8191 lines
426 KiB
HTML
8191 lines
426 KiB
HTML
<html>
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<head>
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<meta name=Generator content="Microsoft Office HTML Filter 2.0">
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<meta http-equiv=Content-Type content="text/html; charset=windows-1252">
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<meta name=Originator content="Microsoft Word 9">
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<title>SWISS EPHEMERIS</title>
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<style>
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<!--
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|
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|
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|
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{margin-bottom:0cm;}
|
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-->
|
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|
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</head>
|
||
|
||
<body lang=DE-CH link=blue vlink=purple style='text-justify-trim:
|
||
punctuation'>
|
||
|
||
<div class=Section1>
|
||
|
||
<p class=MsoToc1><span
|
||
lang=DE><span class=MsoHyperlink><a href="#_Toc335142923"><span lang=EN-US>SWISS EPHEMERIS</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>3</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142924"><span lang=EN-US>Computer ephemeris for developers of
|
||
astrological software</span><span style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>3</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142925"><span lang=EN-US>Introduction</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>4</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142926"><span lang=EN-US>1.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Licensing</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>4</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142927"><span lang=EN-US>2.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Descripition of the ephemerides</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>5</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142928"><span lang=EN-US>2.1</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Planetary and lunar ephemerides</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>5</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142929"><span lang=EN-US>2.1.1</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Three ephemerides</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>5</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142930"><b><span lang=EN-US>1. </span></b><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><b><span
|
||
lang=EN-US>The Swiss Ephemeris</span></b><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>5</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142931"><b><span lang=EN-US>2.</span></b><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD> </span><b><span
|
||
lang=EN-US>The Moshier Ephemeris</span></b><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>6</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142932"><b><span lang=EN-US>3.</span></b><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD> </span><b><span
|
||
lang=EN-US>The full JPL Ephemeris</span></b><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>6</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142933"><span lang=EN-US>2.1.2.1</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Swiss Ephemeris and the Astronomical
|
||
Almanac</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>7</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142934"><span lang=EN-US>2.1.2.2</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Swiss Ephemeris and JPL Horizons
|
||
System</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'><EFBFBD><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>8</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142935"><span lang=EN-US>2.1.2.3</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Differences between Swiss Ephemeris
|
||
1.70 and older versions</span><span style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>8</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142936"><span lang=EN-US>2.1.2.4</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Differences between Swiss Ephemeris
|
||
1.78 and 1.77</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>9</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142937"><span lang=EN-US>2.1.3</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The details of coordinate
|
||
transformation</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>10</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142938"><span lang=EN-US>2.1.4</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The Swiss Ephemeris compression
|
||
mechanism</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'><EFBFBD><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>11</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142939"><span lang=EN-US>2.1.5</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The extension of the time range to
|
||
10'800 years</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>12</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142940"><span lang=EN-US>2.2</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Lunar and Planetary Nodes and
|
||
Apsides</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>13</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142941"><span lang=EN-US>2.2.1</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Mean Lunar Node and Mean Lunar
|
||
Apogee ('Lilith', 'Black Moon')</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>13</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142942"><span lang=EN-US>2.2.2</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The 'True' Node</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>13</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142943"><span lang=EN-US>2.2.3</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The Osculating Apogee (so-called
|
||
'True Lilith' or 'True Dark Moon')</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>14</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142944"><span lang=EN-US>2.2.4</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>The Interpolated or Natural Apogee
|
||
and Perigee (Lilith and Priapus)</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>15</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142945"><span lang=EN-US>2.2.5 </span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Planetary Nodes and Apsides</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>15</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142946"><span lang=EN-US>2.3.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Asteroids</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>18</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142947"><span lang=EN-US>Asteroid ephemeris files</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>18</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142948"><span lang=EN-US>How the asteroids were computed</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>19</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142949"><span lang=IT>Ceres, Pallas, Juno, Vesta</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142950"><span lang=EN-US>Chiron</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142951"><span lang=EN-US>Pholus</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142952"><span lang=EN-US><EFBFBD>Ceres<EFBFBD> - an application program for asteroid
