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<o:Keywords>swe se function time ephemeris</o:Keywords>
<o:Description>Before calling swe_calc(), call swe_set_topo(). position.&#13; swe_sol_eclipse_when_glob( tjd...) &#13;Lunar eclipses:&#13;swe_lun_eclipse_when(tjd...) Swe_calc() returns true positions for these points.</o:Description>
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mso-generic-font-family:roman;
mso-font-pitch:variable;
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@font-face
{font-family:"Yu Mincho Demibold";
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mso-generic-font-family:roman;
mso-font-pitch:variable;
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@font-face
{font-family:"Yu Mincho Light";
mso-font-charset:128;
mso-generic-font-family:roman;
mso-font-pitch:variable;
mso-font-signature:-2147482905 717749503 18 0 131231 0;}
@font-face
{font-family:"\@MS Mincho";
panose-1:2 2 6 9 4 2 5 8 3 4;
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mso-generic-font-family:modern;
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p.MsoNormal, li.MsoNormal, div.MsoNormal
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mso-style-parent:"";
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margin-right:0cm;
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mso-fareast-font-family:"Times New Roman";
mso-ansi-language:EN-US;
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h1
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"<22>berschrift 2";
mso-style-next:Standard;
margin-top:12.0pt;
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mso-padding-alt:0cm 0cm 4.0pt 0cm;
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mso-ansi-language:EN-US;
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h2
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-next:Standard;
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mso-ansi-language:EN-US;
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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;
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mso-pagination:none;
page-break-after:avoid;
mso-outline-level:3;
mso-list:l0 level3 lfo3;
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tab-stops:18.0pt;
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text-autospace:ideograph-numeric;
border:none;
mso-border-bottom-alt:solid windowtext 1.0pt;
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mso-padding-alt:0cm 0cm 1.0pt 0cm;
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color:#4472C4;
mso-ansi-language:EN-US;
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mso-bidi-font-weight:bold;}
h4
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-next:Standard;
margin-top:6.0pt;
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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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tab-stops:18.0pt;
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mso-bidi-font-family:"Times New Roman";
color:#4472C4;
mso-ansi-language:EN-US;
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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;
mso-pagination:none;
mso-outline-level:5;
mso-list:l0 level5 lfo3;
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text-autospace:ideograph-numeric;
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color:#4472C4;
mso-ansi-language:EN-US;
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h6
{mso-style-unhide:no;
mso-style-next:Standard;
margin-top:12.0pt;
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margin-bottom:3.0pt;
margin-left:180.0pt;
text-align:justify;
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mso-pagination:none;
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mso-bidi-font-size:11.0pt;
font-family:"Times New Roman",serif;
color:blue;
mso-ansi-language:EN-US;
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font-weight:normal;}
p.MsoHeading7, li.MsoHeading7, div.MsoHeading7
{mso-style-unhide:no;
mso-style-next:Standard;
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p.MsoHeading8, li.MsoHeading8, div.MsoHeading8
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p.MsoHeading9, li.MsoHeading9, div.MsoHeading9
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text-align:justify;
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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;
font-style:italic;}
p.MsoIndex1, li.MsoIndex1, div.MsoIndex1
{mso-style-noshow:yes;
mso-style-unhide:no;
mso-style-next:Standard;
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p.MsoIndex2, li.MsoIndex2, div.MsoIndex2
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mso-style-next:Standard;
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mso-ansi-language:EN-US;
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p.MsoIndex3, li.MsoIndex3, div.MsoIndex3
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p.MsoIndex4, li.MsoIndex4, div.MsoIndex4
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p.MsoIndex5, li.MsoIndex5, div.MsoIndex5
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p.MsoIndex7, li.MsoIndex7, div.MsoIndex7
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p.MsoIndex9, li.MsoIndex9, div.MsoIndex9
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p.MsoToc1, li.MsoToc1, div.MsoToc1
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p.MsoToc3, li.MsoToc3, div.MsoToc3
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p.MsoToc4, li.MsoToc4, div.MsoToc4
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p.MsoToc5, li.MsoToc5, div.MsoToc5
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p.MsoToc7, li.MsoToc7, div.MsoToc7
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p.MsoToc8, li.MsoToc8, div.MsoToc8
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p.MsoToc9, li.MsoToc9, div.MsoToc9
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p.MsoFootnoteText, li.MsoFootnoteText, div.MsoFootnoteText
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p.MsoCommentText, li.MsoCommentText, div.MsoCommentText
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tab-stops:center 216.0pt right 432.0pt;
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</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>&nbsp;</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 &quot;1-3&quot; \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"'>&#916;</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:
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</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>&nbsp;</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>&nbsp;</o:p></span></p>
</td>
</tr>
</table>
<p class=MsoSubtitle><span lang=EN-US><o:p>&nbsp;</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>&nbsp;</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 &gt; 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;
&quot;interpolated&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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>&lt; 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>&lt; 7&quot; (TT),
&lt; 2&quot; (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>&lt;
0.4 &quot;</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>&lt;
2&quot;</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>&lt;
6&quot;</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>&lt;
