.0cm 11.0cm'><span lang=EN-US>For
|
||
instructions how to reproduce ayanamsha values given in IAE, IENA, Rashtriya
|
||
Panchang, and the Report of the ICRC, please read Appendix E of this
|
||
documentation.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>1) Lahiri ayanamsha (according to IAE 1985,
|
||
our standard Lahiri ayanamsha):</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:63.8pt 5.0cm 11.0cm'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E> </span>23<32>15' 00".658<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>21 March 1956, 0:00 TDT Lahiri,<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Spica (2000) 179<37>58'58<35></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>46) Lahiri ayanamsha (according to ICRC, and
|
||
pre-1985 IAE and IENA):</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:63.8pt 5.0cm 11.0cm'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E> </span>23<32>15' 00".0<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>21 March 1956, 0:00 TDT Lahiri,<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>Spica (2000) 179<37>58'59<35></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The <20>Lahiri ayanamsha<68> was introduced by
|
||
the <i style='mso-bidi-font-style:normal'>Indian Calendar Reform Committee</i> (ICRC)
|
||
on the occasion of the Indian calendar reform in 1955, when the ayanamsha based
|
||
on the star Spica/Citra was declared the Indian standard. It was used
|
||
henceforth not only in astrology but also for sidereal ephemerides and
|
||
calendars published in India. However, the idea that the zodiac should be
|
||
oriented towards the star Spica (Citra in Sanskrti) is older. The Indian
|
||
astronomy historian S. B. Dixit (also written Dikshit) in his important work <i
|
||
style='mso-bidi-font-style:normal'>History of Indian Astronomy</i> (= <i
|
||
style='mso-bidi-font-style:normal'>Bharatiya Jyotih Shastra</i>) in 1896 arrived
|
||
at the conclusion that, given the prominence that Vedic religion gave to the
|
||
cardinal points of the tropical year, the Indian calendar should be reformed
|
||
and no longer be calculated relative to the sidereal, but to the tropical
|
||
zodiac. However, if such a reform could not be brought about due to the rigid
|
||
conservatism of contemporary Vedic culture, then the ayanamsha should be chosen
|
||
in such a way that the sidereal zero point would be in opposition to Spica. In
|
||
this way, it would be in accordance with Grahalaghava, a work by the 16th
|
||
century astronomer Ganeśa Daivaj<61>a which was still in use in the 20th
|
||
century among Indian calendar makers. (<i style='mso-bidi-font-style:normal'>History
|
||
of Indian Astronomy</i>, Part II, p. 323ff.). </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, the Suryasiddhanta, the <20>standard
|
||
work<94> of ancient Hindu astronomy, which was written in the first centuries CE,
|
||
already placed Spica/Citra at 180<38>. Unfortunately, this statement is in
|
||
contradiction with the positions of other stars, in particular with zeta
|
||
Piscium/Revati at 359<35>50<35>, which has caused a lot of confusion. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ayanamsha based on the star Spica/Citra
|
||
became known as <20>Lahiri ayanamsha<68>. It was named after the Calcuttan astronomer
|
||
and astrologer Nirmala Chandra Lahiri (1906-1980), who was a member of the
|
||
Calendar Reform Committee that in 1955 made it the standard for Hindu sidereal
|
||
calendars. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The committee decreed that the ayanamsha
|
||
had the value 23<32>15' 00" on the 21 March 1956, 0:00 Ephemeris Time. It
|
||
became the basis of ayanamsha values given in <i style='mso-bidi-font-style:
|
||
normal'>Indian Ephemeris and Nautical Almanac (IENA)</i>, in<i
|
||
style='mso-bidi-font-style:normal'> Indian Astronomical Ephemeris (IAE)</i>, as
|
||
well as for the <i style='mso-bidi-font-style:normal'>Rashtriya Panchang </i>(<28>National
|
||
Calendar/Almanac<61>). Although not explicitly mentioned, this ayanamsha value is <i
|
||
style='mso-bidi-font-style:normal'>true, not mean</i>, as can be concluded from
|
||
the values given in the 5-year calendar that is included in the Report of the
|
||
ICRC.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Side note concerning the decisions of the
|
||
ICRC, in the words of Vishvas Vasuki in the Bharatiyavidvatparishat forum: <20>The
|
||
committee created a civil solar calendar (equinox to equinox), a religious
|
||
solar calendar based on a fixed ayanAMsha (=deviation from equinoctial colure)
|
||
(23<32> 15<31>) to prevent further drift from seasons, a religious lunar calendar
|
||
closely tied to the religious solar calendar, a asterism tracking variable
|
||
ayanAMsha (23<32> 15<31> 0<>, with annual correction) for the nakShatra wheel. The
|
||
reason for standardizing religious calendars was to be able to determine office
|
||
holidays.<2E>)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The definition of the ayanamsha was
|
||
corrected in <i style='mso-bidi-font-style:normal'>Indian Astronomical
|
||
Ephemeris</i> 1985 (see 1989, page 556, footnote):</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>"According to new determination of the
|
||
location of equinox this initial value has been revised to 23<32>15'00".658
|
||
and used in computing the mean ayanamsha with effect from 1985'."</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Exact information about the reasons for
|
||
this change is unfortunately not given or is hard to get hold of. The mention
|
||
of <20>mean ayanamsha<68> is misleading, though. Again, the value 23<32>15'00".658
|
||
is true ayanamsha, i.e. it includes nutation and is relative to the true
|
||
equinox of date. This must be concluded, at least, from true ayanamsha values
|
||
published in yearly editions of the <i style='mso-bidi-font-style:normal'>Indian
|
||
Astronomical Ephemeris (IAE)</i>.</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;color:#0070C0;mso-fareast-language:
|
||
ZH-CN'>For a comparison of Lahiri ayanamsa values and sidereal ephemerides with
|
||
values given in <i style='mso-bidi-font-style:normal'>Indian Astronomical
|
||
Ephemeris</i>, see Appendix E.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;color:#0070C0;mso-fareast-language:
|
||
ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>43) Lahiri (1940) ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>ayanamsha
|
||
= 22<32>26'45".50 <span style='mso-tab-count:1'><3E><> </span>J1900.0 = 31 Dec.
|
||
1899, 12:00 TT<span style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Spica
|
||
(2000) at 179<37>59'52"<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 1940, however, Lahiri had published a
|
||
different Citra ayanamsha in his Bengali book <i style='mso-bidi-font-style:
|
||
normal'>Panchanga Darpan</i>. Here, the value of <20>mean ayanamsha<68> is given as
|
||
22<B0>26<92>45<94>.50 in 1900, whereas the official value for the same date is
|
||
22<B0>27<92>38<94>. With the standard Lahiri ayanamsha, the position of Spica is
|
||
<93>wrong<94>, i.e. it deviates from 180<38> by about an arc minute, whereas with this
|
||
other ayanamsha it is almost exact. Lahiri obviously wanted to place the star
|
||
exactly at 180<38> for current years. The standard Lahiri position of Spica is
|
||
179<B0>59<92>04 in the year 2000, and 179<37>59<35>08 in 1900. According to the definition
|
||
given in <i style='mso-bidi-font-style:normal'>Panchanga Darpan</i>, however
|
||
calculated with rigorous precession algorithms, the position of Spica in 2000
|
||
was 179<37>59'52<35>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The same book (<i style='mso-bidi-font-style:
|
||
normal'>Panchanga Darpan</i>) was reprinted in 1967 and 1985, thus long after
|
||
the standard definition of the Lahiri ayanamsha had been published by the
|
||
Calendar Reform Committee. Thus, apparently, still considered this his
|
||
definition of ayanamsha more correct than the one chosen by the ICRC. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>44) Lahiri (1972, vernal equinox 285)
|
||
ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>ayanamsha = 0<><span
|
||
style='mso-tab-count:2'><3E><><A0><A0> </span>22 March 285 17:54:02 TT (Lahiri original:
|
||
17:48 ET)<span style='mso-tab-count:2'><3E><><A0><A0><A0> </span>Spica (2000) at 179<37>58'35<33> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom:0cm;
|
||
margin-left:71.0pt;text-indent:14.2pt'><b><span lang=EN-US>mean</span></b><span
|
||
lang=EN-US> Sun<75>s ingress in Aries (using formulae from Simon et alii (1994))</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:71.0pt;text-indent:14.2pt'><span
|
||
lang=EN-US>(<b>true </b>Sun<75>s ingress was on 20 March 19:18:33 TT)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In his <20>Tables of the Sun<75>, p. IX, however,
|
||
which appeared in 1972, Lahiri again gave a different definition of his
|
||
ayanamsha:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>For this purpose the star <i
|
||
style='mso-bidi-font-style:normal'>Spica </i>( </span><span lang=EL
|
||
style='mso-ansi-language:EL'>α</span><span lang=EN-US> Virginis ) has been
|
||
assigned a <i style='mso-bidi-font-style:normal'>Nirayaṇa</i> (i.e.
|
||
sidereal; D.K.)<i style='mso-bidi-font-style:normal'> </i>longitude of 180<38>.
|
||
But as the star has got proper motion, it cannot indicate a fixed initial point
|
||
for all times, even when a fixed value of longitude is assigned to it. It has therefore
|
||
been considered expedient to adopt the vernal equinoctial point of any
|
||
specified date for this purpose. The mean equinoctial point of the mean vernal
|
||
equinox day of 285 A.D., which occurred on March 22, 17<sup>h</sup> 48<sup>m</sup>
|
||
Ephemeris time or 15<sup>h</sup> 57<sup>m</sup> U.T. of that year, has
|
||
accordingly been adopted as the fixed initial point of the Sidereal or Indian <i
|
||
style='mso-bidi-font-style:normal'>Nirayaṇa</i> system of Astronomy.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Exactly the same initial date, however in
|
||
Indian Standard Time, he gave in 1980, in the preface of his <i
|
||
style='mso-bidi-font-style:normal'>Indian Ephemeris</i>. However, the star
|
||
Spica/Citra still does play an important part:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>"The
|
||
initial point of this nirayana or sidereal zodiac was the same as the
|
||
equinoctial point ... of the vernal equinox day of 285 A.D., the mean equinox
|
||
of the year occurring on Sunday March 22, 21h 27m I S.T. At that time both the
|
||
sayana (= tropical, D.K.) and the nirayana (= sidereal) longitudes of the star
|
||
Citra (Spica) were the same as 180<38>00'03", and the longitude of the Mean
|
||
Moon was 351<35>67 and of Mean Sun 360<36>00. It was thus a mean new-moon day
|
||
also."<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Thus,
|
||
Lahiri actually wanted to base his ayanamsha on the mean equinox of a
|
||
"zero ayanamsha year". I.e. the zero date of his ayanamsha should be
|
||
the moment when the *mean* Sun was at zero aries tropically (mean equinox of
|
||
date). Moreover he wanted to have a mean new-moon on the same day also and the
|
||
star Citra/Spica at tropical 0<> Libra/Tula exactly. (For testing, such an
|
||
ayanamsha was added to the Swiss Ephemeris as ayanamsha No. 44.)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>However,
|
||
then Lahiri continues:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>"Due
|
||
to proper motion of the star, the nirayana longitude of Spica has however
|
||
diminished by 65" during the period of 1695 years from 285 A.D. and now
|
||
179<B0>58'58" according to the above ayanamsa system."<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>And:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>"The
|
||
Indian Astronomical Ephemeris of the Government of India has adopted, on the
|
||
basis of the recommendations of the Calendar Reform Committee, a value of
|
||
ayanamsa which is less by only 5".8 than the above."<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Apparently,
|
||
this difference was small enough for him so that he considered it insignificant
|
||
and, "for the sake of uniformity", took over the standard ayanamsha
|
||
recommended by the CRC. The ayanamsha values and sidereal positions of the Sun
|
||
and the Moon which he gives in his ephemeris are in perfect agreement with
|
||
the standard ayanamsha, not with the above-given definition.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>As to
|
||
the 5.8" difference, it must be added that it is only found with the
|
||
Newcomb precession model. If a modern standard model like IAU2006 or Vondr<64>k is
|
||
used, then the difference amounts to 23".<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In <20>Tables of the Sun<75>, Lahiri derives an
|
||
ayanamsha value of 22<32>27<32>43<34>.5 for <20>1900, Jan. 0 (= 31 Dec. 1899; D.K.), 19<sup>h</sup>
|
||
31<sup>m</sup> ET<45>. Using a version of swetest which calculates uses Newcomb
|
||
precession (the formulation of Kinoshita 1975), the following ayanamsha results
|
||
for the same date:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>swetest -b31.12.1899 -t19:31 -p -nonut -p0
|
||
-sid44 -sidbit4096</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>22<32>27'44.02069.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, since Lahiri considered his zero
|
||
date as essential to his ayanamsha, the Swiss Ephemeris calculates it using the
|
||
modern precession model Vondr<64>k 2011, which for the same date provides the
|
||
value 22<32>28' 0.90375.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>From all this, it is obvious that there are
|
||
several <20>Lahiri ayanamsha<68>, and the standard Lahiri ayanamsha which was adopted
|
||
by the ICRC is not exactly what he had intended.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>26) Ayanamsha having Spica/Citra at polar
|
||
longitude 180<38> in 499 CE</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm'><span lang=EN-US>ayanamsha =<span
|
||
style='mso-tab-count:1'><3E><><A0> </span>2.11070444<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>21
|
||
Mar 499,<span style='mso-tab-count:1'><3E> </span>7:30:31.57 UT = noon at Ujjain,
|
||
75.7684565 E</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt'><span lang=EN-US><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Spica at polar ecliptic
|
||
longitude 180<38> on equinox 499<span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0> </span>Spica
|
||
(2000) 180<38>50' 3</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As has been stated, the Suryasiddhanta
|
||
gives the position of Spica/Citra as 180<38> in <b style='mso-bidi-font-weight:
|
||
normal'>polar</b> longitude (ecliptic longitude, but projection along meridian
|
||
lines). </span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>27) True Chitrapaksha ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Spica is always exactly at 180<38> or 0<> Libra
|
||
in ecliptic longitude (not polar!).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Usually ayanamshas are defined by an epoch
|
||
and an initial ayanamsha offset. However, if one wants to make sure that a
|
||
particular fixed star always remains at a precise position, e. g. Spica at
|
||
180<B0>, it does not work this way because the star has some proper motion and is
|
||
not really fixed relative to a fixed reference frame. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the year 285, when the star was conjunct
|
||
the autumnal equinox, its position was 180<38>00<30>17 (swetest -b1.1.285 -pf
|
||
-xfSpica -sid1 -true -bary -head -fTPL -s365 -n2). Only in the year 675
|
||
CE, its position was exactly 180<38>. The motion of the star is partly caused by
|
||
its proper motion. Another part of its motion is apparent only, due to the
|
||
so-called planetary precession, which causes very slow changes in the
|
||
orientation of the ecliptic plane. As can be seen from the description of the
|
||
other <20>Lahiri<72> or Spica-related ayanamshas, non of them has Spica exactly at
|
||
180<B0> on 1 Jan. 2000.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The correct procedure, in order to have the
|
||
star at a constant position, is to calculate the tropical position of Spica for
|
||
the date and subtract it from the tropical position of the planet.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-bidi-font-size:10.0pt'>Many
|
||
thanks to Vinay Jha, PVR Narasimh</span><span lang=EN-US>a Rao, and Avtar
|
||
Krishen Kaul, and D. Senthilathiban for their help in our attempt to understand
|
||
this complicated matter.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488790"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Krishnamurti ayanamshas</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris also has two ayanamshas
|
||
named after the Indian astrologer K.S. Krishnamurti (1908-1972). They are very
|
||
close to the Lahiri ayanamsha, with a difference of only 4 to 5 arcmin. In
|
||
fact, he says that the difference between his ans Lahiri<72>s ayanamsha is
|
||
<93>negligible<94> (Krishnamurti, <i style='mso-bidi-font-style:normal'>Reader 1</i>,
|
||
p. 57), but modern Hindu astrologers won<6F>t be happy with an uncertainty of
|
||
several minutes of arc.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Unfortunately, Krishnamurti did not give
|
||
very precise information about the definition of his ayanamsha (<i
|
||
style='mso-bidi-font-style:normal'>Reader 1</i>, pp. 54-59). He says that the
|
||
ayanamsha was zero in the year 291 CE, however, he does not give an exact date,
|
||
which leaves an uncertainty in ayanamsha of 50<35>. D. Senthilathiban assumes,
|
||
following an old Indian tradition, that Krishnamurti must have had in mind the
|
||
date of the equinox. Based on this assumption, the Swiss Ephemeris offers an
|
||
ayanamsha defined as follows:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>45) Krishnamurti/Senthilathiban ayanamsha
|
||
(derived from zero ayanamsha year 291)</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 241.0pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>0,<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>t0
|
||
= 21 March 291 CE, 6:10:29 TT (=</span><span lang=EN-GB style='font-size:11.0pt;
|
||
font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
|
||
minor-latin;mso-bidi-theme-font:minor-latin;mso-ansi-language:EN-GB;mso-no-proof:
|
||
yes'>4:02:45 UT)</span><span lang=EN-US><span style='mso-tab-count:3'><3E><><A0><A0><A0><A0><A0><A0><A0> </span><span
|
||
style='mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>Spica at 180<38> 5'13<b><i><u><span
|
||
style='color:#0070C0'><o:p></o:p></span></u></i></b></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The exact timing was derived using the
|
||
Swiss Ephemeris and based on the precession theory Vondr<64>k 2011. Senthilathiban
|
||
gives a slightly different time, 4:09 UT. This difference corresponds to less
|
||
than 1 milliarcsec in precession and can be neglected. On the other hand, since
|
||
Senthilathiban prefers to use the IAU standard model IAU 2006, whereas the
|
||
Swiss Ephemeris uses precession Vondr<64>k, his ayanamsha calculation for the year
|
||
2000 differs by about 0.2 arcsec from ours. This difference should be considered
|
||
negligible, too. Modern calculation of precession will improve in the future,
|
||
and this will lead to small changes in this ayanamsha, as well. The Vondr<64>k
|
||
model is particularly good for remote epochs. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In addition to the statement that zero
|
||
ayanamsha year was 291, Krishnamurti also provides a table of ayanamsha values
|
||
for the years 1840 to 2001 (<i style='mso-bidi-font-style:normal'>Reader 1</i>,
|
||
p. 58). Unfortunately, the above ayanamsha definition based on the equinox of
|
||
291 CE does not agree well with this table. It provides values which are about
|
||
1 arcmin too high. Since Krishnamurti wrote in a time when the precession model
|
||
of Newcomb was used, the comparison must of course be done using this precesion
|
||
model. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A better representation of the table values
|
||
is given by our other Krishnamurti ayanamsha:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>5) Krishnamurti ayanamsha (derived from his
|
||
ayanamsha table)</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 241.0pt'><span lang=EN-US>ayanamsha
|
||
=<span style='mso-tab-count:1'><3E><><A0> </span>22.363889,<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>t0 = 1 Jan 1900,<span style='mso-tab-count:8'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>Spica
|
||
at 180<38> 4'52</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This <span class=im>ayanamsha was provided
|
||
by Graham Dawson (astrology program <20>Solar Fire<72>), who had taken it over from
|
||
Robert Hand<6E>s program <20></span><span class=il>Nova</span><span class=im><3E>. We do
|
||
not know who developed it and using what method. Assuming that the table values
|
||
refer to 1 January of each year, the agreement is very good, with only a few
|
||
exceptions. However, it must also be stated that Krishnamurti<74>s table is not
|
||
plausible for all years. This is obvious for the years 1918-1921 where
|
||
identical values are repeated in a way that is not possible with a precession
|
||
rate of about 50<35> per year.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:11.5pt;mso-fareast-font-family:
|
||
DengXian;mso-fareast-theme-font:minor-fareast;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="_x0000_i1062" type="#_x0000_t75" style='width:101.25pt;height:75.75pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image003.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=135 height=101
|
||
src="swisseph-Dateien/image004.png" v:shapes="_x0000_i1062"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ayanamsha based on the year 291 (No.
|
||
45), if calculated using Newcomb precession, is about 54<35> arcsec higher than
|
||
the one based on Krishnamurti<74>s tables (No. 5). (With a modern precession it is
|
||
even 72-73<37> higher).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Senthilathiban in his book, p. 126ff.,
|
||
proposes a different representation of the Krishnamurti table values, assuming
|
||
that they are referred to the 13/14 April of each year, i.e. the date of the
|
||
ingress of the Sun into sidereal Aries. While this assumption is possible, we
|
||
cannot be certain about it since Krishnamurti himself does not tell us. In
|
||
addition, the agreement of the two ayanamshas (Krishnamurti table ayanamsha and
|
||
Krishnamurti/Senthilathiban) becomes even worse, not better. </span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt 5.0cm 241.0pt'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Burgess, E., <i
|
||
style='mso-bidi-font-style:normal'>The Surya Siddanta</i>. A Text-book of Hindu
|
||
Astronomy, Delhi, 2000 (MLBD).</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Dikshit, S(ankara)
|
||
B(alkrishna), <i style='mso-bidi-font-style:normal'>Bharatiya Jyotish Sastra
|
||
(History of Indian Astronomy)</i> (Tr. from Marathi), Govt. of India, 1969,
|
||
part I & II.</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Kollerstrom, Nick, <20>The Star
|
||
Zodiac of Antiquity<74>, in: <i style='mso-bidi-font-style:normal'>Culture &
|
||
Cosmos</i>, Vol. 1, No.2, 1997).</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Lahiri, N. C., <i
|
||
style='mso-bidi-font-style:normal'>Panchanga Darpan</i> (in Bengali), Calcutta,
|
||
1967 (Astro Research Bureau).</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Lahiri, N. C., <i
|
||
style='mso-bidi-font-style:normal'>Tables of the Sun</i>, Calcutta, 1952 (Astro
|
||
Research Bureau).</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Saha, M. N., and Lahiri, N. C.,
|
||
<i style='mso-bidi-font-style:normal'>Report of the Calendar Reform Committee</i>,
|
||
C.S.I.R., New Delhi, 1955.</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The <i style='mso-bidi-font-style:
|
||
normal'>Indian Astronomical Ephemeris</i> for the year 1989, Delhi (Positional
|
||
Astronomy Centre, India Meteorological Department)</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-bottom:2.0pt;mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>P.V.R. Narasimha Rao,
|
||
"Introducing Pushya-paksha Ayanamsha" (2013),</span></p>
|
||
|
||
<p class=ListBullet1 align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-list:l35 level1 lfo47;mso-hyphenate:auto;
|
||
layout-grid-mode:both;mso-layout-grid-align:none;text-autospace:none'><![if !supportLists]><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:Symbol;mso-fareast-font-family:
|
||
Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>http://www.vedicastrologer.org/articles/pp_ayanamsha.pdf.</span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-list:l35 level1 lfo47;mso-hyphenate:auto;
|
||
layout-grid-mode:both;mso-layout-grid-align:none;text-autospace:none'><![if !supportLists]><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;font-family:Symbol;mso-fareast-font-family:
|
||
Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>D. Senthilathiban, </span><i style='mso-bidi-font-style:normal'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:DE'>Study of
|
||
KP Ayanamsa with Modern Precession Theories</span></i><span lang=EN-US
|
||
style='mso-bidi-font-size:10.0pt;mso-fareast-language:DE'>, Seoul, 2019.</span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt'><o:p></o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488791"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.7.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The sidereal zodiac and the
|
||
Galactic Center</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The definition of the tropical zodiac is
|
||
very simple and convincing. It starts at one of the two intersection points of
|
||
the ecliptic and the celestial equator. Similarly, the definition for the house
|
||
circle which is said to be an analogy of the zodiac, is very simple. It starts
|
||
at one of the two intersection points of the ecliptic and the local horizon.
|
||
Unfortunately, sidereal traditions do not provide such a simple definition for
|
||
the sidereal zodiac. The sidereal zodiac is always fixed at some anchor star
|
||
such as Citra (Spica), Revati (zeta Piscium), or Aldebaran and Antares.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Unfortunately, nobody can tell why any of
|
||
these stars should be so important that it could be used as an anchor point for
|
||
the zodiac. In addition, all these solutions are unattractive in that the fixed
|
||
stars actually are not fixed forever but have a small proper motion which over
|
||
a long period of time (such as several millennia) can result in a considerable
|
||
change in position. While it is possible to tie the zodiac to the star Spica in
|
||
a way that it remains at 0<> Libra for all times, all other stars would change
|
||
their positions relative to Spica and relative to this zodiac and would not be
|
||
fixed at all. The appearance of the sky changes over long periods of time. In
|
||
100.000 years, the constellations will look very different from now, and the
|
||
nakshatras (lunar mansions) will get confused. For this reason, a zodiac
|
||
defined by positions of stars is unfortunately not able to provide an
|
||
everlasting reference frame.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For such or also other reasons, some
|
||
astrologers (Raymond Mardyks, Ernst Wilhelm, Rafael Gil Brand, Nick Anthony
|
||
Fiorenza) have tried to define the sidereal zodiac using either the galactic
|
||
centre or the node of the galactic equator with the ecliptic. It is obvious
|
||
that this kind of solution, which would not depend on the position of a single
|
||
star anymore, could provide a philosophically more convincing and very stable
|
||
definition of the zodiac. Fixed stars would be allowed to change their
|
||
positions over very long periods of time, but the zodiac could still be
|
||
considered fixed and <20>sidereal<61>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss astrologer Bruno Huber has
|
||
pointed out that every time the Galactic Center enters the next tropical sign,
|
||
the vernal point enters the previous sidereal sign. E.g., around the time the
|
||
vernal point will enter Aquarius (at the beginning of the so-called Age of
|
||
Aquarius), the Galactic Center will enter from Sagittarius into Capricorn.
|
||
Huber also notes that the ruler of the tropical sign of the Galactic Center is
|
||
always the same as the ruler of the sidereal sign of the vernal point (at the
|
||
moment it is Jupiter, but it will be Saturn in a few hundred years).</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>17) Galactic Center at 0 Sagittarius (and
|
||
the beginning of nakshatra Mula)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A correction of the Fagan ayanamsha by
|
||
about 2 degrees or a correction of the Lahiri ayanamsha by 3 degrees would
|
||
place the Galactic Center at 0<> Sagittarius. Philosophically, this would
|
||
obviously make some sense. Therefore, we added an ayanamsha fixed at the
|
||
Galactic Center in 1999 in Swiss Ephemeris 1.50, when we introduced sidereal
|
||
ephemerides (suggestion by D. Koch, without any astrological background).</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>40) Galactic Center at 0 Capricorn (Cochrane
|
||
Ayanamsha)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A modification of this ayanamsha was
|
||
proposed by David Cochrane in 2017. He believes that it makes more sense to put
|
||
the Galactic Centre at 0<> Capricorn.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>36) Dhruva Galactic Center Middle Mula Ayanamsha
|
||
(Ernst Wilhelm)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A different solution was proposed by the
|
||
American astrologer Ernst Wilhelm in 2004. He projects the galactic centre on
|
||
the ecliptic in polar projection, i.e. along a great circle that passes through
|
||
the celestial north pole (in Sanskrit dhruva) and the galactic centre. The
|
||
point at which this great circle cuts the ecliptic is defined as the middle of
|
||
the nakshatra Mula, which corresponds to sidereal 6<>40<34> Sagittarius.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For Hindu astrologers who follow a
|
||
tradition oriented towards the star Revati (ζ Piscium), this solution may
|
||
be particularly interesting because when the galactic centre is in the middle
|
||
of Mula, then Revati is almost exactly at the position it has in
|
||
Suryasiddhanta, namely 29<32>50 Pisces. Also interesting in this context is the
|
||
fact that the meaning of the Sanskrit word mūlam is <20>root, origin<69>. Mula
|
||
may have been the first of the 27 nakshatras in very ancient times, before the
|
||
Vedic nakshatra circle and the Hellenistic zodiac were conflated and Ashvini,
|
||
which begins at 0<> Aries, became the first nakshatra.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>https://groups.yahoo.com/neo/groups/StudyingKala/conversations/topics/14656;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>private communication with D.
|
||
Koch.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>30) Galactic Centre in the Golden Section
|
||
Scorpio/Aquarius (Rafael Gil Brand)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Another ayanamsha based on the galactic
|
||
centre was proposed by the German-Spanish astrologer Rafael Gil Brand. Gil
|
||
Brand places the galactic centre at the golden section between 0<> Scorpion and
|
||
0<B0> Aquarius. The axis between 0<> Leo and 0<> Aquarius is the axis of the
|
||
astrological ruler system.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha is very close to the ayanamsha
|
||
of the important Hindu astrologer B.V. Raman. (see below)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>Rafael Gil Brand, Himmlische Matrix. Die Bedeutung
|
||
der W<>rden in der Astrologie, M<>ssingen (Chiron), 2014.<o:p></o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;mso-ansi-language:DE'><span style='mso-list:Ignore'><3E><span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
style='mso-ansi-language:DE'>Rafael Gil Brand, "Umrechnung von tropischen
|
||
in siderische Positionen",
|
||
http://www.astrologie-zentrum.net/index.php/8-siderischer-tierkreis/5-umrechnung<o:p></o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488792"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.8.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The sidereal zodiac and the
|
||
Galactic Equator</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Another way to define the ayanamsha based
|
||
on our galaxy would be to start the sidereal ecliptic at the intersection point
|
||
of the ecliptic and the galactic plane (henceforth called the <20>galactic node<64>).
|
||
At present, this point is located near 0 Capricorn. This definition of the ayanamsha
|
||
would be analogous to the definitions of the tropical ecliptic and the house
|
||
circle, both of which are also based on intersections of great circles.
|
||
However, defining this galactic-ecliptic intersection point or node as sidereal
|
||
0 Aries would mean to break completely with the tradition, because it is far
|
||
away from the traditional sidereal zero points.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The following ayanamshas belong in this
|
||
category:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>34) Skydram Ayanamsha (Raymond Mardyks)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(also known as Galactic Alignment Ayanamsha)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was proposed in 1991 by the
|
||
American astrologer Raymond Mardyks. It had the value 30<33> on the autumn equinox
|
||
1998. Consequently, the node (intersection point) of the galactic equator with
|
||
the ecliptic was very close to sidereal 0<> Sagittarius on the same date, and
|
||
there was an interesting <20>cosmic alignment<6E>: The galactic pole pointed exactly
|
||
towards the autumnal equinoctial point, and the galactic-ecliptic node
|
||
coincided with the winter solstitial point (tropical 0<> Capricorn).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mardyks' calculation is based on the
|
||
galactic coordinate system that was defined by the International Astronomical
|
||
Union in 1958.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Source:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Raymond Mardyks, <20>When Stars
|
||
Touch the Earth<74>, in: The Mountain Astrologer Aug./Sept. 1991, pp. 1-4 and
|
||
47-48.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Private communication between
|
||
R. Mardyks and D. Koch in April 2016.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>41) Galactic Node at 5 Sagittarius (Fiorenza
|
||
Ayanamsha)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Another ayanamsha based on the galactic
|
||
equator. It was invented by Nick Anthony Fiorenza and published in his book
|
||
<93>The Star Chart. Sidereal Astrology and the Fixed Stars<72> in 2001. Fiorenza
|
||
thinks that 1 Jan. 2000 should be taken as the date of the alignment of the
|
||
solstitial points with the galactic node. He assumes an ayanamsha value of
|
||
exactly 25<32> on this date. Thus, the vernal point fell on exactly 5<> Pisces in 2000.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Source:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>https://www.lunarplanner.com/siderealastrology.html</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>31) Ayanamsha based on the Galactic Equator
|
||
IAU 1958</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha is based on galactic pole as
|
||
defined by the IAU in 1958, and it is assumed that the galactic equator
|
||
intersects with the ecliptic at sidereal 0<> Sagittarius. This ayanamsha differs
|
||
from the Skydram ayanamsha by only 19 arc seconds, but from Fioreza<7A>s ayanamsha
|
||
by slightly more than 5<>.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>32) Galactic Node at 0<> Sagittarius</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The galactic pole IAU 1958 is in fact
|
||
outdated. According to more recent observations and calculations from the year
|
||
2010, the galactic node with the ecliptic must be corrected by 3'11", and
|
||
the "Galactic Alignment" preponed to 1994 (instead of 1998). With
|
||
this ayanamsha, the galactic node is fixed exactly at sidereal 0<> Sagittarius.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Source:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Liu/Zhu/Zhang, <20>Reconsidering
|
||
the galactic coordinate system<65>, Astronomy & Astrophysics No. AA2010, Oct.