|
||
astrology</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142953"><span lang=EN-US>2.4</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Comets</span><span style='color:
|
||
windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142954"><span lang=EN-US>2.5</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Fixed stars and Galactic Center</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142955"><span lang=EN-US>2.6</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US><EFBFBD>Hypothetical' bodies</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>20</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142956"><span lang=DA>Uranian Planets (Hamburg Planets: Cupido, Hades,
|
||
Zeus, Kronos, Apollon, Admetos, Vulkanus, Poseidon)</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>21</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142957"><span lang=EN-US>Transpluto (Isis)</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>21</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142958"><span lang=EN-US>Harrington</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>21</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142959"><span lang=EN-US>Nibiru</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>22</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142960"><span lang=EN-US>Vulcan</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>22</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142961"><span lang=EN-US>Selena/White Moon</span><span style='color:
|
||
windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>22</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142962"><span lang=EN-US>Dr. Waldemath<74>s Black Moon</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>22</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142963"><span lang=EN-US>The Planets X of Leverrier, Adams, Lowell and
|
||
Pickering</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>22</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142964"><span lang=EN-US>2.7 Sidereal Ephemerides</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>23</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142965"><span lang=EN-US>Sidereal Calculations</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>23</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142966"><span lang=EN-US>The problem of defining the zodiac</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>23</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142967"><span lang=EN-US>The Babylonian tradition and the Fagan/Bradley
|
||
ayanamsha</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>23</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142968"><span lang=EN-US>The Hipparchan tradition</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>24</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142969"><span lang=EN-US>The Spica/Citra tradition and the Lahiri ayanamsha</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>26</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142970"><span lang=EN-US>The sidereal zodiac and the Galactic Center</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>26</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142971"><span lang=EN-US>Other ayanamshas</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>26</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142972"><span lang=EN-US>Conclusions</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>27</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142973"><span lang=EN-US>In search of correct algorithms</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>27</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142974"><span lang=EN-US>More benefits from our new sidereal algorithms:
|
||
standard equinoxes and precession-corrected transits</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>30</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142975"><span lang=EN-US>3. </span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Apparent versus true planetary
|
||
positions</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>30</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142976"><span lang=EN-US>4. </span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Geocentric versus topocentric and
|
||
heliocentric positions</span><span style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>30</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142977"><span lang=EN-US>5. Heliacal Events, Eclipses, Occultations, and
|
||
Other Planetary Phenomena</span><span style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>31</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142978"><span lang=EN-US>5.1. Heliacal Events of the Moon, Planets and
|
||
Stars</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>31</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142979"><span lang=EN-US>5.1.1. Introduction</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>31</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142980"><span lang=EN-US>5.1.2. Aspect determining visibility</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142981"><span lang=EN-US>5.1.2.1. Position of celestial objects</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142982"><span lang=EN-US>5.1.2.2. Geographic location</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142983"><span lang=EN-US>5.1.2.3. Optical properties of observer</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142984"><span lang=EN-US>5.1.2.4. Meteorological circumstances</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142985"><span lang=EN-US>5.1.2.5. Contrast between object and sky
|
||
background</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142986"><span lang=EN-US>5.1.3. Functions to determine the heliacal
|
||
events</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142987"><span lang=EN-US>5.1.3.1. Determining the contrast threshold
|
||
(swe_vis_limit_magn)</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142988"><span lang=EN-US>5.1.3.2. Iterations to determine when the
|
||
studied object is really visible (swe_heliacal_ut)</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>32</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142989"><span lang=EN-US>5.1.3.3. Geographic limitations of
|
||
swe_heliacal_ut() and strange behavior of planets in high geographic latitudes</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>33</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142990"><span lang=EN-US>5.1.3.4. Visibility of Venus and the Moon
|
||
during day</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>33</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142991"><span lang=EN-US>5.1.4. Future developments</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>33</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142992"><span lang=EN-US>5.1.5. References</span><span style='color:
|
||
windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>33</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142993"><span lang=EN-US>5.2. Eclipses, occultations, risings, settings,
|
||