0.1&quot;</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>&lt;
28&quot;</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>&lt;
53&quot;</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>&lt;
129&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>&quot;Frame Bias&quot;
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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&amp;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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison, L.V.,
and Hohenkerk, C.Y., &quot;Measurement of the Earth's Rotation: 720 BCE to CE
2015&quot;, 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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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>&lt;
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>&lt;
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>&lt;
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>&lt;
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>&lt;
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>&lt;
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>&lt;
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>&lt;
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"'>&nbsp;
</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&amp;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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;
</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 &gt; 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"'>&nbsp;
</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"'>&nbsp;
</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 &quot;<span
class=italic>interpolated</span>&quot; or &quot;realistic&quot; apogee and
perigee by Dieter Koch in his publications. Juan Revilla prefers to call them
the &quot;<span class=italic>natural</span>&quot; apogee and perigee. Today,
Dieter Koch would prefer the designation &quot;natural&quot;. The designation
&quot;interpolated&quot; 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 &quot;interpolation method&quot; from the
analytical lunar theory which we have in the form of Moshier's lunar ephemeris.
This &quot;interpolation method&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
style='mso-ansi-language:DE'>Dieter Koch, &quot;Was ist Lilith und welche
Ephemeride ist richtig&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
style='mso-ansi-language:DE'>Dieter Koch and Bernhard Rindgen, &quot;Lilith und
Priapus&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Juan Revilla, &quot;The
Astronomical Variants of the Lunar Apogee - Black Moon&quot;.</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;apsides&quot; 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
&quot;Black Sun&quot;, 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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>(&gt;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
&quot;true&quot;. It is more appropriate to call them &quot;osculating&quot;.
Osculating nodes and apsides are &quot;true&quot; 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 &quot;true&quot; 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 &quot;mean&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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>&nbsp;</o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p>&nbsp;</o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p>&nbsp;</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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&nbsp;</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"'>&nbsp; </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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<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&nbsp;&nbsp;&nbsp; <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&nbsp;&nbsp;&nbsp; <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&nbsp;&nbsp; <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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<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>&nbsp;</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"'>&nbsp; </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>&nbsp;</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>&nbsp;</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"'>&nbsp; </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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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>&nbsp;</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>&nbsp;</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"'>&nbsp; </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"'>&nbsp;
</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'>ayan&#257;&#7747;&#347;a&#7717;</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>, &quot;course (of the Sun), half-year&quot; 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'>a&#7747;&#347;a&#7717;</span></em><span
lang=EN-US>, &quot;part&quot;, thus literally means &quot;part of the
course&quot;. 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'>ayan&#257;&#7747;&#347;a&#7717;</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"'>&nbsp;
</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&quot; 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&quot; (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 &quot;New Tool&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>John P. Britton, &quot;Studies
in Babylonian lunar theory: part III. The introduction of the uniform
zodiac&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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&quot;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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>&nbsp;</o:p></span></p>
<p class=MsoNormal><span lang=EN-US><o:p>&nbsp;</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>&nbsp;</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>D. Pingree, &quot;Precession
and Trepidation in Indian Astronomy&quot;, 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"'>&nbsp;
</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&quot;.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&quot;.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 Gane&#347;a 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&quot; 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>&quot;According to new determination of the
location of equinox this initial value has been revised to 23<32>15'00&quot;.658
and used in computing the mean ayanamsha with effect from 1985'.&quot;</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&quot;.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>&nbsp;</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&quot;.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&quot;<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>&nbsp;</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'>&#945;</span><span lang=EN-US> Virginis ) has been
assigned a <i style='mso-bidi-font-style:normal'>Niraya&#7751;a</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'>Niraya&#7751;a</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'>&quot;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&quot;, 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.&quot;<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