|
||
2010, p. 8.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>33) Ardra Galactic Plane Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(= Galactic equator cuts ecliptic in the
|
||
middle of Mula and the beginning of Ardra)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With this ayanamsha, the galactic equator
|
||
cuts the ecliptic exactly in the middle of the nakshatra Mula. This means that
|
||
the Milky Way passes through the middle of this lunar mansion. Here again, it
|
||
is interesting that the Sanskrit word mūlam means "root,
|
||
origin", and it seems that the circle of the lunar mansions originally
|
||
began with this nakshatra. On the opposite side, the galactic equator cuts the
|
||
ecliptic exactly at the beginning of the nakshatra Ārdrā ("the
|
||
moist, green, succulent one", feminine).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was introduced by the
|
||
American astrologer Ernst Wilhelm in 2004. He used a calculation of the
|
||
galactic node by D. Koch from the year 2001, which had a small error of 2 arc
|
||
seconds. The current implementation of this ayanamsha is based on a new
|
||
position of the Galactic pole found by Chinese astronomers in 2010.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488793"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.9.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Other ayanamshas</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>35) True Mula Ayanamsha (K. Chandra Hari)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With this ayanamsha, the star Mula (λ
|
||
Scorpionis) is assumed at 0<> Sagittarius.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Indian astrologer Chandra Hari is of
|
||
the opinion that the lunar mansion Mula corresponds to the Muladhara Chakra. He
|
||
refers to the doctrine of the Kalapurusha which assigns the 12 zodiac signs to
|
||
parts of the human body. The initial point of Aries is considered to correspond
|
||
to the crown and Pisces to the feet of the cosmic human being. In addition,
|
||
Chandra Hari notes that Mula has the advantage to be located near the galactic
|
||
centre and to have <20>no proper motion<6F>. This ayanamsha is very close to the
|
||
Fagan/Bradley ayanamsha. Chandra Hari believes it defines the original
|
||
Babylonian zodiac.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(In reality, however, the star Mula (λ
|
||
Scorpionis) has a small proper motion, too. As has been stated, the position of
|
||
the galactic centre was not known to the ancient peoples. However, they were
|
||
aware of the fact that the Milky Way crossed the ecliptic in this region of the
|
||
sky.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>K. Chandra Hari, "On the
|
||
Origin of Sidereal Zodiac and Astronomy", in: Indian Journal of History of
|
||
Science, 33(4) 1998.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Chandra Hari,
|
||
"Ayanāṃśa",
|
||
xa.yimg.com/kq/groups/26252194/1355927039/name/Ayanamsha.pdf.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.indiadivine.org/content/topic/1229109-true-ayanamsha-views-of-chandra-hari/.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The following ayanamshas were provided by
|
||
Graham Dawson (<28>Solar Fire<72>), who had taken them over from Robert Hand<6E>s
|
||
Program <20>Nova<76>. Some were also contributed by David Cochrane. Explanations by
|
||
D. Koch:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>2) De Luce Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was proposed by the American
|
||
astrologer Robert DeLuce (1877-1964). It is fixed at the birth of Jesus,
|
||
theoretically at 1 January 1 CE. However, DeLuce de facto used an ayanamsha of
|
||
26<B0>24'47 in the year 1900, which corresponds to 4 June 1 BCE as zero ayanamsha
|
||
date.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>DeLuce believes that this ayanamsha was
|
||
also used in ancient India. He draws this conclusion from the fact that the
|
||
important ancient Indian astrologer Varahamihira, who assumed the solstices on
|
||
the ingress days of the Sun into sidereal Cancer and Capricorn, allegedly lived
|
||
in the 1st century BCE. This dating of Varahamihira has recently become popular
|
||
under the influence of Hindu nationalist ideology (Hindutva). However,
|
||
historically, it cannot be maintained. Varahamihira lived and wrote in the 6th
|
||
century CE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Robert DeLuce, Constellational
|
||
Astrology According to the Hindu System, Los Angeles, 1963, p. 5.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>3) Raman Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was used by the great Indian
|
||
astrologer Bangalore Venkata Raman (1912-1998). It is based on a statement by
|
||
the medieval astronomer Bhaskara II (1184-1185), who assumed an ayanamsha of
|
||
11<B0> in the year 1183 (according to Information given by Chandra Hari,
|
||
unfortunately without giving his source). Raman himself mentioned the year 389
|
||
CE as year of zero ayanamsha in his book Hindu Predictive Astrology, pp.
|
||
378-379.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Although this ayanamsha is very close to
|
||
the galactic ayanamsha of Gil Brand, Raman apparently did not think of the possibility
|
||
to define the zodiac using the galactic centre.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Chandra Hari,
|
||
"Ayanāṃśa",
|
||
xa.yimg.com/kq/groups/26252194/1355927039/name/Ayanamsha.pdf.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>B.V. Raman, Hindu Predictive
|
||
Astrology, pp. 378-379.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>7) Shri Yukteshwar Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was allegedly recommended by
|
||
Swami Shri Yukteshwar Giri (1855-1936). We have taken over its definition from
|
||
Graham Dawson. However, the definition given by Yukteshwar himself in the
|
||
introduction of his work The Holy Science is a confusing. According to his <20>astronomical
|
||
reference books<6B>, the ayanamsha on the spring equinox 1894 was 20<32>54<35>36<33>. At
|
||
the same time he believed that this was the distance of the spring equinox from
|
||
the star Revati, which he put at the initial point of Aries. However, this is
|
||
wrong, because on that date, Revati was actually 18<31>24<32> away from the vernal
|
||
point. The error is explained from the fact that Yukteshwar used the zero ayanamsha
|
||
year 499 CE and an inaccurate Suryasiddhantic precession rate of 360<36>/24<32>000
|
||
years = 54 arcsec/year. Moreover, Yukteshwar is wrong in assigning the
|
||
above-mentioned ayanamsha value to the year 1894; in reality it applies to
|
||
1893.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Since Yukteshwar<61>s precession rate is wrong
|
||
by 4<> per year, astro.com cannot reproduce his horoscopes accurately for epochs
|
||
far from 1900. In 2000, the difference amounts to 6<>40<34>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Although this ayanamsha differs only a few
|
||
arc seconds from the galactic ayanamsha of Gil Brand, Yukteshwar obviously did
|
||
not intend to define the zodiac using the galactic centre. He actually intended
|
||
a Revati-oriented ayanamsha, but committed the above-mentioned errors in his
|
||
calculation.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Source:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Swami Sri Yukteswar, The Holy
|
||
Science, 1949, Yogoda Satsanga Society of India, p. xx.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>8) JN Bhasin Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha was used by the Indian
|
||
astrologer J.N. Bhasin (1908-1983).</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>6) Djwhal Khul Ayanamsha</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha is based on the assumption
|
||
that the Age of Aquarius will begin in the year 2117. This assumption is
|
||
maintained by a theosophical society called Ageless Wisdom, and bases itself on
|
||
a channeled message given in 1940 by a certain spiritual master called Djwhal
|
||
Khul.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Graham Dawson commented it as follows
|
||
(E-mail to Alois Treindl of 12 July 1999): <20>The "Djwhal Khul" ayanamsha
|
||
originates from information in an article in the Journal of Esoteric
|
||
Psychology, Volume 12, No 2, pp91-95, Fall 1998-1999 publ. Seven Ray
|
||
Institute). It is based on an inference that the Age of Aquarius starts in the
|
||
year 2117. I decided to use the 1st of July simply to minimize the possible
|
||
error given that an exact date is not given.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On 7 July 2020, Clifford Ribaudo sent us additional
|
||
information in a mail to Alois Treindl:<br>
|
||
<93>Also, I know the <20>real" source of the 2117 date for the DK (= Djwhal
|
||
Khul) Ayanamsa and the original provenance of it. It was not Lindsay or Robbins
|
||
or the journal of Esoteric Psychology. My friend Keith Bailey, inherited a
|
||
whole bunch of papers from Marion Walter<65>s who was one of the members of the
|
||
<93>DINA<94> group discussed in Alice Bailey<65>s books. DK answered a question from
|
||
Roberto Assagioli and in the answer he mentioned that <20>he would suggest the
|
||
start of the Aquarian Age was 177 years from the date of writing.<2E>. A copy of
|
||
that letter was given to Robbins and then at some point he mentioned it in
|
||
Journal of Esoteric Psychology.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Philipp Lindsay, <20>The Beginning
|
||
of the Age of Aquarius: 2,117 A.D.<2E>,
|
||
http://esotericastrologer.org/newsletters/the-age-of-aquarius-ray-and-zodiac-cycles/.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Esoteric Psychology, Volume 12,
|
||
No 2, pp91-95, Fall 1998-1999 publ. Seven Ray Institute.</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>39) <20>Vedic Ayanamsha<68> according to Sunil
|
||
Sheoran</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This ayanamsha is derived from ancient
|
||
Indian time cycles and astronomical information given in the Mahabharata. Its
|
||
author, Mr. Sunil Sheoran, therefore calls this ayanamsha "Vedic".</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Essential in Sheoran's argumentation is the
|
||
assumption that the two Mahabharatan solar eclipses that were observed from
|
||
Kurukshetra and Dvaraka were 18 years apart, not 36 years as is taught by
|
||
tradition and the Mahabharata itself. Also essential to Sheoran's theory is his
|
||
assumption that the traditional lengths of the yugas are too high and that in
|
||
reality a period of four yugas (caturyuga/mahāyuga) should be 120 years
|
||
rather than 12.000 divine years or 4.320.000 human years. From the mentioned
|
||
eclipse pair and historical considerations, he derives that the Mahabharata war
|
||
must have taken place in the year 827 BCE. Then he dates the beginning of the
|
||
last Manvantara on the winter solstice 4174 BCE. This is Sheoran's ayanamsha
|
||
zero date, to which he assigns the ayanamsha value -60<36>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover it must be mentioned that in
|
||
Sheoran<92>s opinion the nakshatra circle does not begin at the initial point of
|
||
the zodiac, but that 0<> Aries corresponds to 3<>20<32> in Ashvini.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Unfortunately, there are serious problems
|
||
at least in Sheoran linguistic argumentation. As to the time distance between
|
||
the two eclipses, the Mahabharata itself states:
|
||
ṣaṭtriṃśe varṣe, MBh 16.1.1 and 16.2.2. The
|
||
correct translation of this expression is "in the 36th year", whereas
|
||
Sheoran mistakenly attempts to read it as "3 x 6 = 18 years". In
|
||
addition, in texts to do with the durations of the yugas Sheoran reads
|
||
sahasrāṇi as "10" instead of "1000" and
|
||
śatāni as "1" instead of "100". Unfortunately,
|
||
Sanskrit dictionaries and grammar do not allow such translations.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Source:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Sunil Sheoran, "The
|
||
Science of Time and Timeline of World History", 2017, http://goo.gl/av6vEH
|
||
.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488794"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.10.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Conclusions</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We have found that there are basically five
|
||
definitions, not counting the manifold variations:</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo43'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>the Babylonian zodiac with Spica at 29 Virgo or Aldebaran at 15
|
||
Taurus:</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>a)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Fagan/Bradley;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>b)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>refined with Aldebaran at 15 Tau;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>c)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>P. Huber;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>d)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>J.P. Britton.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>the Greek-Hindu-Arabic zodiac with the zero point between 10 and 20<32>
|
||
east of zeta Piscium:</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>e)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Hipparchus;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>f)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Ush<73>shash<73>;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>g)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Sassanian;</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>h)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>true Revati ayanamsha</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>3.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>the Hindu astrological zodiac with Spica at 0 Libra:</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo37'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>i)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Lahiri</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>4.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>ayanamshas based on the Kaliyuga year 3600 or the 23rd year of life
|
||
of Aryabhata.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>5.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>galactic ayanamshas based on the position of the galactic centre or
|
||
the galactic nodes (= intersection points of the galactic equator with the
|
||
ecliptic).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1. is historically the oldest one, but we
|
||
are not sure about its precise astronomical definition. It could have been Aldebaran
|
||
at 15 Taurus and Antares at 15 Scorpio.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488795"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.11.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Ayanamshas with different
|
||
precession rates</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Some Hindu astrologers use ayanamshas based
|
||
on a special precession rate which is different from the modern precession
|
||
algorithm used by the Swiss Ephemeris, usually the precession rate used by the
|
||
inventor of these particular ayanamshas. They should be aware, however, that
|
||
this approach makes only sense if the tropical ephemeris they use is based on
|
||
exactly the same precession model. It is wrong to assume that tropical
|
||
ephemerides are an absolute datum. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Modern ephemerides are generated relative
|
||
to the <i style='mso-bidi-font-style:normal'>sidereal </i>reference frame ICRF
|
||
(International Celestial Reference Frame), which is close to the mean equinox
|
||
on 1 Jan. 2000, 12:00 TT. These <i style='mso-bidi-font-style:normal'>sidereal</i>
|
||
<93>raw<94> ephemerides are transformed into <i style='mso-bidi-font-style:normal'>tropical</i>
|
||
ephemerides using a modern precession model. There are several such models.
|
||
Precession IAU 1976 (Lieske) is still used by JPL Horizons. The current
|
||
standard model recommended by the IAU is IAU 2006 (Capitaine). The Swiss
|
||
Ephemeris currently uses the precession model Vondr<64>k (2011), which is
|
||
particularly good for very-long-term ephemerides. It follows that tropical
|
||
ephemerides will be different depending on the precession model that is used to
|
||
generate them. The differences will be extremely small for planetary positions
|
||
in current decades and centuries, but will grow considerably for remote epochs.
|
||
It also follows that <i style='mso-bidi-font-style:normal'>if sidereal
|
||
positions are calculated using a precession model different from the one that
|
||
was used to create the tropical ephemerides, this is an inconsistent approach</i>.
|
||
<i style='mso-bidi-font-style:normal'>In principle, the same precession model
|
||
should be used for ayanamsha as was used for the creation of the underlying
|
||
tropical ephemeris.<o:p></o:p></i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now, we have the following problem: Some
|
||
ayanamshas were defined at a time when a different precession model was in use,
|
||
either the precession model of Simon Newcomb (1895) or the precession model IAU
|
||
1976. Using different precession models, we will have differences in all the
|
||
three, tropical planetary positions, sidereal ephemeris positions, and
|
||
ayanamsha values. Let us study these differences in a table that shows all the
|
||
three for an ayanamsha that has its zero date on the equinox of the year 291
|
||
CE, on 21 March jul., 6:03 TT. (V stands for precession Vondr<64>k; N for precession
|
||
Newcomb):</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm 6.0cm 276.45pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB;mso-no-proof:yes'><span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>diff. trop. long. Sun<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>diff. ayanamsha<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>diff. sid. long. Sun<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>~ minus<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB;mso-no-proof:yes'>Year<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>(prec
|
||
V-N) in <20><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>(prec V-N) in <20><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>(prec V-N) in <20><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span></span><span lang=EN-US>17.</span></i><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB;mso-no-proof:yes'>650216</span><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US>"</span></i><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB;mso-no-proof:yes'><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US>-3000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>81.648098<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>64.059809<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.588289<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.061927</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US>-2500<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>77.891205<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>60.280286<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.610918<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.039297</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US>-2000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>67.756729<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>50.128935<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.627794<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.022422</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US>-1500<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>55.131415<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>37.492205<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.639210<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.011006</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US>-1000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>42.521677<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>24.875658<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.646019<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.004197</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>31.328666<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>13.679394<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649271<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000944</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><><A0> </span>0<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>22.109197<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>4.458959<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650238<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000022</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB;mso-no-proof:yes'>equ. 291<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>17.650216<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000000<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650216<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span> 0.000000<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E> </span>500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>14.821773<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-2.828337<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650110<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000106</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>9.060393<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-8.589402<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649795<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000421</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>4.277578<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-13.372189<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649767<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000449</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1600<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>3.393108<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-14.256697<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649806<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000410</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1700<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>2.525093<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-15.124766<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649859<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000357</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1800<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>1.671280<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-15.978645<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.649925<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000291</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1900<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>0.829937<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-16.820066<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650003<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000213</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>0.000011<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-17.650081<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650093<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000123</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2100<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-0.818850<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-18.469044<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650194<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.000022</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2200<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-1.626143<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-19.276451<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650307<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000091</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2300<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-2.420577<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-20.071012<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650435<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000219</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2400<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-3.199913<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-20.850493<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650580<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000364</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2500<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-3.960945<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-21.611692<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.650747<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.000531</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3000<span style='mso-spacerun:yes'><3E> </span><span
|
||
style='mso-spacerun:yes'><3E><></span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-7.300452<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-24.952670<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.652218<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.002002</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3500<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-9.010479<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-26.666760<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.656281<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.006065</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>4000<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>-7.165941<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-24.832623<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>17.666682<span
|
||
style='mso-tab-count:4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.016466</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><a name="_Hlk40549423"><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>As can be seen, the choice of precession model has a noticeable impact
|
||
on tropical ephemerides and the ayanamsha value. However, the difference in
|
||
sidereal ephemerides remains almost constant for the whole period considered. <o:p></o:p></span></a></p>
|
||
|
||
<p class=MsoNormal><span style='mso-bookmark:_Hlk40549423'><span lang=EN-GB
|
||
style='mso-ansi-language:EN-GB'>Now, let us assume this ayanamsha was
|
||
introduced at a time when Newcomb precession was used, but we use tropical
|
||
positions based on the modern precession model by Vondrak. <i style='mso-bidi-font-style:
|
||
normal'>If we still want to keep the sidereal ephemerides unchanged</i>, the
|
||
above table shows that we need not necessarily use the old precession model of
|
||
Newcomb; instead, we can use modern precession Vondr<64>k instead, but have to
|
||
subtract a constant value of 17.65022". The sidereal ephemeris will then
|
||
remain identical, but the tropical ephemeris and the ayanamsha will change.
|
||
Here, we must understand that the ayanamsha should not be taken as an absolute
|
||
value, it should only indicate the difference between our tropical and our
|
||
sidereal ephemeris. <a name="_Hlk40941384">With a future update of the
|
||
precession model in the Swiss Ephemeris, the tropical ephemeris and ayanamsha
|
||
will change, but the sidereal ephemeris will not</a>, because the ayanamsha
|
||
value will be adjusted automatically.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-bookmark:_Hlk40549423'><span lang=EN-GB
|
||
style='mso-ansi-language:EN-GB'>Let us also study an explicit comparison of
|
||
tropical and sidereal positions of the Sun based on both precession models
|
||
Vondr<E1>k (V) and Newcomb (N) and also using the above-mentioned correction to
|
||
the ayanamsha:<o:p></o:p></span></span></p>
|
||
|
||
<span style='mso-bookmark:_Hlk40549423'></span>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><a name="_Hlk40588097"><span
|
||
lang=EN-US><o:p> </o:p></span></a></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><i style='mso-bidi-font-style:normal'><span
|
||
lang=EN-US>epoch<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>tropical Sun<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>sidereal Sun<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>ayanamsha<o:p></o:p></span></i></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-US>-1000 V<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0> </span>271<37>14'15.75001<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>289<38>05'52.63883<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>342<34>08'23.11118<span
|
||
style='mso-tab-count:1'><3E> </span></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-US>-1000 N<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>271<37>14'58.27229<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>289<38>05'52.63457<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>342<34>09'05.63773</span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-US>eq291 V<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0> </span>359<35>59'42.34978<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span style='mso-spacerun:yes'><3E><><A0>
|
||
</span>0<>00'00.00000<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>359<35>59'42.34978<span
|
||
style='mso-tab-count:1'><3E> </span></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-US>eq291 N<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span style='mso-spacerun:yes'><3E><><A0>
|
||
</span>0<>00'00.00000<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E><><A0> </span>0<>00'00.00000<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span style='mso-spacerun:yes'><3E><><A0> </span>0<>00'00.00000</span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-US>1900 V<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>280<38>08'54.75103<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>257<35>46'10.69049<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E> </span>22<32>22'44.06054</span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span style='mso-ansi-language:DE'>1900 N<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>280<38>08'55.58096<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>257<35>46'10.69027<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E> </span>22<32>22'44.89070<span style='mso-tab-count:
|
||
1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span style='mso-ansi-language:DE'>2000
|
||
V<span style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>279<37>51'44.39186<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>256<35>05'12.79708<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span style='mso-spacerun:yes'><3E>
|
||
</span>23<32>46'31.59478<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span style='mso-ansi-language:DE'>2000 N<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>279<37>51'44.39187<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>256<35>05'12.79695<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E> </span>23<32>46'31.59492<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span style='mso-ansi-language:DE'><o:p> </o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>As can be seen, the tropical positions of the Sun and the ayanamshas,
|
||
resulting from the two different precession models, are identical only at the
|
||
initial epoch of the JPL ephemeris, on 1 Jan. 2000, whereas at other epochs
|
||
they are different from each other. On the other hand, the sidereal positions
|
||
of the Sun are practically identical at all times, independently of the
|
||
precession model chosen.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
style='mso-bookmark:_Hlk40588097'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>Unfortunately, this makes the search for the <20>correct ayanamsha<68> even
|
||
more confused than many believe. Sidereal astrologers use to ask the question
|
||
whether Lahiri or Krishnamurti or whatever ayanamsha should be used, and they
|
||
believe that the ayanamsha can be defined by some fixed value at some initial
|
||
epoch. However, this is not correct. The start value or start date of an
|
||
ayanamsha, as well as its value on any other date, depend on the precession
|
||
model inherent in the tropical ephemeris used. This fact is usually forgotten.<o:p></o:p></span></span></p>
|
||
|
||
<span style='mso-bookmark:_Hlk40588097'></span>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB'>Note, however, that this correction
|
||
method is not used with all ayanamshas. The above example uses the equinox of
|
||
the year 291 as zero ayanamsha date, which is actually the initial date of the
|
||
Krishnamurti/Senthilathiban ayanamsha. In reality, the described correction
|
||
method is not applied here. The ayanamsha is calculated using the current
|
||
precession model of the Swiss Ephemeris (Vondrak 2011) without any correction.
|
||
Sidereal ephemerides will be allowed to change whenever the precession model
|
||
will be updated.</span><span lang=EN-GB style='font-size:8.0pt;mso-bidi-font-size:
|
||
9.0pt;mso-ansi-language:EN-GB'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB'>Nor should the correction be done
|
||
with the definition of Lahiri ayanamsha as given by Lahiri himself in the
|
||
preface of the 1980 edition of his <20>Indian ephemeris<69>, where zero ayanamsha is
|
||
defined as the mean Sun on the equinox in the year 285. When the Swiss
|
||
Ephemeris updates the precession model, then the zero ayanamsha date will have
|
||
to be corrected, and the ayanamsha calculation will also be done using the new
|
||
precession model without any correction. This will have some impact on sidereal
|
||
ephemerides, however an unavoidable one. <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB'>Moreover, a correction is not
|
||
required with True Chitra Paksha ayanamsha and some other ayanamshas where the
|
||
ayanamsha is based on the real position of a fixed star. When the Swiss
|
||
Ephemeris updates the precession model, this will have practically no impact on
|
||
the sidereal ephemerides or ayanamsha. <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB'>On the other hand, with the other
|
||
definition of Lahiri ayanamsha as used by <i style='mso-bidi-font-style:normal'>Indian
|
||
Astronomical Ephemeris</i>, a correction will be required because the
|
||
definition is not based on some astronomical object or event, but on an
|
||
arbitrary value at an arbitrary epoch, based on the precession model IAU 1976.
|
||
A small correction will therefore be required to the ayanamsha in order to
|
||
provide identical sidereal positions while using our standard precession model
|
||
Vondr<E1>k 2011. <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm 6.0cm 276.45pt'><span
|
||
lang=EN-GB style='mso-ansi-language:EN-GB'>For each ayanamsha, a decision has
|
||
to be taken individually what kind of approach is required.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-GB
|
||
style='mso-ansi-language:EN-GB'>We hope that the Swiss Ephemeris, from version
|
||
2.09 on, handles this correctly, and the user should not have to worry about
|
||
precession models. One should be aware, however, that the values given for some
|
||
ayanamshas will be different from those given in older literature. The reason
|
||
is that the older literature defines the ayanamsha value based on a different
|
||
tropical ephemeris (and precession model) than the Swiss Ephemeris.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-GB
|
||
style='mso-ansi-language:EN-GB'>The following ayanamshas have been corrected
|
||
since version 2.09 by the following values:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><i style='mso-bidi-font-style:
|
||
normal'><span lang=EN-GB style='mso-ansi-language:EN-GB'>ayanamsha<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span><span style='mso-tab-count:2'><3E><><A0><A0> </span>correction<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>prec. model<o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>0 Fagan-Bradley<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'> </span>0.41256<94><span style='mso-tab-count:2'><3E><><A0><A0><A0> </span>Newcomb<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>1 Lahiri<span style='mso-spacerun:yes'><3E> </span><span style='mso-tab-count:
|
||
4'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>-0.13036<94><span style='mso-tab-count:2'><3E><><A0><A0> </span>IAU
|
||
1976<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>3 Raman<span style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:
|
||
3'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>0.82800<94><span style='mso-tab-count:2'><3E><><A0><A0><A0> </span>Newcomb<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-GB style='mso-ansi-language:
|
||
EN-GB'>5 Krishnamurti<span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0> </span>0.82800<94><span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0> </span>Newcomb<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-GB
|
||
style='mso-ansi-language:EN-GB'>43 Lahiri (1967)<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><> </span>0.82800<94><span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0> </span>Newcomb<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>(new ayanamsha!)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488796"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.12.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>On which ecliptic is the
|
||
ayanamsha measured?</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>1.<span style='mso-tab-count:1'><3E> </span>The
|
||
traditional algorithm (implemented in Swiss Ephemeris as default mode)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As has been stated, sidereal planetary
|
||
positions are computed from the following equation:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>sidereal_position = tropical_position <20>
|
||
ayanamsha,</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ayanamsha of a given date t is computed
|
||
from an initial value of the ayanamsha at some initial date (e.g. t0 = 1 Jan
|
||
1900) and the speed of the vernal point, the so-called precession rate:</span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE'>ayanamsha(t) =
|
||
ayanamsha(t0) + precession(t-t0).<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Unfortunately, this procedure is not really
|
||
clean because the two formulae do not operate on exactly the same plane. It may
|
||
work sufficiently well in an ordinary astrologer<65>s practice. However, if very
|
||
high accuracy is wanted over a long period of time, then this approach is too
|
||
simplistic. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The precession of the equinox is not only a
|
||
matter of ecliptical longitude, but a more complex phenomenon. It has two
|
||
components:</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>a)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>The soli-lunar precession: The combined gravitational pull of the
|
||
Sun and the Moon on the equatorial bulge of the Earth causes the Earth axis to
|
||
move very slowly, in the way of a spinning top. As a result of this movement,
|
||
the vernal point moves around the ecliptic with a speed of about 50<35> per year.
|
||
This cycle has a period of roughly 26000 years.</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>b)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>The planetary precession: The Earth orbit itself is not fixed. The
|
||
gravitational influence from the planets causes it to slowly change its
|
||
orientation. As a result, the obliquity of the ecliptic currently decreases by
|
||
47<94> per century. This change also has some impact on the position of the vernal
|
||
point. (Note, however, that relative to the ecliptic of a fixed date, the
|
||
equator keeps an almost constant angle, with a change of only a couple of 0.06<94>
|
||
cty-2.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Because the ecliptic plane is not fixed, it
|
||
is not fully correct to subtract an ayanamsha from the tropical position in
|
||
order to get a sidereal position. Let us take, e.g., the Fagan/Bradley
|
||
ayanamsha, which can be defined by:</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt'><span style='mso-ansi-language:
|
||
DE'>ayanamsha = 24<32>02<30>31.36<94> + P(Je-Js),<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:70.9pt'><span lang=EN-US>where Js is the
|
||
initial epoch or start date of the ayanamsha, in our case 1 Jan. 1950, and Je
|
||
is the <20>end date<74> for which the ayanamsha is to be calculated.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>24<32>02<30>31.36<94> is the value of the ayanamsha
|
||
on the initial date Js = 1 Jan 1950. It is obviously measured on the ecliptic
|
||
of Js itself. P(Je-Js) is the distance of the vernal point at the end epoch Je
|
||
from the position of the vernal point on the start epoch Js = 1 Jan 1950.