and other planetary phenomena</span><span style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142994"><span lang=EN-US>6. </span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>AC, MC, Houses, Vertex</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142995"><span lang=EN-US>6.1.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>House Systems</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'><EFBFBD> </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142996"><span lang=EN-US>6.1.1. Placidus</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142997"><span lang=EN-US>6.1.2. Koch/GOH</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142998"><span lang=EN-US>6.1.3. Regiomontanus</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>34</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335142999"><span lang=IT>6.1.4. Campanus</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143000"><span lang=EN-US>6.1.5. Equal System</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143001"><span lang=EN-US>6.1.6 Vehlow-equal System</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143002"><span lang=EN-US>6.1.7. Axial Rotation System</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143003"><span lang=EN-US>6.1.8. The Morinus System</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143004"><span lang=EN-US>6.1.9. Horizontal system</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143005"><span lang=EN-US>6.1.10. The Polich-Page (<28>topocentric<69>) system</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143006"><span lang=EN-US>6.1.11. Alcabitus system</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143007"><span lang=EN-US>6.1.12. Gauquelin sectors</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>35</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143008"><span lang=EN-US>6.1.13. Krusinski/Pisa/Goelzer system</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>.. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>36</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143009"><span lang=EN-US>6.2. Vertex, Antivertex, East Point and
|
||
Equatorial Ascendant, etc.</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>36</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143010"><span lang=EN-US>6.3.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>House cusps beyond the polar circle</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>37</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143011"><span lang=EN-US>6.3.1.</span><span lang=DE style='font-size:
|
||
12.0pt;color:windowtext;
|
||
text-decoration:none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Implementation in other calculation
|
||
modules:</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>37</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143012"><span lang=EN-US>6.4.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>House position of a planet</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>38</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143013"><span lang=EN-US>6.5.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Gauquelin sector position of a
|
||
planet</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>38</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143014"><span lang=DE
|
||
style='font-family:Times;'><span lang=DE>7.</span></span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span lang=EN-US
|
||
style='font-family:Symbol;'>D</span><span lang=DE><span lang=DE>T (Delta T)</span></span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>39</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143015"><span lang=EN-US>8.</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Programming Environment</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>41</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143016"><span lang=EN-US>9. </span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Swiss Ephemeris Functions</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>41</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143017"><span lang=EN-US>9.1</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Swiss Ephemeris API</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>41</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143018"><span lang=EN-US>Calculation of planets and stars</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>41</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143019"><span lang=EN-US>Date and time conversion</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>41</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143020"><span lang=EN-US>Initialization, setup, and closing functions</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>42</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143021"><span lang=EN-US>House calculation</span><span style='color:
|
||
windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>42</span></a></span></span></p>
|
||
|
||
<p class=MsoToc4><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143022"><span lang=EN-US>Auxiliary functions</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>42</span></a></span></span></p>
|
||
|
||
<p class=MsoToc3><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143023"><span lang=EN-US>Other functions that may be useful</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>43</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143024"><span lang=EN-US>9.2</span><span lang=DE style='font-size:12.0pt;
|
||
color:windowtext;text-decoration:
|
||
none;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US>Placalc API</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>44</span></a></span></span></p>
|
||
|
||
<p class=MsoToc1><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143025"><span lang=EN-US>Appendix</span><span style='color:windowtext;
|
||
display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>44</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143026"><span lang=EN-US>A. The gravity deflection for a planet passing
|
||
behind the Sun</span><span style='color:windowtext;display:none;
|
||
text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>44</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2><span
|
||
class=MsoHyperlink><span lang=DE><a href="#_Toc335143027"><span lang=EN-US>B. The list of asteroids</span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>. </span><span
|
||
style='color:windowtext;display:none;text-decoration:none;'>45</span></a></span></span></p>
|
||
|
||
<p class=MsoToc2></p>
|
||
|
||
</div>
|
||
|
||
<span style='font-size:10.0pt;font-family:"Times New Roman";'><br clear=all style='page-break-before:auto;'>
|
||
</span>
|
||
|
||
<div class=Section2>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><span
|
||
style='font-size:10.0pt;font-family:"Times New Roman";color:windowtext;font-weight:normal'> </span></h1>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;page-break-before:always;'><a name="_Toc335142923"><span lang=EN-US>SWISS EPHEMERIS</span></a><span lang=EN-US><EFBFBD> </span></h1>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142924"><span lang=EN-US>Computer
|
||
ephemeris for developers of astrological software</span></a></h1>
|
||
|
||
<p class=MsoEnvelopeReturn><EFBFBD> 1997 - 2011
|
||
by </p>
|
||
|
||
<p class=MsoEnvelopeReturn>Astrodienst AG</p>
|
||
|
||
<p class=MsoEnvelopeReturn>Dammstr. 23</p>
|
||
|
||
<p class=MsoEnvelopeReturn>Postfach
|
||
(Station)</p>
|
||
|
||
<p class=MsoEnvelopeReturn><EFBFBD>CH-8702 Zollikon / Z<>rich, Switzerland</p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>Tel.