&quot;zero ayanamsha year&quot;. 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'>&quot;Due
to proper motion of the star, the nirayana longitude of Spica has however
diminished by 65&quot; during the period of 1695 years from 285 A.D. and now
179<B0>58'58&quot; according to the above ayanamsa system.&quot;<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'>&quot;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&quot;.8 than the above.&quot;<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, &quot;for the sake of uniformity&quot;, took over the standard ayanamsha
recommended by the CRC. The ayanamsha values and sidereal positions of the Sun
and the Moon&nbsp;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&quot; 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&quot;.<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>&nbsp;</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>&nbsp;</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 &nbsp;-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>&nbsp;</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>&nbsp;</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"'>&nbsp;
</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &amp; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &amp;
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>P.V.R. Narasimha Rao,
&quot;Introducing Pushya-paksha Ayanamsha&quot; (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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </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"'>&nbsp;
</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 (&#950; 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 m&#363;lam 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span
style='mso-ansi-language:DE'>Rafael Gil Brand, &quot;Umrechnung von tropischen
in siderische Positionen&quot;,
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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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&quot;, and
the &quot;Galactic Alignment&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Liu/Zhu/Zhang, <20>Reconsidering
the galactic coordinate system<65>, Astronomy &amp; 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 m&#363;lam means &quot;root,
origin&quot;, 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 &#256;rdr&#257; (&quot;the
moist, green, succulent one&quot;, 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"'>&nbsp;
</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 (&#955;
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 (&#955;
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>K. Chandra Hari, &quot;On the
Origin of Sidereal Zodiac and Astronomy&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Chandra Hari,
&quot;Ayan&#257;&#7747;&#347;a&quot;,
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Chandra Hari,
&quot;Ayan&#257;&#7747;&#347;a&quot;,
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;Djwhal Khul&quot; 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&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;Vedic&quot;.</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/mah&#257;yuga) 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:
&#7779;a&#7789;tri&#7747;&#347;e var&#7779;e, MBh 16.1.1 and 16.2.2. The
correct translation of this expression is &quot;in the 36th year&quot;, whereas
Sheoran mistakenly attempts to read it as &quot;3 x 6 = 18 years&quot;. In
addition, in texts to do with the durations of the yugas Sheoran reads
sahasr&#257;&#7751;i as &quot;10&quot; instead of &quot;1000&quot; and
&#347;at&#257;ni as &quot;1&quot; instead of &quot;100&quot;. 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Sunil Sheoran, &quot;The
Science of Time and Timeline of World History&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&nbsp;</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>&quot;</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>&nbsp;</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&quot;. 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>&nbsp;</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>&nbsp;</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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>&nbsp;</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
&gt;=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>&nbsp;</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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp;&nbsp; </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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&nbsp;</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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: &quot;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.&quot;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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 &amp; aerosol
scattering and ozone &amp; 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"'>&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;
</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 &amp; 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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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&amp;data_type=PDF_HIGH&amp;whole_paper=YES&amp;type=PRINTER&amp;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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;East Point&quot;).</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"'>&nbsp; </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 &amp; 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, &quot;New
precession expressions, valid for long time intervals&quot;, in A&amp;A 534,
A22(2011).</span></p>
<p class=MsoNormal><span lang=EN-US>Simon &amp; alii, &quot;Precession formulae
and mean elements for the Moon and the Planets&quot;, A&amp;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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;
</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
&quot;Geburtsorth<74>usersystem&quot; (GOHS), i.e. the &quot;Birth place house
system&quot;. Walter Koch thought that this system was more related to the
birth place than other systems, because all house cusps are computed with the
&quot;polar height of the birth place&quot;, 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"'>&nbsp;
</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
&quot;Regiomontanus&quot;, 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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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>&quot;Sinusoidal Delta&quot;
(formerly &quot;Neo-Porphyry&quot;) 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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 &quot;Sinusoidal Delta&quot; 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 &quot;sinusoidal ratio&quot; instead of a &quot;sinusoidal
delta&quot;, so this alternate method could be called &quot;Sinusoidal Ratio
houses&quot;. As before, let &quot;x&quot; be the smallest house in the
compressed quadrant. There's a ratio &quot;r&quot; multiplied by it to get the
slightly larger 10th and 12th houses. The value &quot;r&quot; starts out at 1.0
for 90 degree quadrants, and gradually increases as quadrant sizes differ.