|
||
Again, this distance is measured on the ecliptic of Js.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now, the value of ayanamsha is subtracted
|
||
from a planetary position which is referred to the ecliptic of the epoch Je,
|
||
(not Js!). This approach is not really correct. The error may be very small,
|
||
but the ecliptic of Js and the ecliptic of Je are not exactly in the same
|
||
plane.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Precession polynomials found in
|
||
astronomical literature are also relative to Js. E.g. Indian Astronomical
|
||
Ephemeris 1989 (IAE 1989), p. 525, gives the following formula:</span></p>
|
||
|
||
<p class=MsoNormal><span class=im><span style='mso-ansi-language:DE'>P<sub>N</sub>
|
||
= (5029.0966 + 2.22226 * T-0.000042 * T<sup>2</sup>) * t + (1.11161 - 0.000127
|
||
* T) * t<sup>2</sup> - 0.000113 * t<sup>3</sup></span></span><span
|
||
style='mso-ansi-language:DE'><br>
|
||
<span class=im>t= (Je - Js) / 36525 ; T= (Js-2451545) / 36525<span
|
||
style='mso-spacerun:yes'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=im><span lang=EN-US>If the start date Js is
|
||
J2000 (i.e. 1 Jan. 2000, 12:00 TT), then the formula can also be written
|
||
simpler:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=im><span lang=EN-US>P<sub>N</sub> = 5029.0966 *
|
||
t + 1.11161 *<span style='mso-spacerun:yes'><3E> </span>t<sup>2</sup> - 0.000113*t<sup>3</sup><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=im><span lang=EN-US>According to IAE 1989, the
|
||
resulting value PN is <20>referred to the fixed ecliptic and equinox of Js<4A>. Thus,
|
||
in a really correct calculation this value should not be applied to a planetary
|
||
or star position relative to the ecliptic and equinox of Je. However, this is
|
||
exactly what is done when sidereal ephemerides are calculated from tropical
|
||
ones.</span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As a result, an object that does not move
|
||
relative to a fixed sidereal reference frame, still has an apparent motion
|
||
relative a sidereal zodiac. If we compute its precise tropical position for
|
||
several dates and then subtract the Fagan/Bradley or Lahiri ayanamsha for the
|
||
same dates in order to get its sidereal position, then these positions will all
|
||
be slightly different. This difference can be considerable over long periods of
|
||
time. Let us give two examples to illustrate this phenomenon.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Long-term ephemeris of some fictitious star
|
||
near the ecliptic that has no proper motion (small change in longitude):</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-left:-5.6pt;text-align:right;
|
||
text-indent:5.6pt'><b><span lang=EN-US>Date<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-left:-5.6pt;text-align:right;
|
||
text-indent:5.6pt'><b><span lang=EN-US>Longitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-left:-5.6pt;text-align:right;
|
||
text-indent:5.6pt'><b><span lang=EN-US>Latitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-12000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'55.2211</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>55'48.9448</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-11000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'54.9139</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>47'55.3635</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-10000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'46.5976</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>40'31.4551</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-9000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'32.6822</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>33'40.6511</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-8000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'16.2249</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>27'23.8494</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-7000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>16'00.1841</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>21'41.0200</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-6000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'46.8390</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>16'32.9298</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'37.4554</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>12'01.7396</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'32.2252</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>08'10.3657</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'30.4535</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>05'01.3407</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'30.9235</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>02'35.9871</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'32.3268</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>00'54.2786</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>0</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'33.6425</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-0<>00'04.7450</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'34.3645</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-0<>00'22.4060</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'34.5249</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>-0<>00'00.0196</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16;mso-yfti-lastrow:yes'>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>335<33>15'34.5216</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-top:0cm;margin-right:0cm;
|
||
margin-bottom:0cm;margin-left:-5.6pt;text-align:right;text-indent:5.6pt'><span
|
||
lang=EN-US>0<>01'01.1573</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>Long-term
|
||
ephemeris of some fictitious star with high ecliptic latitude and no proper
|
||
motion (bigger change in longitude value):</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Date<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Longitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Latitude<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-12000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>25<32>48'34.9812</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>55'17.4484</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-11000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>25<32>33'30.5709</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>53'56.6536</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-10000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>25<32>18'18.1058</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>53'20.5302</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-9000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>25<32>03'09.2517</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>53'26.8693</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-8000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>24<32>48'12.6320</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>54'12.3747</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-7000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>24<32>33'33.6267</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>55'34.7330</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-6000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>24<32>19'16.3325</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>58<35>57'33.3978</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-5000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>24<32>05'25.4844</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>00'08.8842</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-4000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>23<32>52'06.9457</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>03'21.4346</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>23<32>39'26.8689</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>07'10.0515</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>23<32>27'30.5098</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>11'32.3495</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>23<32>16'21.6081</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>16'25.0618</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>0</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>23<32>06'02.6324</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>21'44.7241</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>22<32>56'35.5649</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>27'28.1195</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>22<32>48'02.6254</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><span
|
||
lang=EN-US>59<35>33'32.3371</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16;mso-yfti-lastrow:yes'>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td width=123 valign=top style='width:92.15pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22<32>40'26.4786</span></p>
|
||
</td>
|
||
<td width=104 valign=top style='width:77.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>59<35>39'54.5816</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>Exactly the same
|
||
kind of thing happens to sidereal planetary positions if one calculates them in
|
||
the traditional way. They are actually given relative to a moving reference
|
||
frame. The <20>fixed zodiac<61> is not really fixed. When observed over long periods
|
||
of time in quick motion, it seems to wobble.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The wobbling of the ecliptic plane also
|
||
influences ayanamshas that are referred to the nodes of the galactic equator
|
||
with the ecliptic.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>2.<span style='mso-tab-count:1'><3E> </span>Consistent
|
||
ayanamsha relative to the ecliptic of date (implemented in Swiss Ephemeris
|
||
>=2.09 as an option)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As described above, the traditional
|
||
approach is to calculate the ayanamsha relative to the ecliptic of Js and then
|
||
apply this value to tropical positions relative to the eclipitic of Je. This
|
||
procedure is obviously inconsistent.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A possible consistent solution would be to
|
||
calculate the precession and ayanamsha relative to the eclipitic of the end
|
||
epoch Je rather than to the ecliptic of the start epoch Js. Then this value
|
||
would be subtracted from tropical planetary or star positions on epoch Je.
|
||
Although the wobbling effect still remains, and positions of a fixed object
|
||
will have slightly different positions at different date, this procedure is at
|
||
least consistent in itself.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>The following
|
||
table shows the differences of solar positions gained in this way from solar
|
||
positions gained in the traditional (inconsistent) way based on Lahiri
|
||
ayanamsha. The solar positions are always calculated form 1 January in the
|
||
Gregorian year.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US>year<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>diff
|
||
in <20><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-3000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-9.633</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2500<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-8.472</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-7.049</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1500<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-5.528</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-4.052</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E> </span>-500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-2.735</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>0<span style='mso-spacerun:yes'><3E><>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-1.656</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><> </span>500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.854</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.334</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.067</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1600<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.040</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1700<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.020</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1800<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.007</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1900<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1920<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1940<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1960<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1980<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2020<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2040<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.002</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2060<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.003</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2080<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.004</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2100<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.005</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2200<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.015</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2300<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.029</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2400<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.046</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.066</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.190</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.304</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>4000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.357</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note that the differences are around a
|
||
millisecond of arc or below for current decades, but greater than an arc second
|
||
2000 years ago.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, if the reference epoch is in the
|
||
remote past, e.g. when ayanamsha is calculated from a zero ayanamsha epoch on the
|
||
equinox 285 CE, then the differences are near zero only near that epoch, but
|
||
amount to 0.65<94> in 2020:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US>year<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>diff
|
||
in <20><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-3000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-4.209</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2500<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-3.250</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-2.279</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1500<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-1.408</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.720</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E> </span>-500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.258</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>0<span style='mso-spacerun:yes'><3E><>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.032</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><> </span>500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.016</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.161</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.395</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1600<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.446</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1700<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.496</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1800<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.546</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1900<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.595</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1920<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.604</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1940<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.614</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1960<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.623</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1980<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.633</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.642</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2020<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.651</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2040<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.660</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2060<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.669</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2080<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.677</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2100<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.686</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2200<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.727</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2300<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.765</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2400<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.799</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.828</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3000 <span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>-0.895</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.810</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>4000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.572</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>3. Projection onto the ecliptic of t0
|
||
(implemented in Swiss Ephemeris as an option)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The opposite solution, which would also be consistent,
|
||
would be to project the planetary positions of end date Je onto the ecliptic of
|
||
the start date of the ayanamsha JS using a correct coordinate transformation.
|
||
E.g., for the Fagan/Bradley ayanamsha, this would be the mean ecliptic of 1950;
|
||
for the Lahiri ayanamsha, the mean ecliptic of 21 March 1956.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If we follow this method, the wobbling
|
||
effect described above under (1) (traditional ayanamsha method) will not occur,
|
||
and an object that has no proper motion will keep its position forever.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The differences from the traditional method
|
||
look quite similar to method 2 above, where the calculation is consistently
|
||
done relative to the ecliptic of date:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US>year<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>diff
|
||
in <20><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-3000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-9.522</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2500<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-9.089</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-7.970</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1500<span
|
||
style='mso-spacerun:yes'><3E> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>-6.402</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-4.763</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E> </span>-500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-3.207</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>0<span style='mso-spacerun:yes'><3E><>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-1.897</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><> </span>500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.939</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.337</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.058</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1600<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.033</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1700<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.016</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1800<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.005</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1900<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1920<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1940<span style='mso-spacerun:yes'><3E> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1960<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1980<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2020<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2040<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2060<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.002</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2080<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.003</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2100<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.004</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2200<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.008</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2300<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.014</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2400<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.019</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.024</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3000<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.030</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3500<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.318</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>4000<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.967</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm'><span lang=EN-US>A comparison of the
|
||
two consistent methods 2 and 3 provides the following differences, which are
|
||
considerably smaller:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt;tab-stops:2.0cm'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US>year<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>diff
|
||
in <20><o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-3000<span
|
||
style='mso-spacerun:yes'><3E><> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.111</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2500<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.617</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-2000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.921</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1500<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.874</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US>-1000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.711</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E> </span>-500<span style='mso-spacerun:yes'><3E><><A0>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.472</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>0<span style='mso-spacerun:yes'><3E><><A0>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.241</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><> </span>500<span style='mso-spacerun:yes'><3E><><A0>
|
||
</span><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.084</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1000<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.003</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.009</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1600<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.006</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1700<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.004</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1800<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.002</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1900<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1920<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1940<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1960<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>1980<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2000<span style='mso-spacerun:yes'><3E><><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2020<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2040<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2060<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2080<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.001</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2100<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.002</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2200<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.006</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2300<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.015</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2400<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.027</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>2500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.042</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.219</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm;tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>3500<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-0.621</span></p>
|
||
|
||
<p class=MsoNormal style='tab-stops:2.0cm'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>4000<span style='mso-spacerun:yes'><3E><> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>-1.324 </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A philosophical side note: This method is
|
||
geometrically more correct than the traditional one, but still has a problem.
|
||
For, if we want to refer everything to the ecliptic of some initial date t0, we
|
||
will have to choose that date very carefully. Its ecliptic ought to be of
|
||
<93>cosmic<94> importance. The ecliptic of 1950 or the one of 1900 or 1956 (Lahiri)
|
||
are obviously meaningless and not suitable as a reference plane. So, how about
|
||
some historical date on which the tropical and the sidereal zero point
|
||
coincided? Although this may be considered as a kind of cosmic anniversary (the
|
||
ancient Indians and Sassanians did so), the ecliptic plane of that time does
|
||
not have an <20>eternal<61> value. E.g., it is different from the ecliptic plane of
|
||
the previous anniversary around the year 26000 BCE, and it is also different
|
||
from the ecliptic plane of the next cosmic anniversary around the year 26000
|
||
CE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Thus, it may be wiser to use method 2, i.e.
|
||
a consistent ayanamsha calculation on the ecliptic of date.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Method 3 can also be used for computations
|
||
of the following kind:</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><a name="_Hlk17748711"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>c)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Astronomers may want to calculate positions referred to a standard
|
||
equinox like J2000, B1950, or B1900, or to any other equinox.</span></a></p>
|
||
|
||
<span style='mso-bookmark:_Hlk17748711'></span>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>d)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Astrologers may be interested in the calculation of
|
||
precession-corrected transits. See explanations in the next chapter.</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>e)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>The algorithm can be applied to any user-defined sidereal mode, if
|
||
the ecliptic of its reference date is considered to be astrologically
|
||
significant.</span></p>
|
||
|
||
<p class=listlettered style='mso-list:l34 level1 lfo48'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>f)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>The algorithm makes the problems of the traditional method visible.
|
||
It shows the dimensions of the inherent inaccuracy of the traditional method.
|
||
(Calculate some star position using the traditional method and compare it to
|
||
the same star<61>s position if calculated using this method.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the planets and for centuries close to
|
||
t0, the difference from the traditional procedure will be only a few arc
|
||
seconds in longitude. Note that the Sun will have an ecliptical latitude of
|
||
several arc minutes after a few centuries.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the lunar nodes, the procedure is as
|
||
follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Because the lunar nodes have to do with
|
||
eclipses, they are actually points on the ecliptic of date, i.e. on the
|
||
tropical zodiac. Therefore, we first compute the nodes as points on the
|
||
ecliptic of date and then project them onto the sidereal zodiac. This procedure
|
||
is very close to the traditional method of computing sidereal positions (a
|
||
matter of arc seconds). However, the nodes will have a latitude of a couple of
|
||
arc minutes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the axes and houses, we compute the
|
||
points where the horizon or the house lines intersect with the sidereal plane
|
||
of the zodiac, not with the ecliptic of date. Here, there are greater
|
||
deviations from the traditional procedure. If t is 2000 years from t0, the
|
||
difference between the ascendant positions might well be 1/2 degree.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>4.<span style='mso-tab-count:1'><3E> </span>Fixed-star-bound
|
||
ecliptic (implemented in Swiss Ephemeris for some selected stars)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One can use a stellar object as an anchor
|
||
for the sidereal zodiac and make sure that a particular stellar object is
|
||
always at a certain position on the ecliptic of date. E.g. one might want to
|
||
have Spica always at 0 Libra or the Galactic Center always at 0 Sagittarius.
|
||
There is nothing against this method from a geometrical point of view. But it
|
||
must be noted that this system is not really fixed either, because it is still
|
||
based on the true ecliptic of date, which is actually moving. Moreover, the
|
||
fixed stars that are used as anchor stars have a small proper motion, as well.
|
||
Thus, if Spica is assumed as a fixed point, then its proper motion, its
|
||
aberration, its gravitational deflection, and its parallax will necessarily
|
||
affect the position and motion of all other stars (in addition to their own
|
||
proper motion, aberration, etc.). Note, the Galactic Centre (Sgr A*) is not
|
||
really fixed either, but has a small apparent motion that reflects the motion
|
||
of the Sun around it.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This solution has been implemented for the
|
||
following stars and fixed positions:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Spica/Citra at 180<38> (<28>True
|
||
Chitra Paksha Ayanamsha<68>)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Revati (zeta Piscium) at
|
||
359<B0>50<92></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Pushya (Asellus Australis) at
|
||
106<B0> (PVR Narasimha Rao)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Mula (lambda Scorpionis) at
|
||
240<B0> (Chandra Hari)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic centre at 0<>
|
||
Sagittarius</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic centre at 0<> Capricorn
|
||
(David Cochrane)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic centre at golden
|
||
section between 0<> Sco and 0<> Aqu (R. Gil Brand)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Polar longitude of galactic
|
||
centre in the middle of nakshatra Mula (E. Wilhelm)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With Swiss Ephemeris versions before 2.05,
|
||
the apparent position of the star relative to the mean ecliptic plane of date
|
||
was used as the reference point of the zodiac. E.g. with the True Chitra
|
||
ayanamsha, the star Chitra/Spica had the apparent position 180<38> exactly.
|
||
However, the true position was slightly different. Since version 2.05, the star
|
||
is always exactly at 180<38>, not only its apparent, but also its true position.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>5. Galactic-equator-based ayanamshas
|
||
(implemented in Swiss Ephemeris)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Some ayanamshas are based on the galactic
|
||
node, i.e. the intersection of the galactic equator with the mean ecliptic of
|
||
date. These ayanamshas include:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic equator (IAU 1958)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic equator true/modern</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo47'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Galactic equator in middle of
|
||
Mula</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Note, the Mardyks ayanamsha, although
|
||
derived from the galactic equator, does not work like this. It is calculated
|
||
using the method described above under 1).)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The galactic node is calculated from the
|
||
true position of the galactic pole, not the apparent one. As a result, if the
|
||
position of the galactic pole is calculated using the ayanamsha that has the
|
||
galactic node at 0<> Sagittarius, then the true position of the pole is exactly
|
||
at sidereal 150<35>, but its apparent position is slightly different from that.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Here again, it must be stated that the
|
||
ecliptic plane used is the true ecliptic of date, which is moving, with the
|
||
only difference that the initial point is defined by the intersection of the ecliptic
|
||
with the galactic equator.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>6. The long-term mean Earth-Sun plane
|
||
(not implemented in Swiss Ephemeris)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To avoid the problem of choice of a
|
||
reference ecliptic, one could use a kind of <20>average ecliptic<69>. The mechanism
|
||
of the planetary precession mentioned above works in a similar way as the
|
||
mechanism of the luni-solar precession. The motion of the Earth orbit can be
|
||
compared to a spinning top, with the Earth mass equally distributed around the
|
||
whole orbit. The other planets, especially Venus and Jupiter, cause it to move
|
||
around an average position. But unfortunately, this <20>long-term mean Earth-Sun
|
||
plane<94> is not really stable either, and therefore not suitable as a fixed
|
||
reference frame.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The period of this cycle is about 75000
|
||
years. The angle between the long-term mean plane and the ecliptic of date is
|
||
currently about 1<>33<33>, but it varies considerably. (This cycle must not be
|
||
confused with the period between two maxima of the ecliptic obliquity, which is
|
||
about 40000 years and often mentioned in the context of planetary precession.
|
||
This is the time it takes the vernal point to return to the node of the
|
||
ecliptic (its rotation point), and therefore the oscillation period of the
|
||
ecliptic obliquity.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>7. The solar system rotation plane
|
||
(implemented in Swiss Ephemeris as an option)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The solar system as a whole has a rotation
|
||
axis, too, and its equator is quite close to the ecliptic, with an inclination
|
||
of 1<>34<33>44<34> against the ecliptic of the year 2000. This plane is extremely
|
||
stable and perhaps the only convincing candidate for a fixed zodiac plane.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This method avoids the problem of method
|
||
3). No particular ecliptic has to be chosen as a reference plane. The only
|
||
remaining problem is the choice of the zero point.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>It does not make much sense to use this
|
||
algorithm for predefined sidereal modes. One can use it for user-defined
|
||
ayanamshas.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488797"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.8.13.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>More benefits from our new
|
||
sidereal algorithms: standard equinoxes and precession-corrected transits</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Method no. 3, the transformation to the
|
||
ecliptic of t0, opens two more possibilities:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>You can compute positions referred to any
|
||
equinox, 2000, 1950, 1900, or whatever you want. This is sometimes useful when
|
||
Swiss Ephemeris data ought to be compared with astronomical data, which are
|
||
often referred to a standard equinox.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are predefined sidereal modes for
|
||
these standard equinoxes:</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>18) J2000</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>19) J1900</span></p>
|
||
|
||
<p class=ayanamsa><span lang=EN-US>20) B1950</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, it is possible to compute
|
||
precession-corrected transits or synastries with very high precision. An
|
||
astrological transit is defined as the passage of a planet over the position in
|
||
your birth chart. Usually, astrologers assume that tropical positions on the
|
||
ecliptic of the transit time has to be compared with the positions on the
|
||
tropical ecliptic of the birth date. But it has been argued by some people that
|
||
a transit would have to be referred to the ecliptic of the birth date. With the
|
||
new Swiss Ephemeris algorithm (method no. 3) it is possible to compute the
|
||
positions of the transit planets referred to the ecliptic of the birth date,
|
||
i.e. the so-called precession-corrected transits. This is more precise than
|
||
just correcting for the precession in longitude (see details in the
|
||
programmer's documentation swephprg.doc, Ch. 8.1).</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488798"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Apparent versus true planetary
|
||
positions</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss ephemeris provides the
|
||
calculation of <span class=italic>apparent</span> or <span class=italic>true</span>
|
||
planetary positions. Traditional astrology works with apparent positions.
|
||
<94>Apparent<94> means that the position where we see the planet is used, not the one
|
||
where it actually is. Because the light's speed is finite, a planet is never
|
||
seen exactly where it is. (see above, 2.1.3 <20>The details of coordinate
|
||
transformation<94>, light-time and aberration) Astronomers therefore make a
|
||
difference between apparent and true positions. However, this effect is below 1
|
||
arc minute.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Most astrological ephemerides provide
|
||
apparent positions. However, this may be wrong. The use of apparent positions
|
||
presupposes that astrological effects can be derived from one of the four
|
||
fundamental forces of physics, which is impossible. Also, many astrologers
|
||
think that astrological <20>effects<74> are a synchronistic phenomenon (the ones
|
||
familiar with physics may refer to the Bell theorem). For such reasons, it
|
||
might be more convincing to work with true positions.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, the Swiss Ephemeris supports
|
||
so-called astrometric positions, which are used by astronomers when they
|
||
measure positions of celestial bodies with respect to fixed stars. These
|
||
calculations are of no use for astrology, though.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488799"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Geocentric, topocentric,
|
||
heliocentric, barycentric, and planetocentric positions</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>More precisely speaking, common ephemerides
|
||
tell us the position where we would see a planet if we stood in the center of
|
||
the Earth and could see the sky. But it has often been argued that a planet<65>s
|
||
position ought to be referred to the geographic position of the observer (or
|
||
the birth place). This can make a difference of several arc seconds with the
|
||
planets and even more than a degree with the Moon! Such a position referred to
|
||
the birth place is called the <span class=italic>topocentric</span> planetary
|
||
position. The observation of transits over the Moon might help to find out
|
||
whether or not this method works better.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For very precise topocentric calculations,
|
||
the Swiss Ephemeris not only requires the geographic position, but also its
|
||
altitude above sea. An altitude of 3000 m (e.g. Mexico City) may make a
|
||
difference of more than 1 arc second with the Moon. With other bodies, this
|
||
effect is of the amount of a 0.01<94>. The altitudes are referred to the
|
||
approximate Earth ellipsoid. Local irregularities of the geoid have been
|
||
neglected.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Our topocentric lunar positions differ from
|
||
the NASA positions (s. the Horizons Online Ephemeris System
|
||
http://ssd.jpl.nasa.gov) by 0.2 - 0.3 arc sec. This corresponds to a geographic
|
||
displacement by a few 100 m and is about the best accuracy possible. In the
|
||
documentation of the Horizons System, it is written that: "The Earth is
|
||
assumed to be a rigid body. ... These Earth-model approximations result in
|
||
topocentric station location errors, with respect to the reference ellipsoid,
|
||
of less than 500 meters."</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss ephemeris also allows the
|
||
computation of <span class=italic>apparent</span> or <span class=italic>true
|
||
topocentric</span> positions.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With the lunar nodes and apogees, Swiss
|
||
Ephemeris does not make a difference between topocentric and geocentric
|
||
positions. There are many ways to define these points topocentrically. The
|
||
simplest one is to understand them as axes rather than points somewhere in
|
||
space. In this case, the geocentric and the topocentric positions are
|
||
identical, because an axis is an infinite line that always points to the same
|
||
direction, not depending on the observer's position.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, the Swiss Ephemeris supports the
|
||
calculation of <span class=italic>heliocentric</span>, <span class=italic>barycentric,
|
||
</span><span class=italic><span style='font-style:normal'>and</span>
|
||
planetetocentric</span> positions of the planets. <i style='mso-bidi-font-style:
|
||
normal'>Heliocentric</i> positions are positions as seen from the center of the
|
||
Sun rather than from the center of the Earth. <i style='mso-bidi-font-style:
|
||
normal'>Barycentric</i> ones are positions as seen from the center of the solar
|
||
system, which is always close to but not identical to the center of the Sun.
|
||
And <i style='mso-bidi-font-style:normal'>planetocentric</i> positions are
|
||
relative to the center of some other object (planet, moon) of the solar system.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488800"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Heliacal Events, Eclipses,
|
||
Occultations, and Other Planetary Phenomena</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488801"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>5.1.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Heliacal Events of the Moon, Planets and Stars</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488802"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.1.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Introduction</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>From Swiss Ephemeris version 1.76 on,
|
||
heliacal events have been included. The heliacal rising and setting of planets
|
||
and stars was very important for ancient Babylonian and Greek astronomy and
|
||
astrology. Also, first and last visibility of the Moon can be calculated, which
|
||
are important for many calendars, e.g. the Islamic, Babylonian and ancient
|
||
Jewish calendars.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The heliacal events that can be determined
|
||
are:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Inferior planets<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Heliacal rising (morning first)</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Heliacal setting (evening last)</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Evening first</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Morning last</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Superior planets and stars<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Heliacal rising</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Heliacal setting</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;text-indent:0cm;mso-list:none'><span
|
||
lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Moon<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Evening first</span></p>
|
||
|
||
<p class=ListBullet1 style='margin-left:1.0cm;mso-list:l35 level2 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:"Courier New";mso-fareast-font-family:"Courier New"'><span
|
||
style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Morning last</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The acronychal risings and settings (also
|
||
called cosmical settings) of superior planets are a different matter. They will
|
||
be added in a future version of the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The principles behind the calculation are
|
||
based on the visibility criterion of Schaefer [1993, 2000], which includes
|
||
dependencies on aspects of:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Position of celestial objects<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>like
|
||
the position and magnitude of the Sun, Moon and the studied celestial object,</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Location and optical properties
|
||
observer<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>like
|
||
his/her location (longitude, latitude, height), age, acuity and possible
|
||
magnification of optical instruments (like binoculars)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Meteorological circumstances<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>mainly
|
||
expressed in the astronomical extinction coefficient, which is determined by
|
||
temperature, air pressure, humidity, visibility range (air quality).</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><strong><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol;font-weight:normal;mso-bidi-font-weight:bold'><span style='mso-list:
|
||
Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span></strong><![endif]><strong><span lang=EN-US
|
||
style='font-family:"Segoe UI",sans-serif'>Contrast between studied object and
|
||
sky background<o:p></o:p></span></strong></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>The
|
||
observer<92>s eye can on detect a certain amount of contract and this contract
|
||
threshold is the main body of the calculations</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the following sections above aspects
|
||
will be discussed briefly and an idea will be given what functions are
|
||
available to calculate the heliacal events. Lastly the future developments will
|
||
be discussed.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488803"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.1.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Aspect determining visibility</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The theory behind this visibility criterion
|
||
is explained by Schaefer [1993, 2000] and the implemented by Reijs [2003] and
|
||
Koch [2009]. The general ideas behind this theory are explained in the
|
||
following subsections.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Position of celestial objects</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To determine the visibility of a celestial
|
||
object it is important to know where the studied celestial object is and what
|
||
other light sources are in the sky. Thus beside determining the position of the
|
||
studied object and its magnitude, it also involves calculating the position of
|
||
the Sun (the main source of light) and the Moon. This is common functions
|
||
performed by Swiss Ephemeris.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Geographic location</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The location of the observer determines the
|
||
topocentric coordinates (incl. influence of refraction) of the celestial object
|
||
and his/her height (and altitude of studied object) will have influence on the
|
||
amount of airmass that is in the path of celestial object<63>s light.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Optical properties of observer</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The observer<65>s eyes will determine the
|
||
resolution and the contrast differences he/she can perceive (depending on age
|
||
and acuity), furthermore the observer might use optical instruments (like
|
||
binocular or telescope).</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Meteorological circumstances</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The meteorological circumstances are very
|
||
important for determining the visibility of the celestial object. These
|
||
circumstances influence the transparency of the airmass (due to Rayleigh & aerosol
|
||
scattering and ozone & water absorption) between the celestial object and
|
||
the observer<65>s eye. This result in the astronomical extinction coefficient
|
||
(AEC: ktot). As this is a complex environment, it is sometimes <20>easier<65> to use
|
||
a certain AEC, instead of calculating it from the meteorological circumstances.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parameters are stored in the datm
|
||
(Pressure [mbar], Temperature [C], Relative humidity [%], AEC [-]) array.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Contrast between object and sky
|
||
background</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>All the above aspects influence the
|
||
perceived brightness of the studied celestial object and its background sky.
|
||
The contrast threshold between the studied object and the background will
|
||
determine if the observer can detect the studied object.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488804"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.1.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Functions to determine the
|
||
heliacal events</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Two functions are seen as the spill of
|
||
calculating the heliacal events:</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Determining the contrast
|
||
threshold (swe_vis_limit_magn)</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Based on all the aspects mentioned earlier,
|
||
the contrast threshold is determine which decides if the studied object is
|
||
visible by the observer or not.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Iterations to determine when
|
||
the studied object is really visible (swe_heliacal_ut)</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In general this procedure works in such a
|
||
way that it finds (through iterations) the day that conjunction/opposition
|
||
between Sun and studied object happens and then it determines, close to Sun<75>s
|
||
rise or set (depending on the heliacal event), when the studied object is
|
||
visible (by using the </span><span class=functions><span lang=EN-US>swe_vis_limit_magn</span></span><span
|
||
lang=EN-US> function).</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Geographic limitations of
|
||
swe_heliacal_ut() and strange behavior of planets in high geographic latitudes</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This function is limited to geographic
|
||
latitudes between 60S and 60N. Beyond that the heliacal phenomena of the
|
||
planets become erratic. We found cases of strange planetary behavior even at
|
||
55N.</span></p>
|
||
|
||
<p class=MsoNormal style='text-indent:14.2pt'><span lang=EN-US>An example:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>At 0E, 55N, with an extinction coefficient
|
||
0.2, Mars had a heliacal rising on 25 Nov. 1957. But during the following weeks
|
||
and months Mars did not constantly increase its height above the horizon before
|
||
Sunrise. In contrary, it disappeared again, i.e. it did a <20>morning last<73> on 18
|
||
Feb. 1958. Three months later, on 14 May 1958, it did a second morning first
|
||
(heliacal rising). The heliacal setting or evening last took place on 14 June
|
||
1959.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Currently, this special case is not handled
|
||
by swe_heliacal_ut(). The function cannot detect <20>morning lasts<74> of Mars and
|
||
following <20>second heliacal risings<67>. The function only provides the heliacal
|
||
rising of 25 Nov. 1957 and the next ordinary heliacal rising in its ordinary
|
||
synodic cycle which took place on 11 June 1960.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, we may find a solution for such
|
||
problems in future releases of the Swiss Ephemeris and even extend the geographic
|
||
range of swe_heliacal_ut() to beyond +/- 60.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Visibility of Venus and the Moon
|
||
during day</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the Moon, swe_heliacal_ut() calculates
|
||
the evening first and the morning last. For each event, the function returns
|
||
the optimum visibility and a time of visibility start and visibility end. Note,
|
||
that on the day of its morning last or evening first, the Moon is often visible
|
||
for almost the whole day. It even happens that the crescent first becomes
|
||
visible in the morning after its rising, then disappears, and again reappears
|
||
during culmination, because the observation conditions are better as the Moon stands
|
||
high above the horizon. The function swe_heliacal_ut() does not handle this in
|
||
detail. Even if the Moon is visible after Sunrise, the function assumes that
|
||
the end time of observation is at Sunrise. The evening fist is handled in the
|
||
same way.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With Venus, we have a similar situation.
|
||
Venus is often accessible to naked eye observation during day, and sometimes
|
||
even during inferior conjunction, but usually only at a high altitude above the
|
||
horizon. This means that it may be visible in the morning at its heliacal
|
||
rising, then disappear and reappear during culmination. (Whoever does not
|
||
believe me, please read the article by H.B. Curtis listed under <20>References<65>.) The
|
||
function swe_heliacal_ut() does not handle this case. If binoculars or a
|
||
telescope is used, Venus may be even observable during most of the day on which
|
||
it first appears in the east.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488805"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.1.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Future developments</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The section of the Swiss Ephemeris software
|
||
is still under development. The acronychal events of superior planets and stars
|
||
will be added. And comparing other visibility criterions will be included; like
|
||
Schoch<92>s criterion [1928], Hoffman<61>s overview [2005] and Caldwall & Laney criterion
|
||
[2005].</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488806"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.1.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>References</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Caldwell, J.A.R., Laney, C.D.,
|
||
First visibility of the lunar crescent, http://www.saao.ac.za/public-info/Sun-Moon-stars/Moon-index/lunar-crescent-visibility/first-visibility-of-lunar-crescent/,
|
||
2005, viewed March, 30th, 2009</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>H.B. Curtis, Venus Visible at
|
||
inferior conjunction, in : Popular Astronomy vol. 18 (1936), p. 44; online at
|
||
http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1936PA.....44...18C&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Hoffman, R.E., Rational design
|
||
of lunar-visibility criteria, The observatory, Vol. 125, June 2005, No. 1186,
|
||
pp 156-168.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Reijs, V.M.M., Extinction angle
|
||
and heliacal events, http://www.iol.ie/~geniet/eng/extinction.htm, 2003, viewed
|
||
March, 30th, 2009</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Schaefer, B., Astronomy and the
|
||
limit of vision, Vistas in astronomy, 36:311, 1993</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Schaefer, B., New methods and
|
||
techniques for historical astronomy and archeoastronomy, Archeoastronomy, Vol.