|
||
+41-44-392 18 18</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>Fax<EFBFBD> +41-44-391 75 74</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>Email
|
||
to devlopers <b><span style='color:blue'>swisseph@astro.ch</span></b></span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoEnvelopeReturn>Authors:
|
||
Dieter Koch and Dr. Alois Treindl</p>
|
||
|
||
<p class=MsoEnvelopeReturn> </p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>Editing
|
||
history:</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>14-sep-97
|
||
Appendix A by Alois</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>15-sep-97
|
||
split docu, swephprg.doc now separate (programming interface)</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>16-sep-97
|
||
Dieter: absolute precision of JPL, position and speed transformations</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=NL>24-sep-97
|
||
Dieter: main asteroids</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>27-sep-1997
|
||
Alois: restructured for better HTML conversion, added public function list</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>8-oct-1997
|
||
Dieter: chapter 4 (houses) added</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>28-nov-1997
|
||
Dieter: chapter 5 (delta t) added</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>20-Jan-1998
|
||
Dieter: chapter 3 (more than...) added, chapter 4 (houses) enlarged</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>14-Jul-98:
|
||
Dieter: more about the precision of our asteroids</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>21-jul-98:
|
||
Alois: houses in PLACALC and ASTROLOG</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=DA>27-Jul-98:
|
||
Dieter: True node chapter improved</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>2-Sep-98:
|
||
Dieter: updated asteroid chapter </span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>29-Nov-1998:
|
||
Alois: added info on Public License and source code availability</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>4-dec-1998:
|
||
Alois: updated asteroid file information</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>17-Dec-1998:
|
||
Alois: Section 2.1.5 added: extended time range to 10'800 years</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>17-Dec-1998:
|
||
Dieter: paragraphs on Chiron and Pholus ephemerides updated</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>12-Jan-1999:
|
||
Dieter: paragraph on eclipses</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>19-Apr-99:
|
||
Dieter: paragraph on eclipses and planetary phenomena</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>21-Jun-99:
|
||
Dieter: chapter 2.27 on sidereal ephemerides</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>27-Jul-99:
|
||
Dieter: chapter 2.27 on sidereal ephemerides completed</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>15-Feb-00:
|
||
Dieter: many things for Version 1.52</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>11-Sep-00:
|
||
Dieter: a few additions for version 1.61</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>24-Jul-01:
|
||
Dieter: a few additions for version 1.62</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>5-jan-2002:
|
||
Alois: house calculation added to swetest for version 1.63</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>26-feb-2002:
|
||
Dieter: Gauquelin sectors for version 1.64</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>12-jun-2003:
|
||
Alois: code revisions for compatibility with 64-bit compilers, version 1.65</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>10-jul-2003:
|
||
Dieter: Morinus houses for Version 1.66</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>12-jul-2004:
|
||
Dieter: documentation of Delta T algorithms implemented with version 1.64</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>7-feb-2005:
|
||
Alois: added note about mean lunar elements, section 2.2.1</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>22-feb-2006:
|
||
Dieter: added documentation for version 1.70, see section 2.1.2.1-3</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>17-jul-2007:
|
||
Dieter: updated documentation of Krusinski-Pisa house system.</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>28-nov-2007:
|
||
Dieter: documentation of new Delta T calculation for version 1.72, see section
|
||
7</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>17-jun-2008:
|
||
Alois: License change to dual license, GNU GPL or Professional License</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>31-mar-2009:
|
||
Dieter: heliacal events</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>26-Feb-2010:
|
||
Alois: manual update, deleted references to CDROM</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn>25-Jan-2011:
|
||
Dieter: Delta T updated, v. 1.77.</p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>2-Aug-2012:
|
||
Dieter: New precession, v. 1.78.</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>23-apr-2013:
|
||
Dieter: new ayanamshas</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>Swiss
|
||
Ephemeris Release history:</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.00<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 30-sept-1997</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.01<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 9-oct-1997<39><37><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> simplified
|
||
houses() and sidtime() functions, Vertex added.</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.02<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 16-oct-1997<39><37><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> houses() changed again</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.03<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 28-oct-1997<39><37><EFBFBD><EFBFBD> minor fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.04<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 8-Dec-1997<39><37><EFBFBD><EFBFBD> minor
|
||
fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.10<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 9-Jan-1998<39><38><EFBFBD><EFBFBD> bug
|
||
fix, pushed to all licensees</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.11<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 12-Jan-98<39><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> minor
|
||
fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.20<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 21-Jan-98<39><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <span
|
||
style='color:red'>NEW</span>: topocentric planets and house positions </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.21<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 28-Jan-98<39> <20><><EFBFBD><EFBFBD><EFBFBD> Delphi
|
||
declarations and sample for Delphi 1.0</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.22<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2-Feb-98<39><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Asteroids moved to subdirectory.