Houses in the large quadrant have &quot;r&quot; multiplied to &quot;x&quot; 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>&quot;Sinusoidal Ratio&quot; 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 &quot;r&quot; and &quot;x&quot; can be computed based on the
quadrant size &quot;q&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&quot;XIV Szkola Astrologii
Humanistycznej&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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 &quot;East Point&quot;
but is usually not located in the east. In celestial geometry, the expression
&quot;East Point&quot; 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 &quot;East Point&quot; 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 &quot;East
Point&quot; 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 &quot;East
Point&quot;. 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>&quot;Co-Ascendant&quot;</span>
and the <span class=italic>&quot;Polar Ascendant&quot;</span>.</span></p>
<p class=MsoNormal><span lang=EN-US>The term <span class=italic>&quot;Co-Ascendant&quot;</span>
seems to have been <b>invented twice</b> by two different people, and it <b>can
mean two different things</b>. The one &quot;Co-Ascendant&quot; 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 &quot;Co-Ascendant&quot;
is then the opposition to this point.</span></p>
<p class=MsoNormal><span lang=EN-US>The second &quot;Co-Ascendant&quot; 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 &quot;Polar Ascendant&quot; finally was
introduced by Michael Munkasey. It is the opposition point of Walter Koch's
version of the &quot;Co-Ascendant&quot;. However, the &quot;Polar
Ascendant&quot; 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
&quot;Polar Ascendant&quot;.</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"'>&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;
</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"'>&nbsp; </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>&nbsp;</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"'>&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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"'>&nbsp;&nbsp; </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>&nbsp;</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"'>&nbsp; </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>&nbsp;</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US style='mso-bidi-font-family:
"Segoe UI"'>&#916;</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 &#916;T (<28>Delta T<>), and is defined
as &#916;T = 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 &#916;T cannot be calculated with accuracy
for the future or the remote past. Future values of &#916;T 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 &#916;T 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 &#916;T
for epochs after 1700. Since 1962, &#916;T 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 &#916;T 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison,
L.V., and Hohenkerk, C.Y., &quot;Measurement of the Earth's Rotation: 720 BCE
to CE 2015&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &#916;T 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 &#916;T values
of Astronomical Almanac are consistent with ndot = -26 arcsec/cty<sup>2</sup>,
those of Stephenson &amp; 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 &#916;T algorithms have been changed
with the Swiss Ephemeris releases 1.64 (Stephenson 1997), 1.72
(Morrison/Stephenson 2004), 1.77 (Espenak &amp; 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 &#916;T 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 &#916;T, 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>&#916;T
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 &#916;T (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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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&quot;</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>&#916;T, 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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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
&gt; diff &gt; -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>&nbsp;</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
&gt; diff &gt; -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>&nbsp;</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
&gt; diff &gt; -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>&nbsp;</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
&gt; diff &gt; -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>&nbsp;</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
&gt; diff &gt; -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>&nbsp;</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>&nbsp;</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>&nbsp;</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 &amp; Meeus ignore Morrison &amp;
Stephenson's values for -700 and -600, whereas the former Swiss Ephemeris
versions used them. For -500 to +1600 Espenak &amp; 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 &#916;T, 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 &#916;T, 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 &#916;T 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 &#61508;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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Borkowski, K. M.,
&quot;ELP2000-85 and the Dynamical Time - Universal Time relation,&quot;
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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &#61508;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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Stephenson, F. R., and L. V.
Morrison, &quot;Long-term changes in the rotation of the Earth: 700 BCE to CE
1980&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R. &amp;
Morrison, L.V., &quot;Long-Term Fluctuations in the Earth's Rotation: 700 BCE
to CE 1990&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]><span lang=EN-US>Stephenson, F.R., Morrison,
L.V., and Hohenkerk, C.Y., &quot;Measurement of the Earth's Rotation: 720 BCE
to CE 2015&quot;, 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp; </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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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"'>&nbsp;
</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
-&gt; 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
-&gt; 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
-&gt; 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"'>&nbsp; </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 &amp; 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
&quot;planets&quot;, 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 &quot;asteroid&quot;
(Greek &quot;star-like&quot;,<o:p></o:p></span></span></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
&quot;planetoid&quot; (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># &quot;something like a planet&quot;).