|
||
XV, 2000, page 121-136</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Schoch, K., Astronomical and
|
||
calendrical tables in Langdon. S., Fotheringham, K.J., The Venus tables of
|
||
Amninzaduga: A solution of Babylonian chronology by means of Venus observations
|
||
of the first dynasty, Oxford, 1928.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488807"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>5.2.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Eclipses, occultations, risings, settings, and other planetary
|
||
phenomena</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris also includes functions
|
||
for many calculations concerning solar and lunar eclipses. You can:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>search for eclipses or occultations,
|
||
globally or for a given geographical position;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>compute global or local
|
||
circumstances of eclipses or occultations;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>compute the geographical
|
||
position where an eclipse is central.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, you can compute for all planets
|
||
and asteroids:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>risings and settings (also for
|
||
stars);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>midheaven and lower heaven
|
||
transits (also for stars);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>height of a body above the
|
||
horizon (refracted and true, also for stars);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>phase angle;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>phase (illumined fraction of
|
||
disc);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>elongation (angular distance
|
||
between a planet and the Sun);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>apparent diameter of a
|
||
planetary disc;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>apparent magnitude.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488808"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Sidereal Time, Ascendant, MC,
|
||
Houses, Vertex</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris package also includes a
|
||
function that computes the Ascendant, the MC, the houses, the Vertex, and the
|
||
Equatorial Ascendant (sometimes called "East Point").</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488809"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.1.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Sidereal Time</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris versions until 1.80 used
|
||
the IAU 1976 formula for Sidereal time. Since version 2.00 it uses sidereal
|
||
time based on the IAU2006/2000 precession/nutation model.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As this solution is not good for the whole
|
||
time range of JPL Ephemeris DE431, we only use it between 1850 and 2050.
|
||
Outside this period, we use a solution based on the long term precession model
|
||
Vondrak 2011, nutation IAU2000 and the mean motion of the Earth according to
|
||
Simon & alii 1994. To make the function continuous we add some constant
|
||
values to our long-term function before 1850 and after 2050.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Vondrak/Capitaine/Wallace, "New
|
||
precession expressions, valid for long time intervals", in A&A 534,
|
||
A22(2011).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Simon & alii, "Precession formulae
|
||
and mean elements for the Moon and the Planets", A&A 282 (1994), p.
|
||
675/678.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488810"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.2.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Astrological House Systems</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The following house methods have been
|
||
implemented so far:</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488811"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Placidus</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This system is named after the Italian monk
|
||
Placidus de Titis (1590-1668). The cusps are defined by divisions of
|
||
semidiurnal and seminocturnal arcs. The 11th cusp is the point on the ecliptic
|
||
that has completed 2/3 of its semidiurnal arc, the 12th cusp the point that has
|
||
completed 1/3 of it. The 2nd cusp has completed 2/3 of its seminocturnal arc,
|
||
and the 3rd cusp 1/3.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488812"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Koch/GOH</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This system is called after the German
|
||
astrologer Walter Koch (1895-1970). Actually it was invented by Fiedrich
|
||
Zanzinger and Heinz Specht, but it was made known by Walter Koch. In
|
||
German-speaking countries, it is also called the
|
||
"Geburtsorth<74>usersystem" (GOHS), i.e. the "Birth place house
|
||
system". Walter Koch thought that this system was more related to the
|
||
birth place than other systems, because all house cusps are computed with the
|
||
"polar height of the birth place", which has the same value as the
|
||
geographic latitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This argumentation shows actually a poor
|
||
understanding of celestial geometry. With the Koch system, the house cusps are
|
||
actually defined by horizon lines at different times. To calculate the cusps 11
|
||
and 12, one can take the time it took the MC degree to move from the horizon to
|
||
the culmination, divide this time into three and see what ecliptic degree was
|
||
on the horizon at the thirds. There is no reason why this procedure should be
|
||
more related to the birth place than other house methods.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488813"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Regiomontanus</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Named after the Johannes M<>ller (called
|
||
"Regiomontanus", because he stemmed from K<>nigsberg) (1436-1476).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The equator is divided into 12 equal parts
|
||
and great circles are drawn through these divisions and the north and south
|
||
points on the horizon. The intersection points of these circles with the
|
||
ecliptic are the house cusps.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488814"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Campanus</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Named after Giovanni di Campani
|
||
(1233-1296).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The vertical great circle from east to west
|
||
is divided into 12 equal parts and great circles are drawn through these
|
||
divisions and the north and south points on the horizon. The intersection
|
||
points of these circles with the ecliptic are the house cusps.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488815"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Equal Systems</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Equal houses from Ascendant</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The zodiac is divided into 12 houses of 30
|
||
degrees each starting from the Ascendant.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Equal houses from Midheaven</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The zodiac is divided into 12 houses of 30
|
||
degrees each starting from MC + 90 degrees.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Vehlow-equal system</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Equal houses with the Ascendant positioned
|
||
in the middle of the first house.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Whole Sign houses</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The first house starts at the beginning of
|
||
the zodiac sign in which the ascendant is. Each house covers a complete sign.
|
||
This method was used in Hellenistic astrology and is still used in Hindu
|
||
astrology.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Whole Sign houses starting at
|
||
0<B0> Aries</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The first house starts at the beginning of
|
||
Aries.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488816"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Porphyry Houses and Related
|
||
House Systems</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Porphyry Houses</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Each quadrants is trisected in three equal
|
||
parts on the ecliptic.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Sripati Houses</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is a traditional Indian house system.
|
||
In a first step, Porphyry houses are calculated. The cusps of each new house
|
||
will be the midpoint between the last and the current. So house 1 will be equal
|
||
to:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt'><span lang=EN-US>H1' = (H1 - H12)
|
||
/ 2 + H12</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt'><span lang=EN-US>H2' = (H2 - H1)
|
||
/ 2 + H1</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>And so on.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Pullen SD (Sinusoidal Delta,
|
||
also known as <20>Neo-Porphyry<72>)</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This house system was invented in 1994 by
|
||
Walter Pullen, the author of the astrology software Astrolog. Like the Porphyry
|
||
house system, this house system is based on the idea that the division of the
|
||
houses must be relative to the ecliptic sections of the quadrants only, not
|
||
relative to the equator or diurnal arcs. For this reason, Pullen originally
|
||
called it <20>Neo-Porphyry<72>. However, the sizes of the houses of a quadrant are
|
||
not equal. Pullen describes it as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>Like Porphyry except instead of simply
|
||
trisecting quadrants, fit the house widths to a sine wave such that the
|
||
2nd/5th/8th/11th houses are expanded or compressed more based on the relative
|
||
size of their quadrants.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In practice, an ideal house size of 30<33>
|
||
each is assumed, then half of the deviation of the quadrant from 90<39> is added
|
||
to the middle house of the quadrant. The remaining half is bisected again into
|
||
quarters, and a quarter is added to each of the remaining houses. Pullen
|
||
himself puts it as follows:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;margin-right:0cm;margin-bottom:
|
||
3.0pt;margin-left:14.2pt'><span lang=EN-US>"Sinusoidal Delta"
|
||
(formerly "Neo-Porphyry") houses</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>Asc<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12th<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>11th<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>MC<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>9th<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>8th<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>7th</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt'><span
|
||
lang=EN-US>+----------+----------+----------+----------+----------+----------+</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt'><span
|
||
lang=EN-US>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>angle<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt'><span
|
||
style='mso-ansi-language:DE'>x+n<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>x<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>x+n<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>x+3n<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>x+4n<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>x+3n<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>In January 2016,
|
||
in a discussion in the Swiss Ephemeris Yahoo Group, Alois Treindl criticized
|
||
that Pullen<65>s code only worked as long as the quadrants were greater than 30<33>,
|
||
whereas negative house sizes resulted for the middle house of quadrants smaller
|
||
than 30<33>. It was agreed upon that in such cases the size of the house had to be
|
||
set to 0.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>https://groups.yahoo.com/neo/groups/swisseph/conversations/topics/5579</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>https://groups.yahoo.com/neo/groups/swisseph/conversations/topics/5606</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Pullen SR (Sinusoidal Ratio)</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On 24 Jan. 2016, during the above-mentioned
|
||
discussion in the Swiss Ephemeris Yahoo Group, Walter Pullen proposed a better
|
||
solution of a sinusoidal division of the quadrants, which does not suffer from
|
||
the same problem. He wrote:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>It's possible to do other than simply add
|
||
sine wave offsets to houses (the "Sinusoidal Delta" house system
|
||
above). Instead, let's proportion or ratio the entire house sizes themselves to
|
||
each other based on the sine wave constants, or multiply instead of add. That
|
||
results in using a "sinusoidal ratio" instead of a "sinusoidal
|
||
delta", so this alternate method could be called "Sinusoidal Ratio
|
||
houses". As before, let "x" be the smallest house in the
|
||
compressed quadrant. There's a ratio "r" multiplied by it to get the
|
||
slightly larger 10th and 12th houses. The value "r" starts out at 1.0
|
||
for 90 degree quadrants, and gradually increases as quadrant sizes differ.
|
||
Houses in the large quadrant have "r" multiplied to "x" 3
|
||
times (or 4 times for the largest quadrant). That results in the (0r, 1r, 3r,
|
||
4r) distribution from the sine wave above. This is summarized in the chart
|
||
below:<3A></span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt;text-indent:14.2pt'><span
|
||
lang=EN-US>"Sinusoidal Ratio" houses</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>Asc<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>12th<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>11th<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>MC<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>9th<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>8th<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span>7th</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>|</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>+----------+----------+----------+----------+----------+----------+</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>angle<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>angle</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:63.8pt 109.9pt 157.5pt 203.7pt 250.6pt 297.7pt'><span
|
||
lang=EN-US>rx<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>x<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>rx<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>r<sup>3</sup>x<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>r<sup>4</sup>x<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>r<sup>3</sup>x</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US><3E>The unique
|
||
values for "r" and "x" can be computed based on the
|
||
quadrant size "q", given the equations rx + x + rx = q, r<sup>3</sup>x
|
||
+ r<sup>4</sup>x + r<sup>3</sup>x = 180 - q.<2E></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>https://groups.yahoo.com/neo/groups/swisseph/conversations/topics/5579</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488817"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.7.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Axial rotation systems</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Meridian system</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The equator is partitioned into 12 equal
|
||
parts starting from the ARMC. Then the ecliptic points are computed that have
|
||
these divisions as their right ascension. Note: The ascendant is different from
|
||
the 1st house cusp.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Carter<65>s poli-equatorial houses</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The equator is partitioned into 12 equal
|
||
parts starting from the right ascension of the ascendant. Then the ecliptic
|
||
points are computed that have these divisions as their right ascension. Note:
|
||
The MC is different from the 10th house cusp.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The prefix <20>poli-<2D> might stand for <20>polar<61>.
|
||
(Speculation by DK.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Carter<65>s own words:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>...the houses are demarcated by circles
|
||
passing through the celestial poles and dividing the equator into twelve equal
|
||
arcs, the cusp of the 1st house passing through the ascendant. This system,
|
||
therefore, agrees with the natural rotation of the heavens and also produces,
|
||
as the Ptolemaic (equal) does not, distinctive cusps for each house ...<2E></span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Charles Carter (1947, 2nd ed.
|
||
1978) Essays on the Foundations of Astrology. Theosophical Publishing House,
|
||
London. p. 158-159.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.exeterastrologygroup.org.uk/2014/12/charles-carters-forgotten-house-system.html</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488818"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.8.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Morinus system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The equator is divided into 12 equal parts
|
||
starting from the ARMC. The resulting 12 points on the equator are transformed
|
||
into ecliptic coordinates. Note: The Ascendant is different from the 1st cusp,
|
||
and the MC is different from the 10th cusp.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488819"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.9.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Horizontal system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The house cusps are defined by division of
|
||
the horizon into 12 directions. The first house cusp is not identical with the
|
||
Ascendant but is located precisely in the east.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488820"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.10.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The Polich-Page (<28>topocentric<69>)
|
||
system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This system was introduced in 1961 by Wendel
|
||
Polich and A.P. Nelson Page. Its construction is rather abstract: The tangens
|
||
of the polar height of the 11th house is the tangens of the geo. latitude
|
||
divided by 3. (2/3 of it are taken for the 12th house cusp.) The philosophical
|
||
reasons for this algorithm are obscure. Nor is this house system more
|
||
<93>topocentric<94> (i.e. birth-place-related) than any other house system. (c.f. the
|
||
misunderstanding with the <20>birth place system<65>.) The <20>topocentric<69> house cusps
|
||
are close to Placidus house cusps except for high geographical latitudes. It
|
||
also works for latitudes beyond the polar circles, wherefore some consider it
|
||
to be an improvement of the Placidus system. However, the striking
|
||
philosophical idea behind Placidus, i.e. the division of diurnal and nocturnal arcs
|
||
of points of the zodiac, is completely abandoned.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488821"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.11.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Alcabitus system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A method of house division which first
|
||
appears with the Hellenistic astrologer Rhetorius (500 A.D.) but is named after
|
||
Alcabitius, an Arabic astrologer, who lived in the 10th century A.D. This is
|
||
the system used in a few remaining examples of ancient Greek horoscopes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The MC and ASC are the 10th- and 1st- house
|
||
cusps. The remaining cusps are determined by the trisection of the semidiurnal
|
||
and seminocturnal arcs of the ascendant, measured on the celestial equator. The
|
||
houses are formed by great circles that pass through these trisection points
|
||
and the celestial north and south poles.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488822"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.12.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Gauquelin sectors</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is the <20>house<73> system used by the
|
||
Gauquelin and their epigones and critics in statistical investigations in
|
||
Astrology. Basically, it is identical with the Placidus house system, i.e.
|
||
diurnal and nocturnal arcs of ecliptic points or planets are subdivided. There
|
||
are a couple of differences, though.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Up to 36 <20>sectors<72> (or house
|
||
cusps) are used instead of 12 houses.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>The sectors are counted in
|
||
clockwise direction.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>There are so-called plus (+)
|
||
and minus (<28>) zones. The plus zones are the sectors that turned out to be
|
||
significant in statistical investigations, e.g. many top sportsmen turned out
|
||
to have their Mars in a plus zone. The plus sectors are the sectors 36 <20> 3, 9 <20>
|
||
12, 19 <20> 21, 28 <20> 30.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>More sophisticated algorithms
|
||
are used to calculate the exact house position of a planet (see chapters 6.4
|
||
and 6.5 on house positions and Gauquelin sector positions of planets).</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488823"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.13.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Krusinski/Pisa/Goelzer system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This house system was first published in
|
||
1994/1995 by three different authors independently of each other:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>by Bogdan Krusinski (Poland).</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>by Milan Pisa (Czech Republic)
|
||
under the name <20>Amphora house system<65>.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>by Georg Goelzer (Switzerland)
|
||
under the name <20>Ich-Kreis-H<>usersystem<65> (<28>I-Circle house system<65>).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Krusinski defines the house system as <20><>
|
||
based on the great circle passing through ascendant and zenith. This circle is
|
||
divided into 12 equal parts (1st cusp is ascendant, 10th cusp is zenith), then
|
||
the resulting points are projected onto the ecliptic through meridian circles.
|
||
The house cusps in space are half-circles perpendicular to the equator and
|
||
running from the north to the south celestial pole through the resulting cusp
|
||
points on the house circle. The points where they cross the ecliptic mark the
|
||
ecliptic house cusps.<2E> (Krusinski, e-mail to Dieter Koch)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>It may seem hard to believe that three
|
||
persons could have discovered the same house system at almost the same time.
|
||
But apparently this is what happened. Some more details are given here, in
|
||
order to refute wrong accusations from the Czech side against Krusinski of
|
||
having <20>stolen<65> the house system.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Out of the documents that Milan Pisa sent
|
||
to Dieter Koch, the following are to be mentioned: Private correspondence from
|
||
1994 and 1995 on the house system between Pisa and German astrologers B<>er and
|
||
Schubert-Weller, two type-written (apparently unpublished) treatises in German
|
||
on the house system dated from 1994. A printed booklet of 16 pages in Czech
|
||
from 1997 on the theory of the house system (<28>Algoritmy noveho systemu
|
||
astrologickych domu<6D>). House tables computed by Michael Cifka for the
|
||
geographical latitude of Prague, copyrighted from 1996. The house system was
|
||
included in the Czech astrology software Astrolog v. 3.2 (APAS) in 1998. Pisa<73>s
|
||
first publication on the house system happened in spring 1997 in <20>Konstelace<63>
|
||
No. 22, the periodical of the Czech Astrological Society.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Bogdan Krusinski first published the house
|
||
system at an astrological congress in Poland, the <20>"XIV Szkola Astrologii
|
||
Humanistycznej" held by Dr Leszek Weres, which took place between
|
||
15.08.1995 and 28.08.1995 in Pogorzelica at cost of the Baltic Sea.<2E> Since then
|
||
Krusinski has distributed printed house tables for the Polish geographical
|
||
latitudes 49-55<35> and floppy disks with house tables for latitudes 0-90<39>. In
|
||
1996, he offered his program code to Astrodienst for implementation of this
|
||
house system into Astrodienst<73>s then astronomical software Placalc. (At that
|
||
time, however, Astrodienst was not interested in it.) In May 1997, Krusinski
|
||
put the data on the web at</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>http://www.ci.uw.edu.pl/~bogdan/astrol.htm
|
||
(now at http://www.astrologia.pl/main/domy.html).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In February 2006 he sent Swiss-Ephemeris-compatible
|
||
program code in C for this house system to Astrodienst. This code was included
|
||
into Swiss Ephemeris Version 1.70 and released on 8 March 2006.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Georg Goelzer describes the same house
|
||
system in his book <20>Der Ich-Kosmos<6F>, which appeared in July 1995 at Dornach,
|
||
Switzerland (Goetheanum). The book has a second volume with house tables
|
||
according to the house method under discussion. The house tables were created
|
||
by Ulrich Leyde. Goelzer also uses a house calculation programme which has the
|
||
time stamp <20>9 April 1993<39> and produces the same house cusps.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>By March 2006, when the house system was
|
||
included in the Swiss Ephemeris under the name of <20>Krusinski houses<65>, neither
|
||
Krusinski nor Astrodienst knew about the works of Pisa and Goelzer. Goelzer
|
||
heard of his co-discoverers only in 2012 and then contacted Astrodienst.</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Conclusion</span></b><span lang=EN-US>:
|
||
It seems that the house system was first <20>discovered<65> and published by Goelzer,
|
||
but that Pisa and Krusinski also <20>discovered<65> it independently. We do not
|
||
consider this a great miracle because the number of possible house
|
||
constructions is quite limited.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488824"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.14.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>APC house system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This house system was introduced by the
|
||
Dutch astrologer L. Knegt and is used by the Dutch Werkgemeenschap van
|
||
Astrologen (WvA, also known as <20>Ram school<6F>).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parallel of declination that goes
|
||
through the ascendant is divided in six equal parts both above and below the
|
||
horizon. Position circles through the north and the south point on the horizon
|
||
are drawn through the division points. The house cusps are where the position
|
||
circles intersect the ecliptic.</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Note</span></b><span lang=EN-US>, the
|
||
house cusps 11, 12, 2, and 3 are not exactly opposite the cusps 5, 6, 8, and 9.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488825"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.2.15.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Sunshine house system</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This house system was invented by Bob
|
||
Makransky and published in 1988 in his book Primary Directions. A Primer of
|
||
Calculation (free download:
|
||
http://www.dearbrutus.com/buyprimarydirections.html).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The diurnal and nocturnal arcs of the Sun are
|
||
trisected, and great circles are drawn through these trisection points and the
|
||
north and the south point on the horizon. The intersection points of these
|
||
great circles with the ecliptic are the house cusps. Note that the cusps 11,
|
||
12, 2, and 3 are not in exact opposition to the cusps 5, 6, 8, and 9.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the polar region and during times where
|
||
the Sun does not rise or set, the diurnal and nocturnal arc are assumed to be
|
||
either 180<38> or 0<>. If the diurnal arc is 0<>, the house cusps 8 <20> 12 coincide
|
||
with the meridian. If the nocturnal arc is 0<>, the cusps 2 <20> 6 coincide with
|
||
the meridian. As with the closely related Regiomontanus system, an MC below the
|
||
horizon and IC above the horizon are exchanged.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488826"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.3.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Vertex, Antivertex, East Point and Equatorial Ascendant etc.</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The <span class=italic>Vertex</span> is the
|
||
point of the ecliptic that is located precisely in western direction. The <span
|
||
class=italic>Antivertex</span> is the opposition point and indicates the
|
||
precise east in the horoscope. It is identical to the 1st house cusp in the
|
||
horizon house system.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is a lot of confusion about this,
|
||
because there is also another point which is called the "East Point"
|
||
but is usually not located in the east. In celestial geometry, the expression
|
||
"East Point" means the point on the horizon which is in precise
|
||
eastern direction. The equator goes through this point as well, at a right
|
||
ascension which is equal to ARMC + 90 degrees. On the other hand, what some
|
||
astrologers call the "East Point" is the point on the ecliptic whose
|
||
right ascension is equal to ARMC + 90 (i.e. the right ascension of the
|
||
horizontal East Point). This point can deviate from eastern direction by 23.45
|
||
degrees, the amount of the ecliptic obliquity. For this reason, the term "East
|
||
Point" is not very well-chosen for this ecliptic point, and some
|
||
astrologers (M. Munkasey) prefer to call it the <span class=italic>Equatorial
|
||
Ascendant</span>, because it is identical to the Ascendant at a geographical
|
||
latitude 0.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Equatorial Ascendant is identical to
|
||
the first house cusp of the <span class=italic>axial rotation system</span>.</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>Note</span></b><span lang=EN-US>: If a
|
||
projection of the horizontal East Point on the ecliptic is wanted, it might
|
||
seem more reasonable to use a projection rectangular to the ecliptic, not
|
||
rectangular to the equator as is done by the users of the "East
|
||
Point". The planets, as well, are not projected on the ecliptic in a right
|
||
angle to the ecliptic.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris supports three more
|
||
points connected with the house and angle calculation. They are part of Michael
|
||
Munkasey's system of the <span class=italic>8 Personal Sensitive Points</span>
|
||
(PSP). The PSP include the <span class=italic>Ascendant</span>, the <span
|
||
class=italic>MC</span>, the <span class=italic>Vertex</span>, the <span
|
||
class=italic>Equatorial Ascendant</span>, the <span class=italic>Aries Point</span>,
|
||
the <span class=italic>Lunar Node</span>, and the <span class=italic>"Co-Ascendant"</span>
|
||
and the <span class=italic>"Polar Ascendant"</span>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The term <span class=italic>"Co-Ascendant"</span>
|
||
seems to have been <b>invented twice</b> by two different people, and it <b>can
|
||
mean two different things</b>. The one "Co-Ascendant" was invented by
|
||
Walter Koch. To calculate it, one has to take the ARIC as an ARMC and compute
|
||
the corresponding Ascendant for the birth place. The "Co-Ascendant"
|
||
is then the opposition to this point.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The second "Co-Ascendant" stems
|
||
from Michael Munkasey. It is the Ascendant computed for the natal ARMC and a
|
||
latitude which has the value 90<39> - birth_latitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The "Polar Ascendant" finally was
|
||
introduced by Michael Munkasey. It is the opposition point of Walter Koch's
|
||
version of the "Co-Ascendant". However, the "Polar
|
||
Ascendant" is not the same as an Ascendant computed for the birth time and
|
||
one of the geographic poles of the Earth. At the geographic poles, the
|
||
Ascendant is always 0 Aries or 0 Libra. This is not the case for Munkasey's
|
||
"Polar Ascendant".</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488827"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.4.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>House cusps beyond the polar circle</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Beyond the polar circle, we proceed as
|
||
follows:</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo40'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>We make sure that the ascendant is always in the eastern hemisphere.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Placidus and Koch house cusps sometimes can, sometimes cannot be
|
||
computed beyond the polar circles. Even the MC doesn't exist always, if one
|
||
defines it in the Placidus manner. Our function therefore automatically
|
||
switches to Porphyry houses (each quadrant is divided into three equal parts)
|
||
and returns a warning.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>3.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Beyond the polar circles, the MC is sometimes below the horizon. The
|
||
geometrical definition of the Campanus and Regiomontanus systems requires in
|
||
such cases that the MC and the IC are swapped. The whole house system is then
|
||
oriented in clockwise direction.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are similar problems with the Vertex
|
||
and the horizon house system for birth places in the tropics. The Vertex is
|
||
defined as the point on the ecliptic that is located in precise western
|
||
direction. The ecliptic east point is the opposition point and is called the
|
||
Antivertex. Our program code makes sure that the Vertex (and the cusps 11, 12,
|
||
1, 2, 3 of the horizon house system) is always located in the western
|
||
hemisphere. Note that for birthplaces on the equator the Vertex is always 0
|
||
Aries or 0 Libra.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Of course, there are no problems in the
|
||
calculation of the Equatorial Ascendant for any place on Earth.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488828"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>6.4.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Implementation in other
|
||
calculation modules:</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>PLACALC</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Placalc is the predecessor of Swiss
|
||
Ephemeris; it is a calculation module created by Astrodienst in 1988 and
|
||
distributed as C source code. Beyond the polar circles, Placalc<6C>s house
|
||
calculation did switch to Porphyry houses for all unequal house systems. Swiss
|
||
Ephemeris still does so with the Placidus and Koch method, which are not
|
||
defined in such cases. However, the computation of the MC and Ascendant was
|
||
replaced by a different model in some cases: Swiss Ephemeris gives priority to
|
||
the Ascendant, choosing it always as the eastern rising point of the ecliptic
|
||
and accepting an MC below the horizon, whereas Placalc gave priority to the MC.
|
||
The MC was always chosen as the intersection of the meridian with the ecliptic
|
||
above the horizon. To keep the quadrants in the correct order, i.e. have an
|
||
Ascendant in the left side of the chart, the Ascendant was switched by 180
|
||
degrees if necessary.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the discussions between Alois Treindl
|
||
and Dieter Koch during the development of the Swiss Ephemeris it was recognized
|
||
that this model is more unnatural than the new model implemented in Swiss
|
||
Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Placalc also made no difference between
|
||
Placidus/Koch on one hand and Regiomontanus/Campanus on the other as Swiss
|
||
Ephemeris does. In Swiss Ephemeris, the geometrical definition of
|
||
Regiomontanus/Campanus is strictly followed, even for the price of getting the
|
||
houses in <20>wrong<6E> order. (see above, Chapter 4.1.)</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>ASTROLOG program as written by
|
||
Walter Pullen</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>While the freeware program Astrolog
|
||
contains the planetary routines of Placalc, it uses its own house calculation
|
||
module by Walter Pullen. Various releases of Astrolog contain different
|
||
approaches to this problem.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>ASTROLOG on our website</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>ASTROLOG is also used on Astrodienst<73>s
|
||
website for displaying free charts. This version of Astrolog used on our
|
||
website however is different from the Astrolog program as distributed on the
|
||
Internet. Our webserver version of Astrolog contains calls to Swiss Ephemeris
|
||
for planetary positions. For Ascendant, MC and houses it still uses Walter
|
||
Pullen's code. This will change in due time because we intend to replace
|
||
ASTROLOG on the website with our own charting software.</span></p>
|
||
|
||
<h4 style='text-indent:0cm;mso-list:l0 level4 lfo3'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Other astrology programs</span></h4>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Because most astrology programs still use
|
||
the Placalc module, they follow the Placalc method for houses inside the polar
|
||
circles. They give priority to keep the MC above the horizon and switch the
|
||
Ascendant by 180 degrees if necessary to keep the quadrants in order.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488829"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.5.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>House position of a planet</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris DLL also provides a
|
||
function to compute the house position of a given body, i.e. in which house it
|
||
is. This function can be used either to determine the house number of a planet
|
||
or to compute its position in a <span class=italic>house horoscope</span>. (A
|
||
house horoscope is a chart in which all houses are stretched or shortened to a
|
||
size of 30 degrees. For unequal house systems, the zodiac is distorted so that
|
||
one sign of the zodiac does not measure 30 house degrees)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note that the actual house position of a
|
||
planet is not always the one that it seems to be in an ordinary chart drawing.
|
||
Because the planets are not always exactly located on the ecliptic but have a
|
||
latitude, they can seemingly be located in the first house, but are actually
|
||
visible above the horizon. In such a case, our program function will place the
|
||
body in the 12th (or 11th or 10th) house, whatever celestial geometry requires.
|
||
However, it is possible to get a house position in the <20>traditional<61> way, if
|
||
one sets the ecliptic latitude to zero.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Although it is not possible to compute
|
||
Placidus house cusps beyond the polar circle, this function will also provide
|
||
Placidus house positions for polar regions. The situation is as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Placidus method works with the
|
||
semidiurnal and seminocturnal arcs of the planets. Because in higher geographic
|
||
latitudes some celestial bodies (the ones within the circumpolar circle) never
|
||
rise or set, such arcs do not exist. To avoid this problem it has been proposed
|
||
in such cases to start the diurnal motion of a circumpolar body at its
|
||
<94>midnight<94> culmination and its nocturnal motion at its midday culmination. This
|
||
procedure seems to have been proposed by Otto Ludwig in 1930. It allows to define
|
||
a planet's house position even if it is within the circumpolar region, and even
|
||
if you are born in the northernmost settlement of Greenland. However, this does
|
||
not mean that it be possible to compute ecliptical house cusps for such
|
||
locations. If one tried that, it would turn out that e.g. an 11th house cusp
|
||
did not exist, but there were two 12th house cusps.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note however, that circumpolar bodies may
|
||
jump from the 7th house directly into the 12th one or from the 1st one directly
|
||
into the 6th one.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Koch method, on the other hand, cannot
|
||
be helped even with this method. For some bodies it may work even beyond the
|
||
polar circle, but for some it may fail even for latitudes beyond 60 degrees.
|
||
With fixed stars, it may even fail in central Europe or USA. (Dieter Koch
|
||
regrets the connection of his name with such a badly defined house system)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note that Koch planets do strange jumps
|
||
when they cross the meridian. This is not a computation error but an effect of
|
||
the awkward definition of this house system. A planet can be east of the
|
||
meridian but be located in the 9th house, or west of the meridian and in the
|
||
10th house. It is possible to avoid this problem or to make Koch house
|
||
positions agree better with the Huber <20>hand calculation<6F> method, if one sets
|
||
the ecliptic latitude of the planets to zero. But this is not more correct from
|
||
a geometrical point of view.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488830"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.6.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Gauquelin sector position of a planet</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The calculation of the Gauquelin sector
|
||
position of a planet is based on the same idea as the Placidus house system, i.e.
|
||
diurnal and nocturnal arcs of ecliptic points or planets are subdivided.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Three different algorithms have been used
|
||
by Gauquelin and others to determine the sector position of a planet.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo39'><a name="_Hlk17748190"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>We can take the ecliptic point of the planet (ecliptical latitude ignored)
|
||
and calculate the fraction of its diurnal or nocturnal arc it has completed</span></a></p>
|
||
|
||
<span style='mso-bookmark:_Hlk17748190'></span>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>We can take the true planetary position (taking into account
|
||
ecliptical latitude) for the same calculation.</span></p>
|
||
|
||
<p class=listnumbered style='mso-list:l44 level1 lfo36'><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI"'><span style='mso-list:
|
||
Ignore'>3.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>We can use the exact times for rise and set of the planet to determine
|
||
the ratio between the time the planet has already spent above (or below) the
|
||
horizon and its diurnal (or nocturnal) arc. Times of rise and set are defined
|
||
by the appearance or disappearance of the center of the planet<65>s disks.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>All three methods are supported by the
|
||
Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Methods 1 and 2 also work for polar
|
||
regions. The Placidus algorithm is used, and the Otto Ludwig method applied
|
||
with circumpolar bodies. I.e. if a planet does not have a rise and set, the
|
||
<93>midnight<94> and <20>midday<61> culminations are used to define its semidiurnal and
|
||
seminocturnal arcs.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>With method 3, we don<6F>t try to do similar.
|
||
Because planets do not culminate exactly in the north or south, a planet can
|
||
actually rise on the western part of the horizon in high geographic latitudes.
|
||
Therefore, it does not seem appropriate to use meridian transits as culmination
|
||
times. On the other hand, true culmination times are not always available. E.g.