|
||
Swe_calc() finds them there.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.23<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 11-Feb-98<39> <20><><EFBFBD><EFBFBD><EFBFBD> two
|
||
minor bug fixes.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.24<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 7-Mar-1998<39><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Documentation for Borland C++
|
||
Builder added</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.25<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 4-June-1998<39><38><EFBFBD><EFBFBD> sample for Borland Delphi-2 added</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.26<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 29-Nov-1998<39><38><EFBFBD><EFBFBD> source added, Placalc API added</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.30<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 17-Dec-1998<39><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span lang=EN-US
|
||
style='color:red;'>NEW</span><span lang=EN-US>:</span><span lang=EN-US style='font-family:
|
||
Arial;'>Time range extended to 10'800 years</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.31<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 12-Jan-1999<39><39><EFBFBD><EFBFBD> <span style='color:red'>NEW</span>: Eclipses</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.40<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 19-Apr-1999<39><39><EFBFBD><EFBFBD> <span style='color:red'>NEW</span>: planetary phenomena</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.50<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 27-Jul-1999 <20><><EFBFBD> <span style='color:red'>NEW</span>: sidereal ephemerides</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.52<EFBFBD><EFBFBD> <20><> 15-Feb-2000
|
||
<EFBFBD><EFBFBD><EFBFBD> Several <span style='color:red'>NEW</span>
|
||
features, minor bug fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.60<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 15-Feb-2000<30><30><EFBFBD><EFBFBD> Major release with many new features and some minor bug fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.61<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 11-Sep-2000<30><30><EFBFBD><EFBFBD> Minor release, additions to se_rise_trans(), swe_houses(),
|
||
ficitious planets</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.62<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 23-Jul-2001<30><31><EFBFBD><EFBFBD><EFBFBD> Minor release, fictitious earth satellites, asteroid numbers
|
||
> 55535 possible</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.63<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 5-Jan-2002<30><32><EFBFBD><EFBFBD> Minor
|
||
release, house calculation added to swetest.c and swetest.exe</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.64<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 7-Apr-2002 <20><><EFBFBD> <span style='color:red'>NEW:</span> occultations of planets,
|
||
minor bug fixes, new Delta T algorithms</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.65<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 12-Jun-2003<30><33><EFBFBD><EFBFBD> Minor release, small code renovations for 64-bit compilation</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.66<EFBFBD><EFBFBD> <20><> 10-Jul-2003<30><33><EFBFBD><EFBFBD> <span style='color:red'>NEW:</span> Morinus
|
||
houses</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.67<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 31-Mar-2005<30><35><EFBFBD><EFBFBD> Minor release: Delta-T updated, minor bug fixes</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.70
|
||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2-Mar-2006<30><36><EFBFBD><EFBFBD> IAU resolutions up to 2005 implemented; "interpolated"
|
||
lunar apsides</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.72<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 28-nov-2007<30><37><EFBFBD><EFBFBD> Delta T calculation according to Morrison/Stephenson 2004</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.74<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 17-jun-2008<30><38><EFBFBD><EFBFBD> License model changed to dual license, GNU GPL or Professional
|
||
License</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.76<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 31-mar-2009<30><39><EFBFBD><EFBFBD> <span style='color:red'>NEW: </span>Heliacal events</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.77<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 25-jan-2011<31><31><EFBFBD><EFBFBD> Delta T calculation updated acc. to Espenak/Meeus 2006, new fixed
|
||
stars file</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.78<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2-aug-2012<31><32><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Precession
|
||
calculation updated acc. to Vondr<64>k et alii 2012</span></p>
|
||
|
||
<p class=MsoEnvelopeReturn><span lang=EN-US>1.79<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 23-apr-2013<31><33><EFBFBD><EFBFBD> New ayanamshas, improved precision of eclipse functions, minor
|
||
bug fixes</span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142925"><span lang=EN-US>Introduction</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:11.0pt;font-family:
|
||
"FuturaBlack BT";'>Swiss Ephemeris</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> is a function
|
||
package for the computation of planetary positions. It includes the planets,
|
||
the moon, the lunar nodes, the lunar apogees, the main asteroids, Chiron,
|
||
Pholus, the fixed stars and several <20>hypothetical<61> bodies. Hundreds of other
|
||
minor planets are included as well. Ephemeris files all numbered asteroids are
|
||
available for download.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The precision of the Swiss Ephemeris is very high. It is <i>at least </i>as
|
||
accurate as the Astromical Almanac, the standard planetary and lunar tables
|
||
astronomers refer to. </span><span lang=EN-US style='font-size:11.0pt;
|
||
font-family:"FuturaBlack BT";'>Swiss Ephemeris</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> will, as we hope,
|
||
be able to keep abreast to the scientific advances in ephemeris computation for
|
||
the coming decades. The expense will be small. In most cases an update of the
|
||
data files will do.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The </span><span lang=EN-US style='font-size:11.0pt;font-family:"FuturaBlack BT";'>Swiss Ephemeris</span><span lang=EN-US
|
||
style='font-size:10.0pt;'> package consists of 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 (in equatorial rectangular
|
||
coordinates referred to the mean equinox 2000 and the solar system barycenter).
|
||
The DLL is mainly the code that reads these files and converts the raw data to
|
||
positions as required in astrology (calculation of light-time, transformation
|
||
to the geocenter and the true equinox of date, etc.).</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Full <b>C source code</b> is included with the Swiss Ephemeris, so that
|
||
not-Windows programmers can create a linkable or shared library in their
|
||
environment and use it with their application.</span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142926"><span lang=EN-US>1.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Licensing</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris is not a product for end users. It is a toolset for
|
||
programmers to build into their astrological software. <br><br></span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Swiss Ephemeris is made available by its authors under a dual
|
||
licensing<EFBFBD> system. The software
|
||
developer, who uses any part of Swiss Ephemeris<69> in his or her software, must choose between one of the two
|
||
license models, which are</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> a) GNU public license version 2
|
||
or later</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> b) Swiss Ephemeris Professional
|
||
License</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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<EFBFBD> or her whole software project under
|
||
the GNU GPL or a compatible license.<2E>
|
||
See http://www.gnu.org/licenses/old-licenses/gpl-2.0.html</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>If the developer choses the Swiss Ephemeris Professional license,<2C> he must follow the instructions as found in
|
||
http://www.astro.com/swisseph/<2F> and
|
||
purchase the Swiss Ephemeris Professional Edition from Astrodienst and sign the
|
||
corresponding license contract.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><b><span lang=EN-US style='font-size:10.0pt;'>Professional license:</span></b><span lang=EN-US
|
||
style='font-size:10.0pt;'> The license fee for the first
|
||
license is Swiss Francs (CHF) 750.- , and CHF 400.-<2D> for each additional license by the same licensee. An unlimited
|
||
license is available for CHF 1550.-. </span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142927"><span lang=EN-US>2.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Descripition of the ephemerides</span></a></h1>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142928"><span lang=EN-US>2.1<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Planetary and lunar ephemerides</span></a></h2>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142929"><span lang=EN-US>2.1.1<EFBFBD><EFBFBD><EFBFBD> Three ephemerides</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris package allows planetary and lunar computations from
|
||
any of the following three astronomical ephemerides:</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142930"><b><span lang=EN-US>1. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> The Swiss Ephemeris</span></b></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The core part of Swiss Ephemeris is a compression of the JPL-Ephemeris
|
||
DE406.<2E> Using a sophisticated mechanism,
|
||
we succeeded in reducing JPL's 200 MB storage to only 18 MB. The agreement with
|
||
DE406 is<69> within 1 milli-arcsecond
|
||
(0.001<EFBFBD>).<2E> Since the inherent
|
||
uncertainty of the JPL ephemeris for most of its time range is much greater,
|
||
Swiss Ephemeris should be completely satisfying even for computations demanding
|
||
very high accuracy.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The time range of the JPL ephemeris is 3000 BC to 3000 AD or 6000 years.