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
&quot;asteroids&quot; (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># &quot;comets&quot;?) 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>&quot;between
rivers&quot;, 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>&quot;soul&quot;, 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 &quot;peace&quot;<o:p></o:p></span></span></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
&quot;heroine&quot;<o:p></o:p></span></span></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 &quot;Trojans&quot; 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
&quot;spies&quot; in the Greek army and some Greek &quot;spies&quot;<o:p></o:p></span></span></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 &quot;spy&quot; 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 &quot;Cubewano&quot; 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
&quot;Isis-Transpluto&quot;<o:p></o:p></span></span></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># &quot;the untamed one&quot;,
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 &quot;second Moon&quot;
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># &quot;soul&quot;, 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
&quot;identical&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;Generate
Ephemeris&quot;, 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>&nbsp;</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 &quot;other options&quot;. You
can ignore the other fields and leave them as they are.</span></p>
<p class=MsoNormal><span lang=EN-US>The parameters &quot;-j2000 -icrs
-fTPAD&quot; 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 &quot;-noaberr -nodefl&quot;
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 &quot;-ejplde431.eph&quot;
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 &quot;Current Settings&quot; 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
&quot;extra precision&quot;, scroll down and click on &quot;use settings
above&quot;.</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 &quot;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 &quot;Current Settings&quot; 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 &quot;TT&quot;
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 &quot;Use
Specified Times&quot;. After that click on &quot;Generate Ephemeris&quot;
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>&nbsp;</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>&nbsp;</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: &quot;Apparent RA &amp;
DE&quot;.</span></p>
<p class=MsoNormal><span lang=EN-US>The table now looks as follows:</span></p>
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o:spt="32" o:oned="t" path="m,l21600,21600e" filled="f">
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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 &quot;Use Selected
Settings&quot;.</span></p>
<p class=MsoNormal><span lang=EN-US>After that click on &quot;Generate
Ephemeris&quot; 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>&nbsp;</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>&nbsp;</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. &quot;Inertial Apparent RA
&amp; DE&quot; and</span></p>
<p class=MsoNormal><span lang=EN-US>checkbox 31. &quot;observer ecliptic lon.
&amp; lat.&quot;</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 &quot;Use Selected
Settings&quot;.</span></p>
<p class=MsoNormal><span lang=EN-US>After that click on &quot;Generate
Ephemeris&quot; 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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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
&amp; DEC and</span></p>
<p class=MsoNormal style='margin-left:14.2pt'><span lang=EN-US>31. Observer
ecliptic lon. &amp; 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 &quot;Astronomical
Almanac&quot; 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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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 &quot;Geocentric equatorial
coordinates&quot;.</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&quot;.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"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</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>&nbsp;</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&quot;. 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'>&quot;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.&quot;<br>
&quot;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.&quot;<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&quot; 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>&quot;According to new determination of the
location of equinox this initial value has been revised to 23<32>15'00&quot;.658
and used in computing the mean ayanamsha with effect from 1985'.&quot;</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&quot;.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&quot; 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&quot;.</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>&nbsp;</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&quot;.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>&nbsp;</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>&nbsp;</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&quot;, 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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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: &quot;True Ayanamsa = Mean
Ayanamsa + Nutation in Longitude&quot;. 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 &quot;1989.0&quot;. 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 &quot;1989.0&quot; 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: &nbsp;2433282.500000000 &nbsp; ayanamsa = &nbsp; 23<32>09'31.2539 (Lahiri)
(IAE 1989: 23<32>09'30.79&quot;)</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&quot;</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: &nbsp;2447527.500000000 &nbsp; ayanamsa = &nbsp; 23<32>42'12.3717 (Lahiri)
(IAE 1989: 23<32>42'12.34&quot;)</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&quot;</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: &nbsp;2447892.500000000 &nbsp; ayanamsa = &nbsp; 23<32>43'02.6259 (Lahiri)
(IAE 1989: 23<32>43'02.62&quot;)</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&quot;</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 &quot;Indian Ephemeris and Nautical
Almanac&quot; (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&quot;.53)<span style='mso-spacerun:yes'><3E> </span>diff = 0.00&quot;<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&quot;.20)<span style='mso-spacerun:yes'><3E> </span>diff = 0.06&quot;</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&quot;.46)<span
style='mso-spacerun:yes'><3E> </span>diff = 0.06&quot;</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>&nbsp;</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>&nbsp;</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&quot;)<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&quot;)<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&quot;)<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&quot;)<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&quot; 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&quot;
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>&nbsp;</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.&#10;&#10;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.&#10;&#10;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>&nbsp;</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>&nbsp;</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&quot; 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>&nbsp;</o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='color:red'><o:p>&nbsp;</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>
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