|
||
close to the geographic poles, the Sun culminates only twice a year.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488831"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>6.7.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Improvement of the Placidus house calculation in SE 2.09</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Before Swiss Ephemeris 2.09, our
|
||
calculation of Placidus house positions did not provide greatest possible
|
||
precision with high geographic latitudes (noticed by D. Senthilathiban). The
|
||
Placidus house cusps were calculated with only two iterations. This resulted in
|
||
an accuracy of 1 arcsec until about the geographic latitude 56<35>. On higher
|
||
latitudes, the error was greater for some cusps and for some time of the day.
|
||
For latitudes extremely close to the polar circle the error could even become
|
||
greater than a degree.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This problem has been fixed by using a
|
||
variable number of iterations, which stops when the cusp converges, with n =
|
||
100 as maximum number of iterations. If the iteration does not converge with
|
||
this maximum of iterations, we switch to Porphyry cusps and return a warning.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Example:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Old calculation with SE 2.08:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>sweph2.08/swetest
|
||
-b26.1.2000 -ut8:08 -house30,66.562,P -p</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>date (dmy)
|
||
26.1.2000 greg.<span style='mso-spacerun:yes'><3E><> </span>8:08:00 UT<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span>version 2.08</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>UT:<span style='mso-spacerun:yes'><3E> </span>2451569.838888889<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 63.849300 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>TT:<span style='mso-spacerun:yes'><3E> </span>2451569.839627885<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>geo. long
|
||
30.000000, lat 66.562000, alt 0.000000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Epsilon
|
||
(t/m)<span style='mso-spacerun:yes'><3E><><A0><A0> </span>23<32>26'16.2121<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32>26'21.3741</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>1<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>93<39>10'50.7734</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>2<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>93<39>35'32.4962</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>3<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>94<39>45' 1.3614</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>4<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>96<39>22'19.2129</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>5<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>99<39>30'38.8122</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>house<span style='mso-spacerun:yes'><3E>
|
||
</span>6<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span>107<30>41'47.9654</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>New calculation with SE 2.09:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>swetest
|
||
-b26.1.2000 -ut8:08 -house30,66.562,P -p</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>date (dmy)
|
||
26.1.2000 greg.<span style='mso-spacerun:yes'><3E><> </span>8:08:00 UT<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span>version 2.08.00a</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>UT:<span style='mso-spacerun:yes'><3E> </span>2451569.838888889<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 63.849300 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>TT:<span style='mso-spacerun:yes'><3E> </span>2451569.839627885<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>geo. long
|
||
30.000000, lat 66.562000, alt 0.000000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Epsilon
|
||
(t/m)<span style='mso-spacerun:yes'><3E><><A0><A0> </span>23<32>26'16.2121<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32>26'21.3741</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Nutation<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>-0<> 0'13.1306<span
|
||
style='mso-spacerun:yes'><3E><> </span>-0<> 0' 5.1621</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Houses system P
|
||
(Placidus) for long=<span style='mso-spacerun:yes'><3E> </span>30<33> 0' 0.0000,
|
||
lat=<span style='mso-spacerun:yes'><3E> </span>66<36>33'43.2000</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>1<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>93<39>10'50.7734</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>2<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>93<39>35'32.4962</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>3<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>94<39>45' 1.3614</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>4<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>96<39>22'19.2129</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>house<span
|
||
style='mso-spacerun:yes'><3E> </span>5<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0>
|
||
</span>99<39>34' 5.9429</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>house<span style='mso-spacerun:yes'><3E>
|
||
</span>6<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0> </span>109<30>14' 4.4696</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><a name="_Toc58488832"><![if !supportLists]><span lang=EN-US
|
||
style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI";
|
||
mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:2;
|
||
mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>7.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US style='mso-bidi-font-family:
|
||
"Segoe UI"'>Δ</span><span lang=EN-US>T (Delta T)</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Ephemerides of planets are calculated using
|
||
so called <span class=italic>Terrestrial Time</span> (which replaces former <span
|
||
class=italic>Ephemeris Time</span> (ET)). Terrestrial time is a perfectly
|
||
uniform time measure based on atomic clocks (SI seconds). Computations of
|
||
sidereal time and houses, on the other hand, are calculated using <span
|
||
class=italic>Universal Time</span> (UT). Universal Time is based on the
|
||
rotational period of the Earth (the day), which is not perfectly uniform. The
|
||
difference between TT (ET) and UT is called ΔT (<28>Delta T<>), and is defined
|
||
as ΔT = TT <20> UT.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Earth's rotation decreases slowly,
|
||
currently at the rate of roughly 0.5 <20> 1 second per year, but in an irregular
|
||
and unpredictable way. The value of ΔT cannot be calculated with accuracy
|
||
for the future or the remote past. Future values of ΔT can only be
|
||
determined in hindsight from astronomical observations. Observations of solar
|
||
and lunar eclipses made by ancient Babylonians, Chinese, Greeks, Arabs, and
|
||
scholars of the European Renaissance and early Modern Era can be used to
|
||
determine the approximate value of ΔT for historical epochs after 720 BCE.
|
||
For the remoter past or the future, estimations must be made. Numerous
|
||
occultations of stars by the Moon have provided more exact values for ΔT
|
||
for epochs after 1700. Since 1962, ΔT has been determined from extremely
|
||
accurate measurements of the Earth rotation by the <span class=italic>International
|
||
Earth Rotation and Reference Systems Service</span> (IERS).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris Version 2.06 and later use
|
||
the ΔT algorithms published in:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison,
|
||
L.V., and Hohenkerk, C.Y., "Measurement of the Earth's Rotation: 720 BCE
|
||
to CE 2015", Royal Society Proceedings A, 7 Dec 2016,</span></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>http://rspa.royalsocietypublishing.org/lookup/doi/10.1098/rspa.2016.0404</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>These algorithms are used for epochs before
|
||
1 January 1955. From 1955 on we use the values provided by the Astronomical
|
||
Almanac, pp. K8-9 (since AA 1986). From 1974 on we use values calculated from
|
||
data of the Earth Orientation Department of the US Naval Observatory:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>(TAI-UTC) from:
|
||
ftp://maia.usno.navy.mil/ser7/tai-utc.dat;</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>(UT1-UTC) from:
|
||
ftp://ftp.iers.org/products/eop/rapid/standard/finals.data; or</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>ftp://maia.usno.navy.mil/ser7/finals.all;</span></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>file
|
||
description in: ftp://maia.usno.navy.mil/ser7/readme.finals.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span style='mso-ansi-language:
|
||
DE'>Delta T = TAI-UT1 + 32.184 sec = (TAI-UTC) - (UT1-UTC) + 32.184 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>For epochs before
|
||
1955, the ΔT function adjusts for a value of secular tidal acceleration
|
||
ndot that is consistent with the ephemeris used (LE431 has ndot = -25.80
|
||
arcsec/cty<sup>2</sup>, LE405/406 has ndot = -25.826 arcsec/cty<sup>2</sup>,
|
||
ELP2000 and DE200 ndot = -23.8946 arcsec/cty<sup>2</sup>). The ΔT values
|
||
of Astronomical Almanac are consistent with ndot = -26 arcsec/cty<sup>2</sup>,
|
||
those of Stephenson & alii 2016 with ndot = -25.85 arcsec/cty<sup>2</sup>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For the time after the last tabulated
|
||
value, we use the formula of Stephenson (1997; p. 507), with a modification
|
||
that avoids a discontinuity at the end of the tabulated period. A linear term
|
||
is added that makes a slow transition from the table to the formula over a
|
||
period of 100 years.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The ΔT algorithms have been changed
|
||
with the Swiss Ephemeris releases 1.64 (Stephenson 1997), 1.72
|
||
(Morrison/Stephenson 2004), 1.77 (Espenak & Meeus) and 2.06
|
||
(Stephenson/Morrison/Hohenkerk). These updates have caused changes in
|
||
ephemerides that are based on Universal Time.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Until version 2.05.01, the Swiss Ephemeris
|
||
has used the ΔT values provided by Astronomical Almanac K8-9 starting from
|
||
the year 1633. Before 1600, polynomials published by Espenak and Meeus (2006,
|
||
see further below) were used. These formulae include the long-term formula by
|
||
Morrison/Stephenson (2004, p. 332), which is used for epochs before -500.
|
||
Between the value of 1600 and the value of 1633, a linear interpolation was made.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences in ΔT, SE 2.06 <20> SE 2.05
|
||
(new <20> old)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(with resulting differences for lunar and
|
||
solar ephemerides calculated in UT)</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>ΔT
|
||
sec<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference
|
||
in ΔT (new-old)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>L
|
||
(Moon)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>L
|
||
(Sun)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>75051</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1174</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>644"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>48"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>60203</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>865</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>475"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>36"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>46979</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>588</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>323"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>35377</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>342</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>188"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>14"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>25398</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>129</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>71"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-900</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>23596</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>90</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>49"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-800</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>21860</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>52</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-700</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>20142</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-31</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-17"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-600</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>18373</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-229</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-126"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-9"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>16769</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-325</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-179"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-13"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-400</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>15311</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-119</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-65"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-300</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>13981</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-200</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>12758</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>50</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>27"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-100</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>11623</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>62</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>34"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10557</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>43</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>100</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>9540</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:17'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>200</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>8554</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-31</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-17"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:18'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>300</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>7578</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-53</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-29"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:19'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>400</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6593</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-62</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-34"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:20'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5590</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-81</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-45"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:21'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>600</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4596</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-110</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-60"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:22'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>700</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3649</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-135</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-74"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-6"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:23'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>800</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2786</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-145</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-80"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-6"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:24'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>900</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2045</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-135</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-74"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-6"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:25'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1464</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-94</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-52"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:26'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1100</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1063</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-13</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-7"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:27'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1200</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>802</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>76</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>42"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:28'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1300</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>625</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>141</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>77"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:29'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1400</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>473</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>157</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>86"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:30'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>292</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>97</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>53"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:31'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1600</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>89</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-29</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-16"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.2"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:32'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1700</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>14</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>6.5</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3.6"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.27"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:33'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1800</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>19</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>5.3</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2.9"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.22"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:34'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2.0</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.78</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.43"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.03"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:35'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1920</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>22</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.47</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.26"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.02"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:36'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1940</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>24</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.10</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.05"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:37'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1960</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>33</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:38'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1970</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>40</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:39'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1980</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>51</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:40'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1990</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>57</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:41'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>64</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:42'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2010</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>66</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:43'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2020</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>70</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.00"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:44'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2030</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>74</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-5.9</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3.3"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.24"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:45'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2040</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>76</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-21</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-12"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.87"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:46'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2050</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>78</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-37</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-20"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1.5"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:47'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>94</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-119</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-65"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4.9"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:48'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2200</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>163</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-265</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-145"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-11"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:49'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2300</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>297</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-397</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-218"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-16"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:50'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2400</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>520</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-503</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-276"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-21"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:51'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2500</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>855</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-558</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-307"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-23"</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:52;mso-yfti-lastrow:yes'>
|
||
<td width=66 valign=top style='width:49.6pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td width=65 valign=top style='width:48.65pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3292</span></p>
|
||
</td>
|
||
<td width=105 valign=top style='width:78.95pt;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1004</span></p>
|
||
</td>
|
||
<td width=76 valign=top style='width:2.0cm;padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-551"</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-41"</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US style='color:white;mso-color-alt:windowtext'>Differences
|
||
in </span><span lang=EN-US>ΔT, SE 1.77 <20> SE 1.76</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>Difference in<br>
|
||
seconds<br>
|
||
(new - old)<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US><o:p> </o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-3000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-1100</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-1001</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-900</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-45</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-800</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-57</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-700</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-696</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>(is
|
||
a maximum!)</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>-500</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-14</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
-200</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3
|
||
> diff > -25</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
100</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3
|
||
> diff > -15</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
500</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3
|
||
> diff > -03</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
1600</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>4
|
||
> diff > -16</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
1630</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1
|
||
> diff > -30</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
1700</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.1</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal><span lang=EN-US>| diff |</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:15'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
1900</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.01</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:16;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>until
|
||
2100</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.001</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US><o:p> </o:p></span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>The differences
|
||
for <20>1000 to +1630 are explained as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Espenak & Meeus ignore Morrison &
|
||
Stephenson's values for -700 and -600, whereas the former Swiss Ephemeris
|
||
versions used them. For -500 to +1600 Espenak & Meeus use polynomials
|
||
whereas the former Swiss Ephemeris versions used a linear interpolation between
|
||
Morrison / Stephenson's tabulated values.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences in ΔT, SE 1.72 <20> SE 1.71</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='margin-bottom:0cm;text-align:right'><b><span
|
||
lang=EN-US>Difference in<br>
|
||
seconds<br>
|
||
(new - old)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-4127</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-2130</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-1000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-760</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-20</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-30</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1600</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>10</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1619</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0.5</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1620</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>Differences in ΔT, SE 1.64 <20> SE 1.63</span></p>
|
||
|
||
<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
|
||
style='margin-left:14.2pt;border-collapse:collapse;mso-yfti-tbllook:1184;
|
||
mso-padding-alt:0cm 5.4pt 0cm 5.4pt'>
|
||
<tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Year<o:p></o:p></span></b></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><b><span lang=EN-US>Difference
|
||
in<br>
|
||
seconds<br>
|
||
(new - old)<o:p></o:p></span></b></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:1'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-3000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2900</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:2'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1200</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:3'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1600</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>29</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:4'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1619</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>60</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:5'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1620</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.6</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:6'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1700</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.4</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:7'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1800</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.1</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:8'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1900</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.02</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:9'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1940</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-0.001</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:10'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>1950</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:11'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>0</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:12'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2020</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:13'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>2100</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>23</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr style='mso-yfti-irow:14;mso-yfti-lastrow:yes'>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>3000</span></p>
|
||
</td>
|
||
<td valign=top style='padding:0cm 5.4pt 0cm 5.4pt'>
|
||
<p class=MsoNormal align=right style='text-align:right'><span lang=EN-US>-400</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal style='margin-top:12.0pt'><span lang=EN-US>In 1620, where
|
||
the ΔT table of the Astronomical Almanac starts, there was a discontinuity
|
||
of a whole minute in the old algorithms. This has been fixed with SE 1.64.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The smaller differences for the period
|
||
1620-1955 are due to a correction in the tidal acceleration of the Moon, which
|
||
now has the same value as is also used by JPL for their T calculations.</span></p>
|
||
|
||
<p class=MsoSubtitle><span lang=EN-US>References</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Borkowski, K. M.,
|
||
"ELP2000-85 and the Dynamical Time - Universal Time relation,"
|
||
Astronomy and Astrophysics 205, L8-L10 (1988)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Chapront-Touze, Michelle, and
|
||
Jean Chapront, Lunar Tables and Programs from 4000 B.C. to A.D. 8000, Willmann-Bell
|
||
1991</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Espenak, Fred, and Jean Meeus,
|
||
<93>Five-millennium Catalog of Lunar Eclipses <20>1900 to +3000<30>, 2009, p. 18ff.,</span></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>http://eclipse.gsfc.nasa.gov/5MCSE/TP2009-214174.pdf.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Explanatory Supplement of the
|
||
Astronomical Almanac, University Science Books, 1992, Mill Valley, CA, p.
|
||
265ff.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Morrison, L. V. and F. R.
|
||
Stephenson, Sun and Planetary System, vol 96,73 eds. W. Fricke, G. Teleki,
|
||
Reidel, Dordrecht (1982)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Morrison, L. V., and F.R.
|
||
Stephenson, <20>Historical Values of the Earth<74>s Clock Error T and the
|
||
Calculation of Eclipses<65>, JHA xxxv (2004), pp.327-336</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F. R., and L. V.
|
||
Morrison, "Long-term changes in the rotation of the Earth: 700 BCE to CE
|
||
1980", Philosophical Transactions of the Royal Society of London, Series A
|
||
313, 47-70 (1984)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F. R., and M. A.
|
||
Houlden, Atlas of Historical Eclipse Maps, Cambridge U. Press (1986)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R. &
|
||
Morrison, L.V., "Long-Term Fluctuations in the Earth's Rotation: 700 BCE
|
||
to CE 1990", in: Philosophical Transactions of the Royal Society of
|
||
London, Ser. A, 351 (1995), 165-202.</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F. Richard,
|
||
Historical Eclipses and Earth's Rotation, Cambridge U. Press (1997)</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison,
|
||
L.V., and Hohenkerk, C.Y., "Measurement of the Earth's Rotation: 720 BCE
|
||
to CE 2015", Royal Society Proceedings A, 7 Dec 2016,</span></p>
|
||
|
||
<p class=ListBullet1 style='text-indent:0cm;mso-list:none'><span lang=EN-US>http://rspa.royalsocietypublishing.org/lookup/doi/10.1098/rspa.2016.0404</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>For a comprehensive collection
|
||
of publications and formulae, see R.H. van Gent at<br>
|
||
<span
|
||
style='mso-spacerun:yes'><3E></span>http://www.phys.uu.nl/~vgent/astro/deltatime.htm.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:"Segoe UI";
|
||
mso-bidi-font-family:"Segoe UI";mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:
|
||
2;mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>8.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US><span style='mso-tab-count:
|
||
1'> </span><a name="_Toc58488833">Programming Environment</a></span></h1>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss Ephemeris is written in portable C
|
||
and the same code is used for creation of the 32-bit Windows DLL and the link
|
||
library. All data files are fully portable between different hardware
|
||
architectures.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To build the DLLs, we use Microsoft Visual
|
||
C++ version 5.0 (for 32-bit).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The DLL has been successfully used in the
|
||
following programming environments:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Visual C++ 5.0<span
|
||
style='mso-tab-count:1'><3E> </span>(sample code included in the distribution);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Visual Basic 5.0 (sample code
|
||
and VB declaration file included);</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Delphi 2 and Delphi 3 (32-bit,
|
||
declaration file included).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As the number of users grows, our knowledge
|
||
base about the interface details between programming environments and the DLL
|
||
grows. All such information is added to the distributed Swiss Ephemeris and
|
||
registered users are informed via an email mailing list.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Earlier version up to version 1.61
|
||
supported 16-bit Windows programming. Since then, 16-bit support has been
|
||
dropped.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:"Segoe UI";
|
||
mso-bidi-font-family:"Segoe UI";mso-style-style3d-lightrigtype:13;mso-style-style3d-lightrigdirection:
|
||
2;mso-style-style3d-lightrigrotation-anglatitude:0;mso-style-style3d-lightrigrotation-anglongitude:
|
||
0;mso-style-style3d-lightrigrotation-angrevolution:0'><span style='mso-list:
|
||
Ignore'>9.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US><span style='mso-tab-count:
|
||
1'> </span><a name="_Toc58488834">Swiss Ephemeris Functions</a></span></h1>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488835"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>9.1.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Swiss Ephemeris API</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We give a short overview of the most
|
||
important functions contained in the Swiss Ephemeris DLL. The detailed
|
||
description of the programming interface is contained in the document
|
||
swephprg.doc which is distributed together with the file you are reading.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488836"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.1.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Calculation of planets and
|
||
stars</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* planets, Moon,
|
||
asteroids, lunar nodes, apogees, fictitious bodies;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* input time must be ET/TT */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_calc()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* same, but input
|
||
time must be UT */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_calc_ut()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* fixed stars;
|
||
input time must be ET/TT */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_fixstar()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* fixed stars;
|
||
input time must be UT */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_fixstar_ut()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'> </span><o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488837"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.2.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Date and time conversion</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* delta t from
|
||
Julian day number<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* Ephemeris time (ET) = Universal time (UT) + </span></span><span
|
||
class=functions><span lang=EN-US>swe_deltat</span></span><span
|
||
class=sourcecode><span lang=EN-US>(UT)*/<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_deltat()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* Julian day number
|
||
from year, month, day, hour, */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_date_conversion()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:3'><3E><><A0><A0><A0><A0> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* Julian day number
|
||
from year, month, day, hour */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_julday()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:2'><3E><><A0><A0> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* year, month, day,
|
||
hour from Julian day number */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_revjul()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* UTC to Julian day
|
||
number */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_utc_to_jd()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* Julian day number
|
||
TT to UTC */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_jdet_to_utc()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* Julian day number
|
||
UT1 to UTC */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_jdut1_to_utc()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* utc to time zone
|
||
or time zone to utc*/<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_utc_time_zone()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* get tidal
|
||
acceleration used in </span></span><span class=functions><span lang=EN-US>swe_deltat()</span></span><span
|
||
class=sourcecode><span lang=EN-US> */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_get_tid_acc()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* set tidal acceleration
|
||
to be used in </span></span><span class=functions><span lang=EN-US>swe_deltat()</span></span><span
|
||
class=sourcecode><span lang=EN-US> */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_set_tid_acc()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488838"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.3.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Initialization, setup, and
|
||
closing functions</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* set directory
|
||
path of ephemeris files */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_set_ephe_path()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* set name of JPL
|
||
ephemeris file */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_set_jpl_file()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* close Swiss Ephemeris
|
||
*/<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_close()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488839"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.4.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>House calculation</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* sidereal time */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_sidtime()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* house cusps,
|
||
ascendant, MC, armc, vertex */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_houses()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E><> </span><o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488840"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.5.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Auxiliary functions</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* coordinate
|
||
transformation, from ecliptic to equator or vice-versa. */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_cotrans()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'><3E> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* coordinate
|
||
transformation of position and speed,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* from ecliptic to equator or vice-versa*/<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_cotrans_sp()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* get the name of a
|
||
planet */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_get_planet_name()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<span style='mso-tab-count:1'> </span><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* normalization of
|
||
any degree number to the range 0 ... 360 */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_degnorm()</span></span><span
|
||
class=sourcecode><span lang=EN-US>;<o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;text-indent:0cm;mso-list:l0 level3 lfo3'><a name="_Toc58488841"><![if !supportLists]><span
|
||
lang=EN-US style='mso-fareast-font-family:"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span
|
||
style='mso-list:Ignore'>9.1.6.<span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>Other functions that may be
|
||
useful</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>PLACALC, the predecessor of SWISSEPH,
|
||
included several functions that we do not need for SWISSEPH anymore.
|
||
Nevertheless we include them again in our DLL, because some users of our
|
||
software may have taken them over and use them in their applications. However,
|
||
we gave them new names that were more consistent with SWISSEPH.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>PLACALC used angular measurements in
|
||
centiseconds a lot; a centisecond is 1/100 of an arc second. The C type CSEC or
|
||
centisec is a 32-bit integer. CSEC was used because calculation with integer
|
||
variables was considerably faster than floating point calculation on most CPUs
|
||
in 1988, when PLACALC was written.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the Swiss Ephemeris we have dropped the
|
||
use of centiseconds and use double (64-bit floating point) for all angular
|
||
measurements.</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* normalize
|
||
argument into interval [0..DEG360]<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: csnorm() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_csnorm();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* distance in
|
||
centisecs p1 - p2 normalized to [0..360]<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: difcsn() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_difcsn();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* distance in
|
||
degrees * former function name: difdegn() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_difdegn();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* distance in
|
||
centisecs p1 - p2 normalized to [-180..180[<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: difcs2n() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_difcs2n();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* distance in
|
||
degrees<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: difdeg2n() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_difdeg2n();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* round second, but
|
||
at 29.5959 always down<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: roundsec() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_csroundsec();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* double to long
|
||
with rounding, no overflow check<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: d2l() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_d2l();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* Monday = 0, ... Sunday
|
||
= 6<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: day_of_week() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_day_of_week();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* centiseconds
|
||
-> time string<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: TimeString() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_cs2timestr();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* centiseconds
|
||
-> longitude or latitude string<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: LonLatString() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_cs2lonlatstr();<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>/* centiseconds
|
||
-> degrees string<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E></span>* former function name: DegreeString() */<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=functions><span lang=EN-US>swe_cs2degstr();<o:p></o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;mso-list:l0 level2 lfo3'><a
|
||
name="_Toc58488842"><![if !supportLists]><span lang=EN-US style='mso-fareast-font-family:
|
||
"Segoe UI";mso-bidi-font-family:"Segoe UI"'><span style='mso-list:Ignore'>9.2.<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
|
||
lang=EN-US>Placalc API</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Placalc is a planetary calculation module
|
||
which was made available by Astrodienst since 1988 to other programmers under a
|
||
source code license. Placalc is less well designed, less complete and not as
|
||
precise as the Swiss Ephemeris module. However, many developers of astrological
|
||
software have used it over many years and like it. Astrodienst has used it
|
||
internally since 1989 for a large set of application programs.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To simplify the introduction of Swiss
|
||
Ephemeris in 1997 in Astrodienst's internal operation, we wrote an interface
|
||
module which translates all calls to Placalc functions into Swiss Ephemeris
|
||
functions, and translates the results back into the format expected in the
|
||
Placalc Application Interface (API).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This interface (</span><span
|
||
class=FileName><span lang=DA>swepcalc.c</span></span><span lang=EN-US> and </span><span
|
||
class=FileName><span lang=DA>swepcalc.h</span></span><span lang=EN-US>) is part
|
||
of the source code distribution of Swiss Ephemeris; it is not contained in the
|
||
DLL. All new software should be written directly for the SwissEph API, but
|
||
porting old Placalc software is convenient and very simple with the Placalc
|
||
API.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 4.0pt 0cm'>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;mso-list:none'><a name="_Toc58488843"><span
|
||
lang=EN-US>Appendix</span></a></h1>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;mso-list:none;tab-stops:14.2pt'><a
|
||
name="_Toc58488844"><span lang=EN-US>A. The gravity deflection for a planet
|
||
passing behind the Sun</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The calculation of the apparent position of
|
||
a planet involves a relativistic effect, which is the curvature of space by the
|
||
gravity field of the Sun. This can also be described by a semi-classical
|
||
algorithm, where the photon travelling from the planet to the observer is
|
||
deflected in the Newtonian gravity field of the Sun, where the photon has a
|
||
non-zero mass arising from its energy. To get the correct relativistic result,
|
||
a correction factor 2.0 must be included in the calculation.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A problem arises when a planet disappears
|
||
behind the solar disk, as seen from the Earth. Over the whole 6000 year time
|
||
span of the Swiss Ephemeris, it happens often.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><b><span
|
||
lang=EN-US>Planet<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>Number of passes
|
||
behind the Sun<o:p></o:p></span></b></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Mercury<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>1723</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Venus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>456</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Mars<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>412</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Jupiter<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>793</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Saturn<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span>428</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Uranus<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span>1376</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Neptune<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span>543</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt;tab-stops:70.9pt'><span
|
||
lang=EN-US>Pluto<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>57</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A typical occultation of a planet by the
|
||
Solar disk, which has a diameter of approx. _ degree, has a duration of about
|
||
12 hours. For the outer planets it is mostly the speed of the Earth's movement
|
||
which determines this duration.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Strictly speaking, there is no apparent
|
||
position of a planet when it is eclipsed by the Sun. No photon from the planet
|
||
reaches the observer's eye on Earth. Should one drop gravitational deflection,
|
||
but keep aberration and light-time correction, or should one switch completely
|
||
from apparent positions to true positions for occulted planets? In both cases,
|
||
one would come up with an ephemeris which contains discontinuities, when at the
|
||
moment of occultation at the Solar limb suddenly an effect is switched off.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Discontinuities in the ephemeris need to be
|
||
avoided for several reasons. On the level of physics, there cannot be a
|
||
discontinuity. The planet cannot jump from one position to another. On the
|
||
level of mathematics, a non-steady function is a nightmare for computing any
|
||
derived phenomena from this function, e.g. the time and duration of an
|
||
astrological transit over a natal body, or an aspect of the planet.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Nobody seems to have handled this problem
|
||
before in astronomical literature. To solve this problem, we have used the
|
||
following approach: We replace the Sun, which is totally opaque for
|
||
electromagnetic waves and not transparent for the photons coming from a planet
|
||
behind it, by a transparent gravity field. This gravity field has the same
|
||
strength and spatial distribution as the gravity field of the Sun. For photons
|
||
from occulted planets, we compute their path and deflection in this gravity
|
||
field, and from this calculation we get reasonable apparent positions also for
|
||
occulted planets.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The calculation has been carried out with a
|
||
semi-classical Newtonian model, which can be expected to give the correct
|
||
relativistic result when it is multiplied with a correction factor 2. The mass
|
||
of the Sun is mostly concentrated near its center; the outer regions of the
|
||
Solar sphere have a low mass density. We used the a mass density distribution
|
||
from the Solar standard model, assuming it to have spherical symmetry (our Sun mass
|
||
distribution m<> is from Michael Stix, The Sun, p. 47). The path of photons
|
||
through this gravity field was computed by numerical integration. The
|
||
application of this model in the actual ephemeris could then be greatly
|
||
simplified by deriving an effective Solar mass which a photon <20>sees<65> when it
|
||
passes close by or <20>through<67> the Sun. This effective mass depends only from the
|
||
closest distance to the Solar center which a photon reaches when it travels
|
||
from the occulted planet to the observer. The dependence of the effective mass
|
||
from the occulted planet's distance is so small that it can be neglected for
|
||
our target precision of 0.001 arc seconds.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For a remote planet just at the edge of the
|
||
Solar disk the gravity deflection is about 1.8<94>, always pointing away from the
|
||
center of the Sun. This means that the planet is already slightly behind the
|
||
Solar disk (with a diameter of 1800<30>) when it appears to be at the limb,
|
||
because the light bends around the Sun. When the planet now passes on a central
|
||
path behind the Solar disk, the virtual gravity deflection we compute increases
|
||
to 2.57 times the deflection at the limb, and this maximum is reached at _ of
|
||
the Solar radius. Closer to the Solar center, the deflection drops and reaches
|
||
zero for photons passing centrally through the Sun's gravity field.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We have discussed our approach with Dr.
|
||
Myles Standish from JPL and here is his comment (private email to Alois
|
||
Treindl, 12-Sep-1997):</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:41.3pt;margin-bottom:
|
||
3.0pt;margin-left:1.0cm'><i><span lang=EN-US><3E>... it seems that your approach
|
||
is entirely reasonable and can be easily justified as long as you choose a
|
||
reasonable model for the density of the Sun. The solution may become more
|
||
difficult if an ellipsoidal Sun is considered, but certainly that is an
|
||
additional refinement which cannot be crucial.<2E><o:p></o:p></span></i></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;mso-list:none;tab-stops:14.2pt'><a
|
||
name="_Toc58488845"><span lang=EN-US>B. A list of asteroids</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ====================================<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># At the same time a brief introduction into
|
||
asteroids<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#
|
||
====================================================<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># As of the year 2010, there is no longer any
|
||
CDROM. All<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># parts of Swiss Ephemeris can be downloaded
|
||
in the download area.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Literature:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Lutz D. Schmadel, Dictionary of Minor
|
||
Planet Names,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Springer, Berlin, Heidelberg, New York<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Charles T. Kowal, Asteroids. Their Nature
|
||
and Utilization,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Whiley & Sons, 1996, Chichester,
|
||
England<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># What is an asteroid?<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># --------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Asteroids are small planets. Because there
|
||
are too many<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># of them and because most of them are quite
|
||
small,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># astronomers did not like to call them
|
||
"planets", but<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># invented names like "asteroid"
|
||
(Greek "star-like",<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># because through telescopes they did not
|
||
appear as planetary<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># discs but as star like points) or
|
||
"planetoid" (Greek<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># "something like a planet").
|
||
However they are also often<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># called minor planets.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># The minor planets can roughly be divided
|
||
into two groups.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># There are the inner asteroids, the majority
|
||
of which<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># circles in the space between Mars and
|
||
Jupiter, and<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># there are the outer asteroids, which have
|
||
their realm<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># beyond Neptune. The first group consists of
|
||
rather<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># dense, Earth-like material, whereas the
|
||
Transneptunians<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># mainly consist of water ice and frozen
|
||
gases. Many comets<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># are descendants of the
|
||
"asteroids" (or should one say<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># "comets"?) belt beyond Neptune.