|
||
We have <b>extended </b>this time range to 10'800 years, from <span
|
||
style='color:red'>2 Jan 5401 BC to 31 Dec 5399</span>. The details of this
|
||
extension are described below in section 2.1.5.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Each Swiss Ephemeris file covers a period of 600 years; there are 18
|
||
planetary files, 18 Moon files and 18 main-asteroid files for the whole time
|
||
range of 10'800 years. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The file names are as follows:</span></p>
|
||
|
||
<table border=0 cellspacing=0 cellpadding=0 style='margin-left:.25pt;
|
||
border-collapse:collapse;'>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border:solid black .5pt;
|
||
border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-style:normal'>Planetary file</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border:solid black .5pt;
|
||
border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Moon file</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border:solid black .5pt;
|
||
border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Main asteroid file</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR>Time range</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=PT-BR style='font-family:"Courier New";
|
||
font-style:normal'>seplm54.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>semom54.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm54.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR>5401 BC <20> 4802 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=PT-BR style='font-family:"Courier New";
|
||
font-style:normal'>seplm48.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>semom48.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm48.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR>4801 BC <20> 4202 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=PT-BR style='font-family:"Courier New";
|
||
font-style:normal'>seplm42.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>semom42.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm42.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>4201 BC <20> 3602 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";
|
||
font-style:normal'>seplm36.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>semom36.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm36.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>3601 BC <20> 3002 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";color:blue;font-style:normal'>seplm30.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";color:blue;'>semom30.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm30.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>3001 BC <20> 2402 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";color:blue;font-style:normal'>seplm24.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";color:blue;'>semom24.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm24.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>2401 BC <20> 1802 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";color:blue;font-style:normal'>seplm18.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";color:blue;'>semom18.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm18.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>1801 BC <20> 1202 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";color:blue;font-style:normal'>seplm12.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";color:blue;'>semom12.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm12.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>1201 BC <20> 602 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=EN-US style='font-family:"Courier New";color:blue;font-style:normal'>seplm06.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";color:blue;'>semom06.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=PT-BR
|
||
style='font-family:"Courier New";'>seasm06.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>601 BC <20> 2 BC</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";color:blue;
|
||
font-style:normal'>sepl_00.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";color:blue;'>semo_00.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-GB
|
||
style='font-family:"Courier New";'>seas_00.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-GB>1 BC <20> 599 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";color:blue;
|
||
font-style:normal'>sepl_06.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";color:blue;'>semo_06.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_06.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>600 AD <20> 1199 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";color:blue;
|
||
font-style:normal'>sepl_12.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";color:blue;'>semo_12.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_12.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>1200 AD <20> 1799 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";color:blue;
|
||
font-style:normal'>sepl_18.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";color:blue;'>semo_18.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_18.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>1800 AD <20> 2399 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";color:blue;
|
||
font-style:normal'>sepl_24.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";color:blue;'>semo_24.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_24.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>2400 AD <20> 2999 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";font-style:
|
||
normal'>sepl_30.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>semo_30.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_30.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>3000 AD <20> 3599 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";font-style:
|
||
normal'>sepl_36.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>semo_36.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_36.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>3600 AD <20> 4199 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";font-style:
|
||