|
||
The first Transneptunian<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># objects (except Pluto) were discovered only
|
||
after 1992<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># and none of them has been given a name as
|
||
yet.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># The largest asteroids<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Most asteroids are actually only debris of
|
||
collisions<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># of small planets that formed in the
|
||
beginning of the<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># solar system. Only the largest ones are
|
||
still more<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># or less complete and round planets.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Ceres<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># 913 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>goddess of corn and harvest<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Pallas<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 523 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>goddess of wisdom, war and liberal arts<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Vesta<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># 501 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>goddess of the hEarth fire<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>10<span style='mso-tab-count:1'><3E><><A0><A0> </span>Hygiea<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 429 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>goddess of health<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>511<span style='mso-tab-count:1'><3E><><A0> </span>Davida<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 324 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>after an astronomer David P. Todd<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>704<span style='mso-tab-count:1'><3E><><A0> </span>Interamnia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span># 338 km<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>"between
|
||
rivers", ancient name of<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>its discovery place Teramo<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>65<span style='mso-tab-count:1'><3E><><A0><A0> </span>Cybele<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 308 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>Phrygian Goddess, = Rhea, wife of Kronos-Saturn<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>52<span style='mso-tab-count:1'><3E><><A0><A0> </span>Europa<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 292 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>beautiful mortal woman, mother of Minos by Zeus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>87<span style='mso-tab-count:1'><3E><><A0><A0> </span>Sylvia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 282 km<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>451<span style='mso-tab-count:1'><3E><><A0> </span>Patientia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span># 280 km<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>patience<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>31<span style='mso-tab-count:1'><3E><><A0><A0> </span>Euphrosyne<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span># 270 km<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>one
|
||
of the three Graces, benevolence<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>15<span style='mso-tab-count:1'><3E><><A0><A0> </span>Eunomia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># 260 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>one of the Hours, order and law<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>324<span style='mso-tab-count:1'><3E><><A0> </span>Bamberga<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># 252 km<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span>after
|
||
a city in Bavaria<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Juno<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># 248 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>wife of Zeus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>16<span style='mso-tab-count:1'><3E><><A0><A0> </span>Psyche<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># 248 km<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span>"soul", name of a nymph<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Asteroid families<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># -----------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Most asteroids live in families. There are
|
||
several kinds<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># of families.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># - There are families that are separated
|
||
from each other<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># by orbital resonances with Jupiter or other
|
||
major planets.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># - Other families, the so-called Hirayama
|
||
families, are the<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># relics of asteroids that broke apart long
|
||
ago when they<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># collided with other asteroids.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># - Third, there are the Trojan asteroids
|
||
that are caught<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># in regions 60 degrees ahead or behind a
|
||
major planet<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># (Jupiter or Mars) by the combined
|
||
gravitational forces<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># of this planet and the Sun.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Near Earth groups:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Aten family: they cross Earth; mean
|
||
distance from Sun is less than Earth<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2062<span style='mso-tab-count:1'><3E><> </span>Aten<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># an Egyptian Sun god<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2100<span style='mso-tab-count:1'><3E><> </span>Ra-Shalom<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span># Ra is an Egyptian Sun god, Shalom is
|
||
Hebrew "peace"<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># was discovered during Camp
|
||
David mid-east peace conference<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Apollo family: they cross Earth; mean
|
||
distance is greater than Earth<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1862<span style='mso-tab-count:1'><3E><> </span>Apollo<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># Greek Sun god<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1566<span style='mso-tab-count:1'><3E><> </span>Icarus<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># wanted to fly to the sky, fell into
|
||
the ocean<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Icarus crosses Mercury, Venus,
|
||
Earth, and Mars<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># and has his perihelion very
|
||
close to the Sun<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3200<span style='mso-tab-count:1'><3E><> </span>Phaethon<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># wanted to drive the solar chariot,
|
||
crashed in flames<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Phaethon crosses Mercury,
|
||
Venus, Earth, and Mars<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># and has his perihelion very
|
||
close to the Sun<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Amor family: they cross Mars, approach Earth<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1221<span style='mso-tab-count:1'><3E><> </span>Amor<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Roman love god<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>433<span style='mso-tab-count:1'><3E><><A0> </span>Eros<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Greek love god<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Mars Trojans:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># -------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>5261<span style='mso-tab-count:1'><3E><> </span>Eureka<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># a mars Trojan<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Main belt families:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># -------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Hungarias: asteroid group at 1.95 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>434<span style='mso-tab-count:1'><3E><><A0> </span>Hungaria<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># after Hungary<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Floras: Hirayama family at 2.2 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>8<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Flora<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of flowers<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Phocaeas: asteroid group at 2.36 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>25<span style='mso-tab-count:1'><3E><><A0><A0> </span>Phocaea<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># maritime town in Ionia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Koronis family: Hirayama family at 2.88 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>158<span style='mso-tab-count:1'><3E><><A0> </span>Koronis<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># mother of Asklepios by Apollo<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Eos family: Hirayama family at 3.02 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>221<span style='mso-tab-count:1'><3E><><A0> </span>Eos<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of dawn<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Themis family: Hirayama family at 3.13 AU<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>24<span style='mso-tab-count:1'><3E><><A0><A0> </span>Themis<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># goddess of justice<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Hildas: asteroid belt at 4.0 AU, in 3:2
|
||
resonance with Jupiter<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#
|
||
--------------------------------------------------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># The Hildas have fairly eccentric orbits
|
||
and, at their<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># aphelion, are very close to the orbit of
|
||
Jupiter. However,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># at those times, Jupiter is ALWAYS somewhere
|
||
else. As<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Jupiter approaches, the Hilda asteroids
|
||
move towards<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># their perihelion points.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>153<span style='mso-tab-count:1'><3E><><A0> </span>Hilda<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># female first name, means
|
||
"heroine"<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># a single asteroid at 4.26 AU, in 4:3
|
||
resonance with Jupiter<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>279<span style='mso-tab-count:1'><3E><><A0> </span>Thule<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># mythical center of Magic in the
|
||
uttermost north<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Jupiter Trojans:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ----------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Only the Trojans behind Jupiter are
|
||
actually named after Trojan heroes,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># whereas the "Trojans" ahead of
|
||
Jupiter are named after Greek heroes that<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># participated in the Trojan war. However
|
||
there have been made some mistakes,<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># i.e. there are some Trojan
|
||
"spies" in the Greek army and some Greek "spies"<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># in the Trojan army.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Greeks ahead of Jupiter:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>624<span style='mso-tab-count:1'><3E><><A0> </span>Hector<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># Trojan "spy" in the Greek army,
|
||
by far the greatest<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Trojan hero and the greatest
|
||
Trojan asteroid<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>588<span style='mso-tab-count:1'><3E><><A0> </span>Achilles<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># slayer of Hector<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1143<span style='mso-tab-count:1'><3E><> </span>Odysseus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Trojans behind Jupiter:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1172<span style='mso-tab-count:1'><3E><> </span><3E>neas<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3317<span style='mso-tab-count:1'><3E><> </span>Paris<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>884<span style='mso-tab-count:1'><3E><><A0> </span>Priamus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Jupiter-crossing asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3552<span style='mso-tab-count:1'><3E><> </span>Don
|
||
Quixote<span style='mso-tab-count:1'><3E><><A0><A0> </span># perihelion near Mars,
|
||
aphelion beyond Jupiter;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># you know Don Quixote, don't
|
||
you?<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>944<span style='mso-tab-count:1'><3E><><A0> </span>Hidalgo<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># perihelion near Mars, aphelion near
|
||
Saturn;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># after a Mexican national hero<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>5335<span style='mso-tab-count:1'><3E><> </span>Damocles<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># perihelion near Mars, aphelion near
|
||
Uranus;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># the man sitting below a sword
|
||
suspended by a thread<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Centaurs:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2060<span style='mso-tab-count:1'><3E><> </span>Chiron<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># perihelion near Saturn, aphelion
|
||
near Uranus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># educator of heros, specialist
|
||
in healing and war arts<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>5145<span style='mso-tab-count:1'><3E><> </span>Pholus<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># perihelion near Saturn, aphelion
|
||
near Neptune<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># seer of the gods, keeper of
|
||
the wine of the Centaurs<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>7066<span style='mso-tab-count:1'><3E><> </span>Nessus<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># perihelion near Saturn, aphelion in
|
||
Pluto's mean distance<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># ferryman, killed by Hercules,
|
||
kills Hercules<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Plutinos:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># These are objects with periods similar to
|
||
Pluto, i.e. objects<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># that resonate with the Neptune period in a
|
||
3:2 ratio.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># There are no Plutinos included in Swiss
|
||
Ephemeris so far, but<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># PLUTO himself is considered to be a Plutino
|
||
type asteroid!<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Cubewanos:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ----------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># These are non-Plutiono objects with periods
|
||
greater than Pluto.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># The word "Cubewano" is derived
|
||
from the preliminary designation<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># of the first-discovered Cubewano: 1992 QB1<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>20001<span style='mso-tab-count:1'><3E> </span>1992
|
||
QB1<span style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># will be given the name of a
|
||
creation deity<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># (fictitious catalogue number
|
||
20001!)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Other Transplutonians:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>20001 1996 TL66<span style='mso-tab-count:
|
||
1'><3E><><A0><A0><A0><A0><A0> </span># mean solar distance 85 AU, period 780 years<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
Asteroids that challenge hypothetical planets astrology<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#
|
||
------------------------------------------------------------------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>42<span style='mso-tab-count:1'><3E><><A0><A0> </span>Isis<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># not identical with
|
||
"Isis-Transpluto"<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Egyptian lunar goddess<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>763<span style='mso-tab-count:1'><3E><><A0> </span>Cupido<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># different from Witte's Cupido<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Roman god of sexual desire<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4341<span style='mso-tab-count:1'><3E><> </span>Poseidon<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># not identical with Witte's Poseidon<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Greek name of Neptune<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4464<span style='mso-tab-count:1'><3E><> </span>Vulcano<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># compare Witte's Vulkanus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># and intramercurian
|
||
hypothetical Vulcanus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Roman fire god<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>5731<span style='mso-tab-count:1'><3E><> </span>Zeus<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># different from Witte's Zeus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Greek name of Jupiter<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1862<span style='mso-tab-count:1'><3E><> </span>Apollo<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># different from Witte's Apollon<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Greek god of the Sun<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>398<span style='mso-tab-count:1'><3E><><A0> </span>Admete<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># compare Witte's Admetos<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># "the untamed one",
|
||
daughter of Eurystheus<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Asteroids that challenge Dark Moon astrology<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#
|
||
--------------------------------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1181<span style='mso-tab-count:1'><3E><> </span>Lilith<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># not identical with Dark Moon 'Lilith'<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># first evil wife of Adam<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3753<span style='mso-tab-count:1'><3E><> </span>Cruithne<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># often called the "second Moon"
|
||
of Earth;<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># actually not a Moon, but an
|
||
asteroid that<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># orbits around the Sun in a
|
||
certain resonance<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># with the Earth.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span><span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># After the first Celtic group
|
||
to come to the British Isles.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
Also try the two points 60 degrees in front of and behind the<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
Moon, the so called Lagrange points, where the combined<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
gravitational forces of the Earth and the Moon might imprison<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
rocks and stones. There have been some photographic hints<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
that there are clouds of such material around these points.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US><span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>#
|
||
They are called the Kordylewski clouds.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Other asteroids<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>5<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Astraea<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># a goddess of justice<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>6<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Hebe<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of youth<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>7<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Iris<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># rainbow goddess, messenger of the
|
||
gods<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>8<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Flora<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of flowers and gardens<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>9<span style='mso-tab-count:1'><3E><><A0><A0><A0> </span>Metis<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of prudence<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>10<span style='mso-tab-count:1'><3E><><A0><A0> </span>Hygiea<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># goddess of health<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>14<span style='mso-tab-count:1'><3E><><A0><A0> </span>Irene<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># goddess of peace<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>16<span style='mso-tab-count:1'><3E><><A0><A0> </span>Psyche<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># "soul", a nymph<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>19<span style='mso-tab-count:1'><3E><><A0><A0> </span>Fortuna<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># goddess of fortune<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Some frequent names:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># --------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># There are thousands of female first names
|
||
in the asteroids list.<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Very interesting for relationship charts!<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>78<span style='mso-tab-count:1'><3E><><A0><A0> </span>Diana<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>170<span style='mso-tab-count:1'><3E><><A0> </span>Maria<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>234<span style='mso-tab-count:1'><3E><><A0> </span>Barbara<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>375<span style='mso-tab-count:1'><3E><><A0> </span>Ursula<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>412<span style='mso-tab-count:1'><3E><><A0> </span>Elisabetha<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>542<span style='mso-tab-count:1'><3E><><A0> </span>Susanna<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Wisdom asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># -----------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>134<span style='mso-tab-count:1'><3E><><A0> </span>Sophrosyne<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span># equanimity, healthy mind and
|
||
impartiality<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>197<span style='mso-tab-count:1'><3E><><A0> </span>Arete<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># virtue<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>227<span style='mso-tab-count:1'><3E><><A0> </span>Philosophia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>251<span style='mso-tab-count:1'><3E><><A0> </span>Sophia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># wisdom (Greek)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>259<span style='mso-tab-count:1'><3E><><A0> </span>Aletheia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># truth<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>275<span style='mso-tab-count:1'><3E><><A0> </span>Sapientia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span># wisdom (Latin)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Love asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ---------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>344<span style='mso-tab-count:1'><3E><><A0> </span>Desiderata<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>433<span style='mso-tab-count:1'><3E><><A0> </span>Eros<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>499<span style='mso-tab-count:1'><3E><><A0> </span>Venusia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>763<span style='mso-tab-count:1'><3E><><A0> </span>Cupido<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1221<span style='mso-tab-count:1'><3E><> </span>Amor<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1387<span style='mso-tab-count:1'><3E><> </span>Kama<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Indian god of sexual desire<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1388<span style='mso-tab-count:1'><3E><> </span>Aphrodite<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span># Greek love Goddess<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1389<span style='mso-tab-count:1'><3E><> </span>Onnie<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># what is this, after 1387 and 1388 ?<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1390<span style='mso-tab-count:1'><3E><> </span>Abastumani<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span># and this?<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># The Nine Muses<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># --------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>18<span style='mso-tab-count:1'><3E><><A0><A0> </span>Melpomene<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0> </span># Muse of tragedy<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>22<span style='mso-tab-count:1'><3E><><A0><A0> </span>Kalliope<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0> </span># Muse of heroic poetry<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>23<span style='mso-tab-count:1'><3E><><A0><A0> </span>Thalia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># Muse of comedy<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>27<span style='mso-tab-count:1'><3E><><A0><A0> </span>Euterpe<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># Muse of music and lyric poetry<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>30<span style='mso-tab-count:1'><3E><><A0><A0> </span>Urania<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0> </span># Muse of astronomy and astrology<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>33<span style='mso-tab-count:1'><3E><><A0><A0> </span>Polyhymnia<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0> </span># Muse of singing and rhetoric<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>62<span style='mso-tab-count:1'><3E><><A0><A0> </span>Erato<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># Muse of song and dance<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>81<span style='mso-tab-count:1'><3E><><A0><A0> </span>Terpsichore<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span># Muse of choral dance and song<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>84<span style='mso-tab-count:1'><3E><><A0><A0> </span>Klio<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span># Muse of history<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Money and big busyness asteroids<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># --------------------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>19<span style='mso-tab-count:1'><3E><><A0><A0> </span>Fortuna<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0> </span># goddess of fortune<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>904<span style='mso-tab-count:1'><3E><><A0> </span>Rockefellia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1338<span style='mso-tab-count:1'><3E><> </span>Duponta<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3652<span style='mso-tab-count:1'><3E><> </span>Soros<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Beatles asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4147<span style='mso-tab-count:1'><3E><> </span>Lennon<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4148<span style='mso-tab-count:1'><3E><> </span>McCartney<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4149<span style='mso-tab-count:1'><3E><> </span>Harrison<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>4150<span style='mso-tab-count:1'><3E><> </span>Starr<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Composer Asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># -------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2055<span style='mso-tab-count:1'><3E><> </span>Dvorak<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1814<span style='mso-tab-count:1'><3E><> </span>Bach<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1815<span style='mso-tab-count:1'><3E><> </span>Beethoven<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1034<span style='mso-tab-count:1'><3E><> </span>Mozartia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3941<span style='mso-tab-count:1'><3E><> </span>Haydn<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>And there are many more...<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Astrodienst asteroids:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># ----------------------<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Programmers group:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>3045<span style='mso-tab-count:1'><3E><> </span>Alois<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2396<span style='mso-tab-count:1'><3E><> </span>Kochi<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>2968<span style='mso-tab-count:1'><3E><> </span>Iliya<span
|
||
style='mso-tab-count:1'><3E><><A0><A0><A0><A0><A0><A0><A0><A0> </span># Alois' dog<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># artists group:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>412<span style='mso-tab-count:1'><3E><><A0> </span>Elisabetha<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Production family:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>612<span style='mso-tab-count:1'><3E><><A0> </span>Veronika<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1376<span style='mso-tab-count:1'><3E><> </span>Michelle<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1343<span style='mso-tab-count:1'><3E><> </span>Nicole<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1716<span style='mso-tab-count:1'><3E><> </span>Peter<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Children group<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>105<span style='mso-tab-count:1'><3E><><A0> </span>Artemis<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>1181<span style='mso-tab-count:1'><3E><> </span>Lilith<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Special interest group<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>564<span style='mso-tab-count:1'><3E><><A0> </span>Dudu<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>349<span style='mso-tab-count:1'><3E><><A0> </span>Dembowska<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>484<span style='mso-tab-count:1'><3E><><A0> </span>Pittsburghia<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US>#<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># By the year 1997, the statistics of
|
||
asteroid names looked as follows:<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Men (mostly family names) 2551<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Astronomers 1147<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Women (mostly first names) 684<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Mythological terms 542<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Cities, harbours buildings 497<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Scientists (no astronomers) 493<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Relatives of asteroid discoverers 277<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Writers 249<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Countries, provinces, islands 246<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Amateur astronomers 209<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Historical, political figures 176<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Composers, musicians, dancers 157<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Figures from literature, operas 145<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Rivers, seas, mountains 135<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Institutes, observatories 116<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Painters, sculptors 101<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:19.85pt;tab-stops:2.0cm 5.0cm 8.0cm'><span
|
||
class=sourcecode><span lang=EN-US># Plants, trees, animals 63</span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;mso-list:none;tab-stops:14.2pt'><a
|
||
name="_Toc58488846"><span lang=EN-US>C. How to Compare the Swiss Ephemeris with
|
||
Ephemerides of the JPL Horizons System</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Time and again people complain that they
|
||
find serious differences between the Swiss Ephemeris and JPL Horizons.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Comparing the Swiss Ephemeris with output
|
||
from the JPL Horizons web interface is unfortunately not trivial. In the
|
||
following, examples are given how you could proceed to arrive at
|
||
"identical" positions.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>First, if you use the Swiss Ephemeris test
|
||
program swetest on your personal computer, please make sure you are using the
|
||
most recent version of it. It can be downloaded from</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.astro.com/ftp/swisseph/programs/.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Alternatively, you could use the online
|
||
Swiss Ephemeris test page at</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.astro.com/swisseph/swetest.htm
|
||
.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note that if you are using an old version
|
||
of the Swiss Ephemeris, then your test results could be less satisfying.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If you choose to use swetest on your own
|
||
computer, you must install the JPL data file de431.eph.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the file is too big, then you can
|
||
download the files sepl_18.se1 and semo_18.se1 from here:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.astro.com/ftp/swisseph/ephe/</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note, however, that our implementation of
|
||
JPL algorithms works only with an original JPL file!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the sepl* and semo* files are used, the
|
||
algorithms of Astronomical Almanac will be used.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Using the online test page will be easier,
|
||
because you need not worry about correct installation, and you will have the
|
||
JPL data file available.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488847"><span lang=EN-US>Test 1: Astrometric
|
||
Positions ICRF/J2000</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In your Internet browser call the following
|
||
URL:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://ssd.jpl.nasa.gov/horizons.cgi</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The following default settings appear:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_8" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:342pt;
|
||
height:117.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image005.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=458 height=159
|
||
src="swisseph-Dateien/image006.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This means, JPL proposes to calculate a
|
||
geocentric ephemeris of Mars in one-day steps from today for a whole month.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If you click on the button "Generate
|
||
Ephemeris", the following output will appear:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_9" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:315.75pt;
|
||
height:48.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image007.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=423 height=67
|
||
src="swisseph-Dateien/image008.png" v:shapes="Picture_x0020_9"><![endif]></span></p>
|
||
|
||
<p class=image><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E></span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_10" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:302.25pt;
|
||
height:77.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image009.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=405 height=105
|
||
src="swisseph-Dateien/image010.png" v:shapes="Picture_x0020_10"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To reproduce this using the Swiss
|
||
Ephemeris, one must call swetest with the following parameters:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-ut0 -p4 -j2000 -icrs -fTPAD -n3 -ejplde431.eph -noaberr -nodefl<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.2016 greg. 0:00:00 UT version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>UT:
|
||
2457686.500000000 delta t: 68.423889 sec<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>TT:
|
||
2457686.500791943<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>26'13.53062930<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation 0<> 0'
|
||
0.00000000 0<> 0' 0.00000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars 19h22'24.4737
|
||
-24<32> 9'33.4190<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Mars 19h25'29.3663
|
||
-24<32> 2'30.7408<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Mars 19h28'34.3430
|
||
-23<32>55'14.1576<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If you are using the Swiss Ephemeris online
|
||
test page, then you can enter the whole parameter string</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-b25.10.2016 -ut0 -p4 -j2000 -icrs -fTPAD
|
||
-n3 -ejplde431.eph -noaberr -nodefl</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>in the field "other options". You
|
||
can ignore the other fields and leave them as they are.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parameters "-j2000 -icrs
|
||
-fTPAD" tell swetest to provide the positions in right ascension and
|
||
declination relative to the reference frame ICRF/J2000.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parameters "-noaberr -nodefl"
|
||
tell the program to ignore aberration of light and gravitational light
|
||
deflection, but include light-time in the calculation. These are so-called
|
||
astrometric positions.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parameter "-ejplde431.eph"
|
||
tells swetest to use the newest JPL ephemeris DE431. Note this will only work
|
||
if you have installed the DE431 data file on your computer or if you use the
|
||
Swiss Ephemeris online test page.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The above comparison may be satisfying but
|
||
it is not optimal. Please scroll up to "Current Settings" and click
|
||
on [change] in the following line:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Table Settings [change] : defaults</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the lower table, activate the checkbox
|
||
"extra precision", scroll down and click on "use settings
|
||
above".</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_11" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:327.75pt;
|
||
height:21.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image011.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=439 height=31
|
||
src="swisseph-Dateien/image012.png" v:shapes="Picture_x0020_11"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Scroll down, click on the button <20>Use
|
||
Settings Above<76>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then click on the button "Generate
|
||
Ephemeris<94> again.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now JPL provides four more digits.</span></p>
|
||
|
||
<p class=image><span lang=EN-US><!--[if gte vml 1]><v:shape id="Grafik_x0020_43"
|
||
o:spid="_x0000_i1057" type="#_x0000_t75" style='width:303pt;height:86.25pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image013.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=404 height=115
|
||
src="swisseph-Dateien/image013.png" v:shapes="Grafik_x0020_43"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The comparison is still not optimal,
|
||
because it is made in Universal Time (UT), and UT is understood as UTC, whereas
|
||
the Swiss Ephemeris defines the parameter -ut as UT1. Since the current version
|
||
of the Swiss Ephemeris (2.05.01) does not know a parameter for UTC, comparisons
|
||
should be made in Terrestrial Time (TT). If the input date is in the current or
|
||
a future year, there also may be considerable differences in Delta T values
|
||
used by JPL and Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To create an ephemeris for TT using JPL
|
||
Horizons, scroll up to "Current Settings" and click on [change] in
|
||
the following line:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Time Span [change] : Start=2016-10-25,
|
||
Stop=2016-11-24, Step=1 d</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the Start Time field add "TT"
|
||
behind the date.</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_13" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:212.25pt;
|
||
height:18.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image014.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=285 height=27
|
||
src="swisseph-Dateien/image015.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then click on the button "Use
|
||
Specified Times". After that click on "Generate Ephemeris"
|
||
again.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The new output shows:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_14" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:315.75pt;
|
||
height:35.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image016.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=423 height=49
|
||
src="swisseph-Dateien/image017.png" v:shapes="Picture_x0020_14"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>...</span></p>
|
||
|
||
<p class=image><span lang=DE-CH style='mso-ansi-language:DE-CH'><o:p> </o:p></span></p>
|
||
|
||
<p class=image><span lang=EN-US><!--[if gte vml 1]><v:shape id="Grafik_x0020_44"
|
||
o:spid="_x0000_i1054" type="#_x0000_t75" style='width:312.75pt;height:87pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image018.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=417 height=116
|
||
src="swisseph-Dateien/image018.png" v:shapes="Grafik_x0020_44"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>...</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then call swetest as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -j2000 -icrs -fTPAD -n3 -ejplde431.eph -noaberr -nodefl<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 25.10.2016
|
||
greg. 0:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>26'13.5306<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation 0<> 0'
|
||
0.0000 0<> 0' 0.0000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars 19h22'24.3273
|
||
-24<32> 9'33.7482<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Mars 19h25'29.2198
|
||
-24<32> 2'31.0810<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Mars 19h28'34.1965
|
||
-23<32>55'14.5088<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><o:p> </o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now the agreement is perfect, the precision
|
||
thus better than 1 mas.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488848"><span lang=EN-US>Test 2: Inertial
|
||
Apparent Positions, RA and DE, in ICRF</span></a><span lang=EN-US> </span></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now we are going to test apparent positions
|
||
relative to the International Celestial Reference Frame (ICRF). This option was
|
||
introduced in JPL Horizons version 4.70 in June 2020.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the current settings of JPL Horizons
|
||
click on [change] in the following line:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Table Settings [</span><span
|
||
class=FileName><span lang=DA style='mso-fareast-font-family:"DengXian Light";
|
||
mso-fareast-theme-font:major-fareast'>change</span></span><span lang=EN-US>] :
|
||
extra precision=YES</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the upper options table uncheck all
|
||
checkboxes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After that activate</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>checkbox 45: "Apparent RA &
|
||
DE".</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The table now looks as follows:</span></p>
|
||
|
||
<p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t32" coordsize="21600,21600"
|
||
o:spt="32" o:oned="t" path="m,l21600,21600e" filled="f">
|
||
<v:path arrowok="t" fillok="f" o:connecttype="none"/>
|
||
<o:lock v:ext="edit" shapetype="t"/>
|
||
</v:shapetype><v:shape id="Gerade_x0020_Verbindung_x0020_mit_x0020_Pfeil_x0020_35"
|
||
o:spid="_x0000_s1028" type="#_x0000_t32" style='position:absolute;left:0;
|
||
text-align:left;margin-left:328.5pt;margin-top:181.95pt;width:38.5pt;height:.5pt;
|
||
flip:y;z-index:251659264;visibility:visible;mso-wrap-style:square;
|
||
mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
|
||
mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
|
||
mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;
|
||
mso-position-horizontal-relative:text;mso-position-vertical:absolute;
|
||
mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
|
||
mso-width-relative:page;mso-height-relative:page' o:gfxdata="UEsDBBQABgAIAAAAIQC2gziS/gAAAOEBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRQU7DMBBF
|
||
90jcwfIWJU67QAgl6YK0S0CoHGBkTxKLZGx5TGhvj5O2G0SRWNoz/78nu9wcxkFMGNg6quQqL6RA
|
||
0s5Y6ir5vt9lD1JwBDIwOMJKHpHlpr69KfdHjyxSmriSfYz+USnWPY7AufNIadK6MEJMx9ApD/oD
|
||
OlTrorhX2lFEilmcO2RdNtjC5xDF9pCuTyYBB5bi6bQ4syoJ3g9WQ0ymaiLzg5KdCXlKLjvcW893
|
||
SUOqXwnz5DrgnHtJTxOsQfEKIT7DmDSUCaxw7Rqn8787ZsmRM9e2VmPeBN4uqYvTtW7jvijg9N/y
|
||
JsXecLq0q+WD6m8AAAD//wMAUEsDBBQABgAIAAAAIQA4/SH/1gAAAJQBAAALAAAAX3JlbHMvLnJl
|
||
bHOkkMFqwzAMhu+DvYPRfXGawxijTi+j0GvpHsDYimMaW0Yy2fr2M4PBMnrbUb/Q94l/f/hMi1qR
|
||
JVI2sOt6UJgd+ZiDgffL8ekFlFSbvV0oo4EbChzGx4f9GRdb25HMsYhqlCwG5lrLq9biZkxWOiqY
|
||
22YiTra2kYMu1l1tQD30/bPm3wwYN0x18gb45AdQl1tp5j/sFB2T0FQ7R0nTNEV3j6o9feQzro1i
|
||
OWA14Fm+Q8a1a8+Bvu/d/dMb2JY5uiPbhG/ktn4cqGU/er3pcvwCAAD//wMAUEsDBBQABgAIAAAA
|
||
IQCQls/sCAIAAFUEAAAOAAAAZHJzL2Uyb0RvYy54bWysVE1v2zAMvQ/YfxB0X+wka9AZcXpIl16K
|
||
LVi33hV9OEL1BUpNnH8/Sk7cdRt6GOaDIIl8j3wk5eVNbw05SIjau5ZOJzUl0nEvtOta+uP75sM1
|
||
JTExJ5jxTrb0JCO9Wb1/tzyGRs783hshgSCJi80xtHSfUmiqKvK9tCxOfJAOjcqDZQmP0FUC2BHZ
|
||
ralmdb2ojh5EAM9ljHh7OxjpqvArJXn6qlSUiZiWYm6prFDWXV6r1ZI1HbCw1/ycBvuHLCzTDoOO
|
||
VLcsMfIM+g8qqzn46FWacG8rr5TmsmhANdP6NzUPexZk0YLFiWEsU/x/tPzLYQtEi5bOF5Q4ZrFH
|
||
dxKYkORRwk478ew6YnUiWyW1IfOrXLJjiA0i124LWTTv3UO49/wpoq16ZcyHGAa3XoElyujwiJNS
|
||
qoX6SV+acRqbIftEOF5+vL7+dIUt42hazHGXuVmTSXLMADHdSW9J3rQ0JmC626e1dw6b7mEIwA73
|
||
MQ3ACyCDjctr9EaLjTamHKDbrQ2QA8NJ2Wxq/M4RX7klps1nJ0g6BaxUAs1cZ+TZM9MW+YPioj2d
|
||
jBxCfpMKC43K5kV7GXE5hhRP05EFPTNEYWojqH4bdPbNMFnGfgTO3gaO3iWid2kEWu08/A2c+kuq
|
||
avC/qB60Ztk7L05buEwDzm7p3fmd5cfx67nAX/4Gq58AAAD//wMAUEsDBBQABgAIAAAAIQD7N9rh
|
||
3wAAAAsBAAAPAAAAZHJzL2Rvd25yZXYueG1sTI/BboMwEETvlfoP1lbqrTEplBSCiaqoVXpNmg9w
|
||
8AYQ9ppiE8jf1zk1x50dzbwpNrPR7IKDay0JWC4iYEiVVS3VAo4/Xy/vwJyXpKS2hAKu6GBTPj4U
|
||
Mld2oj1eDr5mIYRcLgU03vc5565q0Ei3sD1S+J3tYKQP51BzNcgphBvNX6Mo5Ua2FBoa2eO2wao7
|
||
jEZAtdupbu6n4283JnrPP6/Z8nsrxPPT/LEG5nH2/2a44Qd0KAPTyY6kHNMC0rdV2OIFxGmcAQuO
|
||
VZwE5XRTkgx4WfD7DeUfAAAA//8DAFBLAQItABQABgAIAAAAIQC2gziS/gAAAOEBAAATAAAAAAAA
|
||
AAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10ueG1sUEsBAi0AFAAGAAgAAAAhADj9If/WAAAAlAEA
|
||
AAsAAAAAAAAAAAAAAAAALwEAAF9yZWxzLy5yZWxzUEsBAi0AFAAGAAgAAAAhAJCWz+wIAgAAVQQA
|
||
AA4AAAAAAAAAAAAAAAAALgIAAGRycy9lMm9Eb2MueG1sUEsBAi0AFAAGAAgAAAAhAPs32uHfAAAA
|
||
CwEAAA8AAAAAAAAAAAAAAAAAYgQAAGRycy9kb3ducmV2LnhtbFBLBQYAAAAABAAEAPMAAABuBQAA
|
||
AAA=
|
||
" strokecolor="red" strokeweight="1.5pt">
|
||
<v:stroke endarrow="block" joinstyle="miter"/>
|
||
<o:lock v:ext="edit" shapetype="f"/>
|
||
</v:shape><![endif]--><![if !vml]><span style='mso-ignore:vglayout;position:
|
||
relative;z-index:251659264'><span style='left:0px;position:absolute;left:437px;
|
||
top:-50049px;width:55px;height:12px'><img width=55 height=12
|
||
src="swisseph-Dateien/image019.png" v:shapes="Gerade_x0020_Verbindung_x0020_mit_x0020_Pfeil_x0020_35"></span></span><![endif]><span
|
||
lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_31"
|
||
o:spid="_x0000_i1053" type="#_x0000_t75" style='width:522.75pt;height:325.5pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image020.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=697 height=434
|
||
src="swisseph-Dateien/image021.png" v:shapes="Grafik_x0020_31"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Below the table click on "Use Selected
|
||
Settings".</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After that click on "Generate
|
||
Ephemeris" again. The output will show:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_30" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:341.25pt;
|
||
height:81.75pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image022.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=455 height=109
|
||
src="swisseph-Dateien/image022.png" v:shapes="Grafik_x0020_30"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then call swetest as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>swetest -b25.10.2016 -p4
|
||
-j2000 -icrs -fTPAD -n3 -ejplde431.eph<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>date (dmy) 25.10.2016
|
||
greg.<span style='mso-spacerun:yes'><3E><> </span>0:00:00 TT<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>version 2.08.00a<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast;mso-ansi-language:DE'>UT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2457686.499207094<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 68.507111 sec<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast;mso-ansi-language:DE'>TT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast;mso-ansi-language:DE'>Epsilon
|
||
(t/m)<span style='mso-spacerun:yes'><3E><><A0><A0> </span>23<32>26'13.53063031<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32>26'13.53063031<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast;mso-ansi-language:DE'>Nutation<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0></span>0<> 0' 0.00000000<span
|
||
style='mso-spacerun:yes'><3E><><A0> </span>0<> 0' 0.00000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast;mso-ansi-language:DE'>25.10.2016
|
||
Mars<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>19h22'23.9762<span
|
||
style='mso-spacerun:yes'><3E> </span>-24<32> 9'35.1525<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>26.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>19h25'28.8623<span
|
||
style='mso-spacerun:yes'><3E> </span>-24<32> 2'32.5179<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'>27.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>19h28'33.8325<span
|
||
style='mso-spacerun:yes'><3E> </span>-23<32>55'15.9790<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'><o:p> </o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This matches very well again, the differences
|
||
being smaller than 0.001 arc second.</span><span lang=EN-US style='mso-fareast-font-family:
|
||
"DengXian Light";mso-fareast-theme-font:major-fareast'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488849"><span lang=EN-US>Test 3: Apparent
|
||
Positions, True Equinox of Date, RA, DE, Ecliptic Longitude and Latitude</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now we are going to test apparent positions
|
||
relative to the true equinox of date.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the current settings of JPL Horizons
|
||
click on [change] in the following line:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Table Settings [</span><span
|
||
class=FileName><span lang=DA style='mso-fareast-font-family:"DengXian Light";
|
||
mso-fareast-theme-font:major-fareast'>change</span></span><span lang=EN-US>] :
|
||
extra precision=YES</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the upper options table uncheck all
|
||
checkboxes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After that activate</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>checkbox 2. "Inertial Apparent RA
|
||
& DE" and</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>checkbox 31. "observer ecliptic lon.
|
||
& lat."</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The table now looks as follows:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_16" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:453pt;
|
||
height:267.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image023.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=606 height=359
|
||
src="swisseph-Dateien/image024.png" v:shapes="Picture_x0020_16"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Below the table click on "Use Selected
|
||
Settings".</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After that click on "Generate
|
||
Ephemeris" again. The output will show:</span></p>
|
||
|
||
<p class=image><span lang=EN-US><!--[if gte vml 1]><v:shape id="Grafik_x0020_46"
|
||
o:spid="_x0000_i1050" type="#_x0000_t75" style='width:450.75pt;height:82.5pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image025.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=601 height=110
|
||
src="swisseph-Dateien/image025.png" v:shapes="Grafik_x0020_46"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then call swetest as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -fTPADlb -n3 -ejplde431.eph -jplhora<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 25.10.2016
|
||
greg. 0:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT:
|
||
2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true)
|
||
23<B0>26' 5.1372<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
7.1942 -0<> 0' 8.4288<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars
|
||
19h23'24.4849 -24<32> 7'29.0250 288.9700710 -2.0525051<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Mars
|
||
19h26'29.2727 -24<32> 0'22.2459 289.6832956 -2.0365320<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Mars
|
||
19h29'34.1403 -23<32>53' 1.5764 290.3981125 -2.0204721<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This matches very well again, the
|
||
differences being smaller than 0.001 arc second.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The parameter -jplhora tells the program to
|
||
emulate the methods of JPL horizons.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Better precision for current or recent
|
||
dates would require daily updates for unpredictable motions of the celestial
|
||
pole (free core nutation) and other micro-improvements. We are not freaky
|
||
enough to do that.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488850"><span lang=EN-US>Test 4: Heliocentric
|
||
Apparent Positions, Ecliptic Longitude and Latitude</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now, let us do the same calculations
|
||
heliocentrically by changing the observer location to <20>@sun<75>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_9" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:378.75pt;
|
||
height:94.5pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image026.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=505 height=126
|
||
src="swisseph-Dateien/image026.png" v:shapes="Grafik_x0020_9"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now the resulting ephemeris looks as
|
||
follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_40" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:447.75pt;
|
||
height:75.75pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image027.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=597 height=101
|
||
src="swisseph-Dateien/image027.png" v:shapes="Grafik_x0020_40"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>And we just add the parameter -hel to the
|
||
swetest command we have used above:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -fTPADlb -n3 -ejplde431.eph -jplhora -hel<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h24'25.8882<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>53' 6.8990<span
|
||
style='mso-spacerun:yes'><3E> </span>333.5274937<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7959670<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h26'50.3458<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>38'56.8013<span
|
||
style='mso-spacerun:yes'><3E> </span>334.1625958<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7909547<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h29'14.5668<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>24'42.1490<span
|
||
style='mso-spacerun:yes'><3E> </span>334.7977357<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7857221</span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Here, we have a considerable difference
|
||
between Horizons and swetest. Why?</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The answer is found when we scroll down in
|
||
the Horizons output. There we read:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_41" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:441.75pt;
|
||
height:66pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image028.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=589 height=88
|
||
src="swisseph-Dateien/image028.png" v:shapes="Grafik_x0020_41"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>So, they are using the 2009 equator of the
|
||
Sun, whereas swetest uses the true Earth equator of date. There is nothing
|
||
wrong with either calculation, just Horizons does something different than
|
||
swetest. Horizons<6E>s positions cannot be reproduced using swetest, and the
|
||
swetest data cannot be reproduced using Horizons.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As for the other two values (ObsEcLon and
|
||
ObsEcLat), Horizons states:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_42" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:6in;
|
||
height:47.25pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image029.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=576 height=63
|
||
src="swisseph-Dateien/image029.png" v:shapes="Grafik_x0020_42"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This means that in order to reproduce these
|
||
values, we have to add the following parameters <20>-j2000 -icrs<72> to swetest:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -fTPADlb -n3 -ejplde431.eph -jplhora -hel -j2000 -icrs<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h23'32.8216<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>58'15.5314<span
|
||
style='mso-spacerun:yes'><3E> </span></span></span><span class=sourcecode><span
|
||
lang=EN-US style='color:red'>333.2945511<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7951619</span><span lang=EN-US><o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h25'57.3574<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>44' 6.7775<span
|
||
style='mso-spacerun:yes'><3E> </span></span></span><span class=sourcecode><span
|
||
lang=EN-US style='color:red'>333.9296388<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7901721<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Mars<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>22h28'21.6564<span
|
||
style='mso-spacerun:yes'><3E> </span>-11<31>29'53.4295<span
|
||
style='mso-spacerun:yes'><3E> </span></span></span><span class=sourcecode><span
|
||
lang=EN-US style='color:red'>334.5647705<span style='mso-spacerun:yes'><3E>
|
||
</span>-1.7849622<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>These values (the red ones) again match
|
||
very well with Horizons<6E>s data ObsEcLon and ObsEcLat.</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><o:p> </o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488851"><span lang=EN-US>Test 5: Ephemerides
|
||
before 1962</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The swetest call of Test 3 can reproduce
|
||
JPL Horizons positions very well for its whole time range. For dates in the
|
||
year 1800, Horizons provides the following data:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_18" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:448.5pt;
|
||
height:72.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image030.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=600 height=99
|
||
src="swisseph-Dateien/image031.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Using the above swetest parameters, we get
|
||
the following values from SE 2.07 on:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.1800
|
||
-p4 -fTPADlb -n3 -ejplde431.eph -jplhora<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.1800 greg. 0:00:00 TT<span style='mso-tab-count:2'><3E><> </span>version
|
||
2.06.01b03<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2378793.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>28'
|
||
3.5798<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
5.9992 0<> 0' 8.9010<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.1800 Mars 3h17'43.4887
|
||
17<B0>14' 9.2071 51.5928231 -0.9812193<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.1800 Mars 3h16'26.6082
|
||
17<B0>12'27.6742 51.2899907 -0.9289476<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.1800 Mars 3h15'
|
||
7.5294 17<31>10'37.9300 50.9781652 -0.8760415<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is better than 2 milliarcsec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If comparing BCE dates, please note that
|
||
the Swiss Ephemeris uses astronomical year numbering whereas JPL Horizons uses
|
||
historical year numbering. The latter omits the year 0 so that the astronomical
|
||
year 0 corresponds to the historical year 1 BCE.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>E.g. you can set the date parameters in
|
||
Horizons as follows:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_19" o:spid="_x0000_i1044" type="#_x0000_t75" alt="horizons_bc"
|
||
style='width:453pt;height:231.75pt;visibility:visible;mso-wrap-style:square'
|
||
o:bordertopcolor="#bfbfbf" o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf"
|
||
o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image032.png" o:title="horizons_bc"/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=606 height=311
|
||
src="swisseph-Dateien/image033.png" alt="horizons_bc" v:shapes="Picture_x0020_19"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The output is:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_20" o:spid="_x0000_i1043" type="#_x0000_t75" alt="horizons_bc2"
|
||
style='width:302.25pt;height:66.75pt;visibility:visible;mso-wrap-style:square'
|
||
o:bordertopcolor="#bfbfbf" o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf"
|
||
o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image034.png" o:title="horizons_bc2"/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=405 height=91
|
||
src="swisseph-Dateien/image035.png" alt="horizons_bc2" v:shapes="Picture_x0020_20"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This can be reproduced using the Swiss
|
||
Ephemeris only <strong><span style='font-family:"Segoe UI",sans-serif'>if the
|
||
year is entered as -9900 (not 9901!)</span></strong>:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b1.1.-9900
|
||
-p0 -fTPlb -ejplde431.eph -jplhora -n2<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 1.1.-9900
|
||
jul. 0:00:00 TT<span style='mso-tab-count:2'><3E><> </span>version 2.06.01b03<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: -1894917.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 24<32>
|
||
9'53.63485083<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation 0<>
|
||
0'14.26577554 0<> 0' 0.69489094<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>01.01.-9900 Sun 206.2288423
|
||
-0.0001386<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>02.01.-9900 Sun 207.1940735
|
||
-0.0001706<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The deviation amounts to only 3
|
||
milliarcsec.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488852"><span lang=EN-US>Test 6: Jupiter
|
||
versus Jupiter Barycentre</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is another problem with planets that
|
||
have a system of satellites, e.g. Jupiter.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Scroll up and click on [change] in the
|
||
following line:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Target Body [</span><span class=FileName><span
|
||
lang=DA>change</span></span><span lang=EN-US>] :<span style='mso-tab-count:
|
||
1'> </span>Mars [499]</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then enter Jupiter in the field <20>Lookup the
|
||
specified body<64> and click on the button <20>Search<63>:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_21" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:453.75pt;
|
||
height:176.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image036.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=607 height=237
|
||
src="swisseph-Dateien/image037.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then select <20>Jupiter<65> from the droplist and
|
||
click on the button <20>Select Indicated Body<64>:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_22" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:362.25pt;
|
||
height:203.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image038.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=485 height=273
|
||
src="swisseph-Dateien/image039.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After that, click on the button <20>Generate
|
||
Ephemeris<94> again.</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="_x0000_i1040" type="#_x0000_t75" style='width:451.5pt;height:77.25pt;
|
||
visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image040.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=604 height=105
|
||
src="swisseph-Dateien/image041.png" v:shapes="_x0000_i1040"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then call swetest using the same parameters
|
||
that have been used for Mars:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p5 -fTPADlb -n1 -ejplde431.eph -jplhora<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.2016 greg. 0:00:00 ET<span style='mso-tab-count:2'><3E><> </span>version
|
||
2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>26'
|
||
5.1372<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
7.1942 -0<> 0' 8.4288<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Jupiter 12h37'35.2750
|
||
-2<>50'16.5904 189.7497445 1.1132117<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Jupiter
|
||
12h38'21.2913 -2<>55' 5.7347 189.9574345 1.1144628<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Jupiter
|
||
12h39' 7.1802 -2<>59'53.7050 190.1644967 1.1157502<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Here we find a difference that did not
|
||
appear with Mars. It amounts to 0.02 arcsec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is explained by the fact that the
|
||
Swiss Ephemeris provides the position of the barycentre of the system of
|
||
Jupiter with his Moons, whereas JPL provides the position of the planet itself.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If we had selected <20>Jupiter Barycenter<65> in
|
||
the drop list instead of <20>Jupiter<65>, then we would have arrived at the following
|
||
positions.</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_24" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:450pt;
|
||
height:77.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image042.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=602 height=105
|
||
src="swisseph-Dateien/image043.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is very close to the value provided by
|
||
the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A similar effect could be observed with
|
||
other planets that have Moons. In fact, it also appears with Mars, however his Moons
|
||
are so extremely small that the effect did not appear in our comparison further
|
||
above.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The fundamental JPL ephemeris DE431 does
|
||
not provide the position of the centre of the disk of a planet, but only the
|
||
centre of gravity of the planet<65>s satellite system. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488853"><span lang=EN-US>Test 7: Jupiter<65>s
|
||
Center of Body</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Since Swiss Ephemeris version 2.10 (Nov.
|
||
2020), the center of Jupiter<65>s body can also be calculated as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p5 -cob -fTPADlb -n3 -ejplde431.eph -jplhora<span style='mso-spacerun:yes'><3E>
|
||
</span>(note -cob)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.2016 greg. 0:00:00 ET<span style='mso-tab-count:2'><3E><> </span>version
|
||
2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT:
|
||
2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true)
|
||
23<B0>26' 5.1372<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
7.1942 -0<> 0' 8.4288<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Jupiter 12h37'35.2762
|
||
-2<>50'16.5997 189.7497501 1.1132113<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016 Jupiter 12h38'21.2937
|
||
-2<>55' 5.7523 189.9574457 1.1144622<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016 Jupiter 12h39'
|
||
7.1824 -2<>59'53.7197 190.1645068 1.1157500<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><o:p> </o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The same output can also be generated using
|
||
this command:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-pv -xv9599 -fTPADlb -n3 -ejplde431.eph -jplhora<span
|
||
style='mso-spacerun:yes'><3E> </span>(note -pv -xv9599)<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Horizons provides the following data:</span></p>
|
||
|
||
<p class=MsoNormal><span style='mso-ansi-language:DE;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_23" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:451.5pt;
|
||
height:77.25pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image040.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=604 height=105
|
||
src="swisseph-Dateien/image041.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Again, we have an accuracy of 1 mas.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Important: All hitherto ephemerides and
|
||
astrology softwares provide only the barycenter of the Jupiter system, i.e. the
|
||
center of mass of Jupiter together with all his moons, not the center of
|
||
Jupiter<92>s body or the real planet. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Software developers who want to implement
|
||
centers of body have to know that the performance of this calculation is not as
|
||
good as with the barycenters. Moreover, the time range is currently limited to
|
||
the years 1900 to 2047.</span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-numeric ideograph-other'><span class=sourcecode><span
|
||
lang=EN-US style='mso-fareast-language:ZH-CN'><o:p> </o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488854"><span lang=EN-US>Test 8: Geocentric
|
||
Position of a Planetary Moon</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This test requires Swiss Ephemeris version
|
||
2.10 and the ephemeris files sepm* of directory sat.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We initialise Horizons to calculate
|
||
geocentric apparent positions of Jupiter Moon Io:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_45" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:383.25pt;
|
||
height:94.5pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image044.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=511 height=126
|
||
src="swisseph-Dateien/image044.png" v:shapes="Grafik_x0020_45"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The output is as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_48" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:269.25pt;
|
||
height:71.25pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image045.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=359 height=95
|
||
src="swisseph-Dateien/image045.png" v:shapes="Grafik_x0020_48"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To reproduce this, swetest requires the
|
||
parameters <20>-pv -xv9501<30>. (For the numbering of the planetary Moons, we use
|
||
Horizons<92>s number + 9000, thus for Io 9000+501.) </span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-pv -xv9501 -fTPlb -n3 -ejplde431.eph -jplhora<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>189.7447220<span
|
||
style='mso-spacerun:yes'><3E><> </span>1.1123951<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>189.9522434<span
|
||
style='mso-spacerun:yes'><3E><> </span>1.1156229<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>190.1792187<span
|
||
style='mso-spacerun:yes'><3E><> </span>1.1144514<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US><o:p> </o:p></span></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488855"><span lang=EN-US>Test 9:
|
||
Planetocentric Position of a Planetary Moon</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now, we try the same choosing Jupiter
|
||
himself as the observer location. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Depending on the selected moon, accuracy
|
||
will usually be better than 1 arcsec, but not always. With some
|
||
very-fast-moving, such as Phobos and Deimos, we cannot reach that. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover, it must be noted that the current
|
||
comparisons were made with Io<49>s ephemeris of 11 September 2020. This date is
|
||
given on the output page of Horizons:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_51" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:444pt;
|
||
height:81.75pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image046.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=592 height=109
|
||
src="swisseph-Dateien/image046.png" v:shapes="Grafik_x0020_51"><![endif]></span><span
|
||
lang=EN-US><span style='mso-spacerun:yes'><3E></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Before a comparison is made, it should be
|
||
made sure that Horizons has not updated its ephemeris. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The date of our Swiss Ephemeris file is
|
||
seen in its header:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_52" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:504.75pt;
|
||
height:60pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image047.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=673 height=80
|
||
src="swisseph-Dateien/image047.png" v:shapes="Grafik_x0020_52"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the <20>Revised<65> date in Horizons is
|
||
younger than the one in the Swiss Ephemeris file, then it is likely that the
|
||
latter is outdated and has lost accuracy.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now, to do the comparison, in the field <20></span><span
|
||
lang=EN-US style='font-family:"Arial",sans-serif;color:black;background:white'>Specify
|
||
Origin: Named Body or Site<74>, we enter </span><span lang=EN-US><3E>@599<39> for
|
||
Jupiter, center of body.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_49" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:382.5pt;
|
||
height:96pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image048.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=510 height=128
|
||
src="swisseph-Dateien/image048.png" v:shapes="Grafik_x0020_49"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The resulting output is:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_50" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:278.25pt;
|
||
height:72.75pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image049.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=371 height=97
|
||
src="swisseph-Dateien/image049.png" v:shapes="Grafik_x0020_50"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The swetest command to reproduce these data
|
||
is:<br>
|
||
</span><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016 -pv -xv9501
|
||
-pc9599 -fTPlb -n3 -ejplde431.eph -j2000 -icrs -jplhora <o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>185.5872647<span
|
||
style='mso-spacerun:yes'><3E> </span>-1.0216308<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>26.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>28.8942489<span
|
||
style='mso-spacerun:yes'><3E><> </span>1.7046449<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>27.10.2016
|
||
Io/Jupiter<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>232.9244695<span
|
||
style='mso-spacerun:yes'><3E> </span>-2.1166255<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This demonstrates the high accuracy of the
|
||
planetary moons in the Swiss Ephemeris very well. The difference is about
|
||
0.01<94>. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If you want to compare other quantities in
|
||
planetocentric mode, you will have to proceed as follows: </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>- choose the quantities in the Horizons
|
||
interface</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>- click on <20>Generate Ephemeris<69></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>- in the output, scroll down to the
|
||
explanations at the bottom of the page</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>- read und try to understand what exactly
|
||
Horizons does</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>- find out if swetest can do the same</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In case it does not work, you are welcome
|
||
to ask for help in the Swiss Ephemeris mailing list.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Please note that for <span
|
||
style='color:red'>quantity 2</span> (R.A. and Dec airless apparent), agreement
|
||
between Horizons and swetest is not possible because Horizons uses the 2009
|
||
equator of the planet (e.g. Jupiter) whereas swetest always uses the true
|
||
equator of date of the Earth. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For <span style='color:red'>quantity 45</span>,
|
||
please use this command:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-pv -xv9501 -pc9599 -fTPAD -n3 -ejplde431.eph -j2000 -icrs<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For <span style='color:red'>quantity 1</span>,
|
||
this one:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-pv -xv9501 -pc9599 -fTPAD -n3 -ejplde431.eph -j2000 -icrs -noaberr -nodefl</span></span><span
|
||
lang=EN-US style='font-family:Consolas;color:#C45911'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488856"><span lang=EN-US>Test 10: Topocentric
|
||
Position of a Planet</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To calculate the topocentric position of a
|
||
planet proceed as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Scroll up to <20>Current Settings<67>, change
|
||
Target Body and select Venus.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>After clicking on <20>Select Indicated Body<64>,
|
||
change Time Span, edit</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>Start Time<6D> to <20>2015-09-01 05:00 TT<54> and</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><3E>Stop Time<6D> to <20>2015-09-03<30>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We choose a date near the heliacal rising
|
||
of Venus, where the parallax effect is greater.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then change Table Settings, activate only
|
||
the checkboxes</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt'><span lang=EN-US>2. Apparent RA
|
||
& DEC and</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:14.2pt'><span lang=EN-US>31. Observer
|
||
ecliptic lon. & lat.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>and uncheck all other options.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the lower options table activate the
|
||
option <20>extra precision<6F>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Scroll down and click on the button <20>Use
|
||
Settings Above<76>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Finally change Observer Location. In the
|
||
field <20>Lookup Named Location<6F> enter <20>Jerusalem<65> and click on the Button
|
||
<93>Search<94>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now the current settings should look as
|
||
follows:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_25" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:385.5pt;
|
||
height:132pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image050.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=516 height=178
|
||
src="swisseph-Dateien/image051.jpg" v:shapes="Picture_x0020_25"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Please check carefully if you have exactly
|
||
these data and otherwise correct them.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then click on <20>Generate Ephemeris<69>. The
|
||
output is as follows:</span></p>
|
||
|
||
<p class=image><span style='mso-ansi-language:DE'><!--[if gte vml 1]><v:shape
|
||
id="Picture_x0020_26" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:454.5pt;
|
||
height:84.75pt;visibility:visible;mso-wrap-style:square' o:bordertopcolor="#bfbfbf"
|
||
o:borderleftcolor="#bfbfbf" o:borderbottomcolor="#bfbfbf" o:borderrightcolor="#bfbfbf">
|
||
<v:imagedata src="swisseph-Dateien/image052.png" o:title=""/>
|
||
<w:bordertop type="single" width="6"/>
|
||
<w:borderleft type="single" width="6"/>
|
||
<w:borderbottom type="single" width="6"/>
|
||
<w:borderright type="single" width="6"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=115
|
||
src="swisseph-Dateien/image053.jpg" v:shapes="Picture_x0020_26"><![endif]></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In the current settings you see the
|
||
geographic coordinates of Jerusalem as used by Horizons. You have to transform
|
||
them into decimal values in order to use them with swetest.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Now call swetest as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b01.09.2015
|
||
-t5 -p3 -fTPADlb -n2 -ejplde431.eph -jplhora -topo35.233305,31.766694,0<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 1.9.2015
|
||
greg. 5:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2457266.708333333<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>geo. long 35.233305,
|
||
lat 31.766694, alt 0.000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Epsilon
|
||
(true) 23<32>26' 5.3157<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Nutation
|
||
0<B0> 0' 1.3321 -0<> 0' 8.7886<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>01.09.2015
|
||
5:00:00 ET Venus 9h 0'32.0966 9<> 3'13.6147 134.9240534 -7.6248475<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>02.09.2015 5:00:00
|
||
ET Venus 8h59'56.4969 9<>12'43.0988 134.7370775 -7.5147577<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This is very precise again. The geocentric
|
||
positions would be:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b01.09.2015
|
||
-t5 -p3 -fTPADlb -n2 -ejplde431.eph -jplhora<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 1.9.2015
|
||
greg. 5:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>TT:
|
||
2457266.708333333<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Epsilon
|
||
(true) 23<32>26' 5.3157<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Nutation
|
||
0<B0> 0' 1.3321 -0<> 0' 8.7886<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>01.09.2015
|
||
5:00:00 ET Venus 9h 0'30.9799 9<> 3'25.0943 134.9186940 -7.6230971<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>02.09.2015 5:00:00
|
||
ET Venus 8h59'55.4154 9<>12'54.3289 134.7318831 -7.5130275<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Note, if you specify the time as UT and
|
||
call the Swiss Ephemeris with -ut5 (instead of -t5), then the deviation is
|
||
slightly greater, because Horizons uses UTC, whereas the Swiss Ephemeris uses
|
||
UT1. If the input date is in the current or a future year, there also may be
|
||
differences in Delta T values used by JPL and the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Significant deviations from Horizons only
|
||
appear with the topocentric Moon, where our error can amount to 0.2 arcsec. We
|
||
have not studied this difference so far, so do not know its exact cause.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;mso-list:none;tab-stops:14.2pt'><a
|
||
name="_Toc58488857"><span lang=EN-US>D. How to compare the Swiss Ephemeris with
|
||
Ephemerides of the Astronomical Almanac (apparent positions)</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488858"><span lang=EN-US>Test 7: Astronomical
|
||
Almanac online</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Get a recent "Astronomical
|
||
Almanac" from the library or your bookshelf. If you are too lazy to do
|
||
that, go on the following page:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://asa.usno.navy.mil/SecE/Section_E.html</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>and click on "Geocentric equatorial
|
||
coordinates".</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The position of Mars for today (25 Oct
|
||
2016), 0:00 TT, is given as:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mars 19 23 24.488 -24 07 29.03 1.2088279</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Then call swetest using the following
|
||
parameters:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -fTPADR -ejplde431.eph<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.2016 greg. 0:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>26'
|
||
5.1018<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
7.1942 -0<> 0' 8.4288<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars 19h23'24.4884
|
||
-24<32> 7'29.0249 1.208903220<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is a difference in the distance value
|
||
R. The reason is that AA combines apparent RA and DE with true distance.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To arrive at the same distance value, call
|
||
swetest as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest -b25.10.2016
|
||
-p4 -fTPR -ejplde431.eph -true<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy)
|
||
25.10.2016 greg. 0:00:00 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>TT: 2457686.500000000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Epsilon (true) 23<32>26'
|
||
5.1018<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>Nutation -0<> 0'
|
||
7.1942 -0<> 0' 8.4288<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>25.10.2016 Mars 1.208827910<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>which is identical to AA, but has more
|
||
digits.</span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.0pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:39.7pt;margin-right:14.45pt'>
|
||
|
||
<h3 style='margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:
|
||
0cm;mso-list:none'><a name="_Toc58488859"><span lang=EN-US>Test 8: Astronomical
|
||
Almanac printed</span></a></h3>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If you are not too lazy to get a printed AA
|
||
of a recent year or manage to get pages B68-B70 from AA 2016 in google books,
|
||
there you will find an additional digit both in right ascension and
|
||
declination.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Page B68 gives an example how to calculate
|
||
the apparent position of Venus for 17 April 2016 12:00 UT1, assuming Delta T as
|
||
68s.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On p. B69, the corresponding TT is given as
|
||
JD 2457496.000787.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On p. B70, the result is given as RA =
|
||
0h55m33s.8912, DE = 4<>23'25".333.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss Ephemeris provides the same
|
||
result if called with the following parameters:</span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>swetest
|
||
-bj2457496.000787 -p3 -fTPAD -ejplde431.eph<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span lang=EN-US>date (dmy) 17.4.2016
|
||
greg. 12:01:08 ET version 2.05.02b04<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>TT:
|
||
2457496.000787000<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Epsilon
|
||
(true) 23<32>26' 5.0046<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>Nutation
|
||
-0<> 0' 3.8526 -0<> 0' 8.7703<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span class=sourcecode><span style='mso-ansi-language:DE'>17.04.2016
|
||
12:01:08 ET Venus 0h55'53.8912 4<>23'25.3326<o:p></o:p></span></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>You may find that there is a difference of
|
||
about 0.052 arcsec between JPL Horizons and Astronomical Almanac. For more
|
||
information on this, please read the following paragraph in the general
|
||
documentation of the Swiss Ephemeris:</span></p>
|
||
|
||
<p class=ListBullet1 style='mso-list:l35 level1 lfo12'><a name="_Hlk17743987"><![if !supportLists]><span
|
||
lang=EN-US style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
|
||
Symbol'><span style='mso-list:Ignore'><3E><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span></span><![endif]><span lang=EN-US>http://www.astro.com/swisseph/swisseph.htm?lang=g#_Toc443485363</span></a></p>
|
||
|
||
<span style='mso-bookmark:_Hlk17743987'></span>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(2.1.2.2 Swiss Ephemeris and JPL Horizons
|
||
System)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<div style='mso-element:para-border-div;border:none;border-bottom:solid windowtext 1.5pt;
|
||
padding:0cm 0cm 1.0pt 0cm;margin-left:19.85pt;margin-right:0cm'>
|
||
|
||
<h2 style='margin-left:0cm;mso-list:none;tab-stops:35.4pt'><a
|
||
name="_Toc58488860"><span lang=EN-US>E. How to compare the Swiss Ephemeris
|
||
Lahiri Ayanamsha with Values from <i style='mso-bidi-font-style:normal'>Indian
|
||
Astronomical Ephemeris</i> (IAE)</span></a></h2>
|
||
|
||
</div>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><i style='mso-bidi-font-style:normal'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Problems<o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The
|
||
ayanamsha values and explanations given in <i style='mso-bidi-font-style:normal'>Indian
|
||
Astronomical Ephemeris </i>are unfortunately confusing. Clarification is
|
||
difficult to achieve because older issues of IAE are difficult to get hold of,
|
||
even for Indian members of the Swiss Ephemeris mailing list. In May 2020, </span><span
|
||
lang=EN-US>I (D.K.) contacted the <i style='mso-bidi-font-style:normal'>Positional
|
||
Astronomy Centre (PAC) </i>in Kolkata, the publisher of IAE, for precise
|
||
information. On 29 June, I received a reply from L.M. Jyoti of PAC. My
|
||
questions were not answered in detail, but Mr. Jyoti confirmed the correctness
|
||
of my findings and said they would be important for <20>further modification of
|
||
calculation of Indian Astronomical Ephemeris<69>.</span><span lang=EN-US
|
||
style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt'>As to the precession model used,
|
||
we know from IAE 1989, p. 525, that <20></span><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>Use of the Newcomb's value for general
|
||
precession has been discontinued in this publication with effect from
|
||
1985". In what follows, a new precession formula is given which is taken
|
||
Lieske<92>s publication for the IAU1976 system.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>In IAE
|
||
2019, p. 445, the following information is given:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>"The
|
||
algorithms for precession were based on the IAU (1976) value for the rate of general
|
||
precession in ecliptic longitude. Nutation was given by the 1980 IAU Theory of
|
||
Nutation. However, IAU (1976) rate of precession had been overestimated by
|
||
approximately 3 milliarcseconds per year. Further observations also revealed
|
||
periodic errors of a few milliarcseconds in the 1980 IAU Theory of
|
||
Nutation."<br>
|
||
"As part of the 2000 IAU resolutions, the IAU 2000A precession-nutation
|
||
model was introduced, based on an updated value for the rate of precession and
|
||
a completely new nutation theory."<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>So,
|
||
which of the two precession models is used in IAE2019? Model IAU 1976 or IAU
|
||
2000A?<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>And
|
||
there is more confusion: <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>In its original definition, <20>Lahiri<72> ayanamsha had the value
|
||
23<B0>15'00" on the 21 March 1956, 0:00 Ephemeris Time. The definition was
|
||
corrected by 0.658<94> in Indian Astronomical Ephemeris 1989, page 556, footnote:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>"According to new determination of the
|
||
location of equinox this initial value has been revised to 23<32>15'00".658
|
||
and used in computing the mean ayanamsha with effect from 1985'."</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Thus, the mean (!) value of ayanamsha on
|
||
the said date should be 23<32>15'00".658. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Again, in IAE 2019, p. 385, it says that
|
||
the ayanamsha on this date was 23<32>15'00" exactly!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>So, which initial value is actually used?
|
||
Could the former be mean and the later true? This can be ruled out because
|
||
nutation on that date was over 16".</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>More information is unfortunately not given or is hard to get hold
|
||
of. </span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><i style='mso-bidi-font-style:normal'><span
|
||
lang=EN-US>How to reproduce true ayanamshas given in IAE <o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>IAE 2019, p. 427, gives a table of true ayanamsha values for the
|
||
year 2019 and part of 2020. The values are given with a precision of 0.1
|
||
arcsec. They can be reproduced very precisely using the following assumptions:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>- The initial value 23<32>15' 00".658 is true, not mean (!)
|
||
ayanamsha.</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>- The precession model used is Lieske 1976 (IAU1976) and the
|
||
nutation model is Wahr 1980.</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>The swetest command to be used is:</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><b
|
||
style='mso-bidi-font-weight:normal'><span lang=EN-US><span
|
||
style='mso-spacerun:yes'><3E><> </span>swetest -b1.1.2019 -ut0 -pb -sid1
|
||
-sidbit8192 -fTL -s3 -n130<span style='mso-spacerun:yes'><3E> </span>(SE 2.09
|
||
required!)<o:p></o:p></span></b></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US>This program call works from
|
||
SE 2.09 on. The parameter <span style='color:red'>-sidbit8192 </span>causes the
|
||
program to use this ayanamsha<68>s original precession model, which is IAU1976. <span
|
||
style='color:red'>Please understand that this is only a test option. If you use
|
||
it for horoscopes, the accuracy of the ephemeris will be reduced.</span></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_36" o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;
|
||
margin-left:0;margin-top:15.85pt;width:167.4pt;height:240.4pt;z-index:251661312;
|
||
visibility:visible;mso-wrap-style:square;mso-width-percent:0;
|
||
mso-height-percent:0;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;
|
||
mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0;
|
||
mso-position-horizontal:left;mso-position-horizontal-relative:margin;
|
||
mso-position-vertical:absolute;mso-position-vertical-relative:text;
|
||
mso-width-percent:0;mso-height-percent:0;mso-width-relative:margin;
|
||
mso-height-relative:margin'>
|
||
<v:imagedata src="swisseph-Dateien/image054.png" o:title=""/>
|
||
<w:wrap type="square" anchorx="margin"/>
|
||
</v:shape><![endif]--><![if !vml]><img width=223 height=1
|
||
src="swisseph-Dateien/image055.png" align=left hspace=12 v:shapes="Grafik_x0020_36"><![endif]><span
|
||
lang=EN-US style='font-size:11.0pt'>swetest -b1.1.2019 -ut0 -pb -sid1
|
||
-sidbit8192 -fTL -s3 -n11 (</span><span lang=EN-US>SE 2.09 required!</span><span
|
||
lang=EN-US style='font-size:11.0pt'>)<b style='mso-bidi-font-weight:normal'><o:p></o:p></b></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:24.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>01.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>5.9864<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>04.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>6.5976<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>07.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>7.3284<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>10.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>7.8480<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>13.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>8.1073<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>16.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>8.3970<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>19.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>9.0676<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>22.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'<span style='mso-spacerun:yes'><3E>
|
||
</span>9.8815<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>25.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'10.2273<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>28.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'10.4251<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>31.01.2019<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'10.9122<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>This looks like perfect agreement. Only some very few values,
|
||
outside the above list, differ by 0.1", which seems to be due to a
|
||
systematic difference smaller than 0.001<94> (apparently in precession, not
|
||
nutation!) which can show up in a different rounding. </span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>However, the tabe in IAE 2020 gives greater differences. The rounded
|
||
value often differs by 0.1<94>. Something seems to have been changed, whatever
|
||
that may be.</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><!--[if gte vml 1]><v:shape
|
||
id="Grafik_x0020_34" o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;
|
||
margin-left:0;margin-top:16.5pt;width:158pt;height:241.65pt;z-index:251662336;
|
||
visibility:visible;mso-wrap-style:square;mso-width-percent:0;
|
||
mso-height-percent:0;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;
|
||
mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0;
|
||
mso-position-horizontal:left;mso-position-horizontal-relative:margin;
|
||
mso-position-vertical:absolute;mso-position-vertical-relative:text;
|
||
mso-width-percent:0;mso-height-percent:0;mso-width-relative:margin;
|
||
mso-height-relative:margin'>
|
||
<v:imagedata src="swisseph-Dateien/image056.png" o:title=""/>
|
||
<w:wrap type="square" anchorx="margin"/>
|
||
</v:shape><![endif]--><![if !vml]><img width=211 height=1
|
||
src="swisseph-Dateien/image057.png" align=left hspace=12 v:shapes="Grafik_x0020_34"><![endif]><span
|
||
lang=EN-US style='font-size:11.0pt'>swetest -b1.1.2020 -ut0 -pb -sid1
|
||
-sidbit8192 -fTL -s3 -n11 (</span><span lang=EN-US>SE 2.09 required!</span><span
|
||
lang=EN-US style='font-size:11.0pt'>)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:24.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>01.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'54.8411<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>04.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'55.0918 </span><span lang=EN-US
|
||
style='font-size:11.0pt;font-family:"Wingdings 3";mso-ascii-font-family:"Segoe UI";
|
||
mso-hansi-font-family:"Segoe UI";mso-char-type:symbol;mso-symbol-font-family:
|
||
"Wingdings 3"'><span style='mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'>f</span></span><span
|
||
lang=EN-US style='font-size:11.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>07.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'55.5135 <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>10.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'56.2988<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>13.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'57.0629 </span><span lang=EN-US
|
||
style='font-size:11.0pt;font-family:"Wingdings 3";mso-ascii-font-family:"Segoe UI";
|
||
mso-hansi-font-family:"Segoe UI";mso-char-type:symbol;mso-symbol-font-family:
|
||
"Wingdings 3"'><span style='mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'>f</span></span><span
|
||
lang=EN-US style='font-size:11.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>16.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'57.3750 </span><span lang=EN-US
|
||
style='font-size:11.0pt;font-family:"Wingdings 3";mso-ascii-font-family:"Segoe UI";
|
||
mso-hansi-font-family:"Segoe UI";mso-char-type:symbol;mso-symbol-font-family:
|
||
"Wingdings 3"'><span style='mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'>f</span></span><span
|
||
lang=EN-US style='font-size:11.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>19.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'57.6643 </span><span lang=EN-US
|
||
style='font-size:11.0pt;font-family:"Wingdings 3";mso-ascii-font-family:"Segoe UI";
|
||
mso-hansi-font-family:"Segoe UI";mso-char-type:symbol;mso-symbol-font-family:
|
||
"Wingdings 3"'><span style='mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'>f</span></span><span
|
||
lang=EN-US style='font-size:11.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>22.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'58.3258<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>25.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'59.0403<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:2.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='font-size:11.0pt'>28.01.2020<span
|
||
style='mso-spacerun:yes'><3E><> </span>24<32> 7'59.4289<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='font-size:11.0pt'>31.01.2020<span style='mso-spacerun:yes'><3E><>
|
||
</span>24<32> 7'59.5804 </span><span lang=EN-US style='font-size:11.0pt;
|
||
font-family:"Wingdings 3";mso-ascii-font-family:"Segoe UI";mso-hansi-font-family:
|
||
"Segoe UI";mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'><span
|
||
style='mso-char-type:symbol;mso-symbol-font-family:"Wingdings 3"'>f</span></span><span
|
||
lang=EN-US style='font-size:11.0pt'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>This is very strange. Is it bad manual rounding?</span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US>The table in IAE 1989, p. 512, can be reproduced with high accuracy
|
||
again, except that it seems there are some typos. E.g., for 10 May 1989, we get
|
||
the value 23<32>42'37.4128, whereas IAE has 23<32>42'37.0, which must be a typo
|
||
because almost all other values are very accurate. </span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US><o:p> </o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><i style='mso-bidi-font-style:normal'><span
|
||
lang=EN-US>How to reproduce mean ayanamshas given in IAE<o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The
|
||
mean ayanamshas given in IAE are more difficult to reproduce. This is strange,
|
||
since the only difference between the true and the mean ayanamsha should be the
|
||
nutation, as is also stated on the same page: "True Ayanamsa = Mean
|
||
Ayanamsa + Nutation in Longitude". Since we can reproduce true ayanamshas
|
||
so well, mean ayanamshas should not cause any problem. Unfortunately also, it
|
||
is not clear what is meant by epoch "1989.0". Is it 1 Jan. 0:00 TT or
|
||
12:00 TT or is it the Besselian epoch?<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Using
|
||
precession IAU 1976 and interpreting "1989.0" as 0:00 TT of 1 Jan.,
|
||
our results compare as follows with the mean ayanamshas in IAE 1989, p. 512
|
||
(Swiss Ephemeris version 2.09 is required for all these calculations): <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b1.1.1950 -nonut -fPZ -p -sid1
|
||
-sidbit8192<span style='mso-spacerun:yes'><3E> </span>|grep ayanamsa<span
|
||
style='mso-spacerun:yes'><3E> </span><br>
|
||
TT: 2433282.500000000 ayanamsa = 23<32>09'31.2539 (Lahiri)
|
||
(IAE 1989: 23<32>09'30.79")</span><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;color:#231F20;mso-fareast-language:DE'><span style='mso-spacerun:yes'><3E>
|
||
</span>diff = 0.46"</span><span lang=EN-US style='mso-bidi-font-size:10.0pt;
|
||
mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b1.1.1989 -nonut -fPZ -p -sid1
|
||
-sidbit8192<span style='mso-spacerun:yes'><3E> </span>|grep ayanamsa<br>
|
||
TT: 2447527.500000000 ayanamsa = 23<32>42'12.3717 (Lahiri)
|
||
(IAE 1989: 23<32>42'12.34")</span><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;color:#231F20;mso-fareast-language:DE'><span style='mso-spacerun:yes'><3E>
|
||
</span>diff = 0.03"</span><span lang=EN-US style='mso-bidi-font-size:10.0pt;
|
||
mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b1.1.1990 -nonut -fPZ -p -sid1
|
||
-sidbit8192<span style='mso-spacerun:yes'><3E> </span>|grep ayanamsa<br>
|
||
TT: 2447892.500000000 ayanamsa = 23<32>43'02.6259 (Lahiri)
|
||
(IAE 1989: 23<32>43'02.62")</span><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;color:#231F20;mso-fareast-language:DE'><span style='mso-spacerun:yes'><3E>
|
||
</span>diff = 0.01"</span><span lang=EN-US style='mso-bidi-font-size:10.0pt;
|
||
mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The
|
||
1950 value has a considerably greater difference. This is explained by the fact
|
||
that exactly the same value is given in "Indian Ephemeris and Nautical
|
||
Almanac" (IENA) 1965, thus in a publication from a time before precession
|
||
IAU 1976 existed. (IENA is the predecessor of IAE, which started in 1978.) It
|
||
therefore seems that this value was taken over from an older publication, not
|
||
calculated anew.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>This
|
||
obvious inconsistency of data is unfortunately not documented.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>For IAE
|
||
2019, p. 429, we find the following differences in mean ayanamshas, if the time
|
||
assumed is 12:00 TT on 1 Jan.(!):<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b1.1.2000 -t12 -p -sid1 -fTL -nonut
|
||
-sidbit8192<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>TT:<span style='mso-spacerun:yes'><3E>
|
||
</span>2451545.000000000<span style='mso-spacerun:yes'><3E><> </span>ayanamsa
|
||
=<span style='mso-spacerun:yes'><3E><> </span>23<32>51'25.5324 (Lahiri) (IAE 2019: </span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;color:#231F20;mso-fareast-language:
|
||
DE'>23<32>51<35>25".53)<span style='mso-spacerun:yes'><3E> </span>diff = 0.00"<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b1.1.2019 -t12 -p -sid1 -fTL -nonut
|
||
-sidbit8192<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>TT:<span style='mso-spacerun:yes'><3E>
|
||
</span>2458485.000000000<span style='mso-spacerun:yes'><3E><> </span>ayanamsa
|
||
=<span style='mso-spacerun:yes'><3E><> </span>24<32> 7'21.1353 (Lahiri) (IAE 2019: </span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;color:#231F20;mso-fareast-language:
|
||
DE'>23<32>07<30>21".20)<span style='mso-spacerun:yes'><3E> </span>diff = 0.06"</span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>swetest
|
||
-b1.1.2020 -t12 -p -sid1 -fTL -nonut -sidbit8192<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>TT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2458850.000000000<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E><>
|
||
</span>24<32> 8'11.3962 (Lahiri) (IAE 2019: </span><span lang=EN-US
|
||
style='mso-bidi-font-size:10.0pt;color:#231F20;mso-fareast-language:DE'>23<32>08<30>11".46)<span
|
||
style='mso-spacerun:yes'><3E> </span>diff = 0.06"</span><span lang=EN-US
|
||
style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>With no
|
||
other precession model can we arrive at a better agreement with the mean
|
||
ayanamsha. Perhaps they used some simplified precession algorithm, starting
|
||
from an accurate value in 2000.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>How to reproduce mean ayanamshas in Indian
|
||
Ephemeris and Nautical Almanac </span><span lang=EN-US>(IENA)</span></i><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'> <o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>IENA is
|
||
the predecessor of IAE by which it was replaced in 1978. Its ayanamsha tables
|
||
have exactly the same layout as IAE. Since ayanamsha was still based on the
|
||
original ICRC definition (exactly 23<32>15<31> on 21 March 1956, its values must be
|
||
compared with Swiss Ephemeris ayanamsha No. 46 (SE_SIDM_LAHIRI_ICRC).<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The
|
||
edition of 1973 explains the calculation of ayanamsha as follows:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='font-size:11.5pt;mso-fareast-font-family:DengXian;mso-fareast-theme-font:
|
||
minor-fareast;mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_33"
|
||
o:spid="_x0000_i1029" type="#_x0000_t75" style='width:453.75pt;height:254.25pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image058.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=605 height=339
|
||
src="swisseph-Dateien/image059.png" v:shapes="Grafik_x0020_33"><![endif]></span><span
|
||
lang=DE-CH style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE-CH;mso-fareast-language:
|
||
ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>Unfortunately, we are not informed, that the
|
||
value adopted in 1956 is true ayanamsha, what nutation value was subtracted,
|
||
and how they arrived ath the given formulae. <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>On p. 445, it provides the following mean
|
||
ayanamshas:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=DE-CH style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE-CH;mso-fareast-language:
|
||
ZH-CN;mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_32"
|
||
o:spid="_x0000_i1028" type="#_x0000_t75" style='width:363.75pt;height:65.25pt;
|
||
visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image060.jpg" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=485 height=87
|
||
src="swisseph-Dateien/image061.jpg" v:shapes="Grafik_x0020_32"><![endif]></span><span
|
||
lang=DE-CH style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE-CH;mso-fareast-language:
|
||
ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>Using the above formula and the Besselian
|
||
epoch, we get:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>1950.0<span style='mso-tab-count:1'><3E><><A0><A0> </span>tjd=2433282.42345905<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>23.1585533205<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0> </span>23<32>09'30.79195<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>1973.0<span style='mso-tab-count:1'><3E><><A0><A0> </span>tjd=2441682.99403101<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>23.4797232708<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0> </span>23<32>28'47.00377<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>1974.0<span style='mso-tab-count:1'><3E><><A0><A0> </span>tjd=2442048.23622979<span
|
||
style='mso-tab-count:1'><3E><><A0><A0> </span>23.4936879217<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0> </span>23<32>29'37.27652<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>This is
|
||
pretty accurate. Now, the Swiss Ephemeris does not use the above formula but a
|
||
rigorous precession calculation using the Kinoshita (1975) formulation of
|
||
Newcomb precession. The mean ayanamshas for the same dates are:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>(Swiss
|
||
Ephemeris version 2.09 is required for all these calculations)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -pb -fTL -bj2433282.42345905 -nonut
|
||
-sid46 -sidbit8192 -s3 -n1<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>31.12.1949 22:09:47 TT<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32> 9'30.72050620<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0> </span>(diff = 0.07")<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -pb -fTL -bj2441682.99403101 -nonut
|
||
-sid46 -sidbit8192 -s3 -n1<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>31.12.1972 11:51:24 TT<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32>28'46.93310<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0> </span>(diff = 0.07")<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -pb -fTL -bj2442048.23622979 -nonut
|
||
-sid46 -sidbit8192 -s3 -n1<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>31.12.1973 17:40:10 TT<span
|
||
style='mso-spacerun:yes'><3E><> </span>23<32>29'37.20587<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0> </span>(diff = 0.07")<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>The initital date for the above formula,
|
||
i.e. 1900, Jan 0.5 ET = 31 Dec. 1899, 12 ET provides:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -pb -fTL -bj2415020.0 -nonut -sid1 -sidbit8192
|
||
-s3 -n1<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:6.0pt;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>31.12.1899 12:00:00 TT<span
|
||
style='mso-spacerun:yes'><3E><> </span>22<32>27'37.54705<span style='mso-tab-count:
|
||
2'><3E><><A0><A0><A0><A0><A0> </span>(diff 0.1")<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The
|
||
reason for the constant difference of 0.07" from 1950 to 1973 could be
|
||
that we chose the wrong initial ayanamsha value. True ayanamsha on 21 March
|
||
1956 was 23<32>15<31>. For mean aynamasha, we have to subtract nutation. We chose to
|
||
subtract Woolard nutation, which was published 1953, however used by IENA/IAE
|
||
only from 1960 on. Thus, a small correction of our initial value by 0.07"
|
||
could help to reproduce the mean ayanamshas. With true ayanamshas, as given in
|
||
IENA, however, an error of about 0.1 arcsec will remain, for unknown reasons.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Thus,
|
||
there is currently no way to reproduce these values precisely using the Swiss
|
||
Ephemeris because we do not have accurate information about what algorithms
|
||
exactly were used. Another problem may be that the Swiss Ephemeris does its
|
||
calculations in full precision, whereas IENA used some simplified algorithms.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>How to reproduce true ayanamsha values given
|
||
in the Report of the Calendar Reform Committee and in Rashtriya Panchang<o:p></o:p></span></i></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>The <i
|
||
style='mso-bidi-font-style:normal'>Report of the ICRC </i>gives the ayanamsha
|
||
value 23<32>15<31> 0<> for the 1<sup>st</sup> of Caitra = 21 March 1956 (there are no
|
||
page numbers). <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN;
|
||
mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_10" o:spid="_x0000_i1027"
|
||
type="#_x0000_t75" alt="Ein Bild, das Text enth<74>lt. Automatisch generierte Beschreibung"
|
||
style='width:696pt;height:146.25pt;visibility:visible;mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image062.png" o:title="Ein Bild, das Text enth<74>lt"/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=928 height=195
|
||
src="swisseph-Dateien/image063.png"
|
||
alt="Ein Bild, das Text enth<74>lt. Automatisch generierte Beschreibung"
|
||
v:shapes="Grafik_x0020_10"><![endif]></span><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>This
|
||
can be reproduced as follows:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b21.3.1956 -p -sid46 -sidbit8192 <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>date (dmy) 21.3.1956 greg.<span
|
||
style='mso-spacerun:yes'><3E><> </span></span><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>0:00:00 TT<span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0> </span>version 2.08.00b<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>UT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2435553.499636440<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 31.411589 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>TT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2435553.500000000<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E><>
|
||
</span>23<32>15' 0.0000 (Lahiri ICRC)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>For the
|
||
1st of Phalguna = 20 February 1959, it gives the ayanamsha value 23<32>17<31>16<31>.
|
||
Using swetest, this is reproduced as follows:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b20.2.1959 -p -sid46 -sidbit8192 <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>date (dmy) 20.2.1959 greg.<span
|
||
style='mso-spacerun:yes'><3E><> </span>0:00:00 TT<span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0> </span>version
|
||
2.08.00b<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>UT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2436619.499620988<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 32.746598 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE;mso-fareast-language:
|
||
ZH-CN'>TT:<span style='mso-spacerun:yes'><3E> </span>2436619.500000000<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E><>
|
||
</span>23<32>17'15.9648 (Lahiri ICRC)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE;mso-fareast-language:
|
||
ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>Rashtriya Panchang </span></i><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>of <i
|
||
style='mso-bidi-font-style:normal'>1961</i>, using the same ayanamsha, provides
|
||
ayanamsha 23<32>18<31>47<34> on 1<sup>st</sup> of Caitra = 22 March 1961:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN;
|
||
mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_29" o:spid="_x0000_i1026"
|
||
type="#_x0000_t75" style='width:281.25pt;height:191.25pt;visibility:visible;
|
||
mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image064.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=375 height=255
|
||
src="swisseph-Dateien/image065.png" v:shapes="Grafik_x0020_29"><![endif]></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>Using
|
||
sweetest, we get:<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b22.3.1961 -p -sid46 -sidbit8192 <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>date (dmy) 22.3.1961 greg.<span
|
||
style='mso-spacerun:yes'><3E><> </span>0:00:00 TT<span style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0> </span>version
|
||
2.08.00b<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>UT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2437380.499610181<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 33.680306 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE;mso-fareast-language:
|
||
ZH-CN'>TT:<span style='mso-spacerun:yes'><3E> </span>2437380.500000000<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E><>
|
||
</span>23<32>18'47.3511 (Lahiri ICRC)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
style='mso-bidi-font-size:10.0pt;mso-ansi-language:DE;mso-fareast-language:
|
||
ZH-CN'><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><i
|
||
style='mso-bidi-font-style:normal'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>Rashtriya Panchang </span></i><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>of 2019
|
||
has the following value for the 1<sup>st</sup> of Caitra<i style='mso-bidi-font-style:
|
||
normal'> </i>or 22 March 2019:<i style='mso-bidi-font-style:normal'><o:p></o:p></i></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN;
|
||
mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Grafik_x0020_39" o:spid="_x0000_i1025"
|
||
type="#_x0000_t75" style='width:546pt;height:156pt;visibility:visible;
|
||
mso-wrap-style:square'>
|
||
<v:imagedata src="swisseph-Dateien/image066.png" o:title=""/>
|
||
</v:shape><![endif]--><![if !vml]><img border=0 width=728 height=208
|
||
src="swisseph-Dateien/image066.png" v:shapes="Grafik_x0020_39"><![endif]></span><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'><o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>swetest -b22.3.2019 -p -sid1 -sidbit8192 <o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span lang=EN-US style='mso-bidi-font-size:
|
||
10.0pt;mso-fareast-language:ZH-CN'>date (dmy) 22.3.2019 greg.<span
|
||
style='mso-spacerun:yes'><3E><> </span></span><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>0:00:00 TT<span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0><A0><A0><A0> </span>version 2.08.00b<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='margin-bottom:0cm;text-align:left;
|
||
mso-pagination:widow-orphan;mso-hyphenate:auto;layout-grid-mode:both;
|
||
text-autospace:ideograph-other'><span style='mso-bidi-font-size:10.0pt;
|
||
mso-ansi-language:DE;mso-fareast-language:ZH-CN'>UT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2458564.499198334<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 69.263905 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>TT:<span
|
||
style='mso-spacerun:yes'><3E> </span>2458564.500000000<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E><>
|
||
</span>24<32> 7'16.2053 (Lahiri)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>In a
|
||
nutshell: Publications of IENA and IAE provide confusing and incomplete
|
||
explanations for their calculation of ayanamsha. Due to the lack of reliable
|
||
information, possibly also due to manual rounding errors and typos, it is
|
||
difficult to accurately reproduce all data of IAE. Nevertheless, there is
|
||
agreement to a second of arc or better.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal align=left style='text-align:left;mso-pagination:widow-orphan;
|
||
mso-hyphenate:auto;layout-grid-mode:both;text-autospace:ideograph-other'><span
|
||
lang=EN-US style='mso-bidi-font-size:10.0pt;mso-fareast-language:ZH-CN'>It
|
||
seems that precession IAU 1976 and nutation 1980 (Wahr) have been used since
|
||
1985 for true ayanamshas, and the Swiss Ephemeris can reproduce them accurately
|
||
using ayanamsha No. 1 (SE_SIDM_LAHIRI), with some exceptions which are
|
||
difficult to explain (IAE 2020). In editions of IAE/IENA before 1985, Newcomb
|
||
precession and Woolard nutation was used, and their true ayanamshas can be
|
||
reproduced with an accuracy of 0.1" using ayanamsha No. 46
|
||
(SE_SIDM_LAHIRI_ICRC). The reason for the remaining small error is unknown.<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US style='color:red'>Important:</span></b><span
|
||
lang=EN-US style='color:red'> </span><span lang=EN-US>In your software, <i
|
||
style='mso-bidi-font-style:normal'>you should <b>not</b> use the option
|
||
-sidbit8192 or the SE_SIDBIT</i><3E> that corresponds to it. It really only serves
|
||
the purpose to test IAE values of ayanamsha, i.e. whether they are
|
||
theoretically consistent with the Swiss Ephemeris. <i style='mso-bidi-font-style:
|
||
normal'>Nor should you aim at exact agreement of Swiss Ephemeris ayanamsha values
|
||
with IAE values</i> (up to 2020 at least), because the latter are based on outdated
|
||
precession and nutation models. Also note that the option has practically no
|
||
effect for planetary positions. E.g. let us calculate the position of the Sun
|
||
for 3000 BCE with and without the option:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>swetest
|
||
-b21.3.-3000 -ut0 -p0 -sid1 -fTPL -s3 -n1 -nonut -sidbit8192 </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>date (dmy)
|
||
21.3.-3000 jul.<span style='mso-spacerun:yes'><3E><> </span>0:00:00 UT<span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0> </span>version 2.09.01</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>UT:<span style='mso-spacerun:yes'><3E> </span>625387.500000000<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 75045.869961 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>TT:<span style='mso-spacerun:yes'><3E> </span>625388.368586458<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E>
|
||
</span>314<31>45'13.0909 (Lahiri)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Epsilon (m)<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0> </span><span
|
||
style='mso-spacerun:yes'><3E></span>24<32> 1'34.0132</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>21.03.-3000
|
||
Sun<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>21<32>24' 5.8667</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>swetest
|
||
-b21.3.-3000 -ut0 -p0 -sid1 -fTPL -s3 -n1 -nonut </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>date (dmy)
|
||
21.3.-3000 jul.<span style='mso-spacerun:yes'><3E><> </span>0:00:00 UT<span
|
||
style='mso-tab-count:2'><3E><><A0><A0><A0> </span>version 2.09.01</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>UT:<span style='mso-spacerun:yes'><3E> </span>625387.500000000<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0> </span>delta t: 75045.869961 sec<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span style='mso-ansi-language:
|
||
DE'>TT:<span style='mso-spacerun:yes'><3E> </span>625388.368586458<span
|
||
style='mso-spacerun:yes'><3E><> </span>ayanamsa =<span style='mso-spacerun:yes'><3E>
|
||
</span>314<31>44'30.0027 (Lahiri)<o:p></o:p></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:0cm'><span lang=EN-US>Epsilon (m)<span
|
||
style='mso-spacerun:yes'><3E><><A0><A0><A0><A0> </span>24<32> 1'16.5231</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>21.03.-3000
|
||
Sun<span style='mso-spacerun:yes'><3E><><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0><A0> </span>21<32>24' 5.9904</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As can be seen, the position of the Sun is
|
||
practically identical in both calculations, only the value of ayanamsha differs
|
||
considerably. The reason is that the one calculation gives the ayanamsha
|
||
relative to a tropical ephemeris which is based on the precession model IAU
|
||
1976 whereas the other provides a value relative to a tropical ephemeris which
|
||
is based on the more modern precession model Vondr<64>k 2011. Of course, the
|
||
latter is desirable, not the former. For an in-depth understanding of this
|
||
phenomenon, please study chapter 2.7.11 <i style='mso-bidi-font-style:normal'>Ayanamshas
|
||
with different precession rates</i>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><o:p> </o:p></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='color:red'><o:p> </o:p></span></p>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:footnote-list'><![if !supportFootnotes]><br clear=all>
|
||
|
||
<hr align=left size=1 width="33%">
|
||
|
||
<![endif]>
|
||
|
||
<div style='mso-element:footnote' id=ftn1>
|
||
|
||
<p class=footnote><a style='mso-footnote-id:ftn1' href="#_ftnref1" name="_ftn1"
|
||
title=""><span class=MsoFootnoteReference><span lang=EN-US><span
|
||
style='mso-special-character:footnote'><![if !supportFootnotes]><span
|
||
class=MsoFootnoteReference><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
|
||
11.0pt;font-family:"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></span></a><span
|
||
lang=EN-US> 9<>11 = Swiss Ephemeris ayanamsha numbers</span></p>
|
||
|
||
</div>
|
||
|
||
<div style='mso-element:footnote' id=ftn2>
|
||
|
||
<p class=footnote><a style='mso-footnote-id:ftn2' href="#_ftnref2" name="_ftn2"
|
||
title=""><span class=MsoFootnoteReference><span lang=EN-US><span
|
||
style='mso-special-character:footnote'><![if !supportFootnotes]><span
|
||
class=MsoFootnoteReference><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
|
||
11.0pt;font-family:"Segoe UI",sans-serif;mso-fareast-font-family:"Times New Roman";
|
||
mso-ansi-language:EN-US;mso-fareast-language:AR-SA;mso-bidi-language:AR-SA'>[2]</span></span><![endif]></span></span></span></a><span
|
||
lang=EN-US> <span style='mso-spacerun:yes'><3E></span>5<>24<32></span></p>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</body>
|
||
|
||
</html>
|