normal'>sepl_42.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>semo_42.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>seas_42.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT>4200 AD <20> 4799 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=118 valign=top style='width:88.55pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:
|
||
0cm 0cm 0cm 0cm'>
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;layout-grid-mode:char'><span
|
||
lang=IT style='font-family:"Courier New";font-style:
|
||
normal'>sepl_48.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=IT
|
||
style='font-family:"Courier New";'>semo_48.se1</span></p>
|
||
</td>
|
||
<td width=113 valign=top style='width:3.0cm;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US
|
||
style='font-family:"Courier New";'>seas_48.se1</span></p>
|
||
</td>
|
||
<td width=155 valign=top style='width:115.9pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>4800 AD <20> 5399 AD</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-size:8.0pt;font-style:normal'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The <span style='color:blue'>blue file names</span> in the table
|
||
indicate that a file is derived directly from the JPL data, whereas the other
|
||
files are derived from Astrodienst's own numerical integration.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>All Swiss Ephemeris files for Version 1 have the file suffix .se1.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>A planetary file is about<75> 500
|
||
kb, a lunar file 1300 kb. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Swiss Ephemeris files are distributed with the SWISSEPH package. They
|
||
are also available for download from Astrodienst's web server.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><b><span lang=EN-US style='font-size:10.0pt;'>The time range of the Swiss Ephemeris </span></b></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'>Start date<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2 Jan 5401 BC (jul. calendar)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> = JD<4A><44> -251291.5</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'>End date<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 31
|
||
Dec 5399 AD (greg. Cal.) <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> = JD
|
||
3693368.5</span></p>
|
||
|
||
<p class=MsoNormal><b><span lang=EN-US>A note
|
||
on year numbering: </span></b></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are
|
||
two numbering systems for years before the year 1 AD. The historical numbering
|
||
system (indicated with BC) has no year zero. Year 1 BC is followed directly by
|
||
year 1 AD.</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 AD.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
historical year 1 BC corresponds to astronomical year 0,</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>the
|
||
historical your 2 BC corresponds to astronomical year -1, etc.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In this
|
||
document 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 BC, it is historical style.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142931"><b><span lang=EN-US>2.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> The Moshier Ephemeris</span></b></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This is a semi-analytical approximation of the JPL planetary and lunar
|
||
ephemerides, currently based on the DE404 ephemeris, developed by Steve
|
||
Moshier. Its deviation from JPL is well below 1 arc second with the planets and
|
||
a few arc seconds with the moon. <i>No data files</i> are required for this
|
||
ephemeris, as all data are linked into the program code already.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This may be sufficient accuracy for most astrologers, 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>However, if you work with the 'true' lunar node, which is derived from
|
||
the lunar ephemeris, you will have to accept an error of about 1 arc minute. To
|
||
get a position better than an arc second, you will have to spend 1.3 MB for the
|
||
lunar ephemeris file 'semo_18.se1' of Swiss Ephemeris.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The advantage of the Moshier 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 and Swiss Ephemeris.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Moshier Ephemeris covers the interval from 3000 BC to 3000 AD.
|
||
However, <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:<3A> <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. <20> (Moshier, http://www.moshier.net/aadoc.html). </span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142932"><b><span lang=EN-US>3.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> The full JPL Ephemeris</span></b></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This is the full precision state-of-the-art ephemeris. It provides the
|
||
highest precision and is the basis of the Astronomical Almanac.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL is the Jet Propulsion Laboratory of NASA in Pasadena, CA, USA (see <u><span
|
||
style='color:blue'>http://www.jpl.nasa.gov</span></u> ). 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 DE405/DE406. As most previous ephemerides, it
|
||
has been created by Dr. Myles Standish.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the <i>inner planets</i>, Standish shows that within the period
|
||
1600 <20> 2160 there is a maximum difference of 0.1 <20> 0.2<EFBFBD> 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<EFBFBD> over that period. However, for the
|
||
period 1980 <20> 2000 the deviations between DE200 and DE406 are below 0.01<EFBFBD> for <i>all</i>
|
||
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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the <i>outer planets</i>, 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<EFBFBD> before 1910 and after 2010, and increases rapidly in more remote past or
|
||
future.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the <i>moon</i>, there is an increasing difference of 0.9<EFBFBD>/cty</span><sup><span
|
||
lang=EN-US style='font-size:8.0pt;'>2</span></sup><span
|
||
lang=EN-US style='font-size:10.0pt;'> between 1750 and
|
||
2169. It comes mainly from errors in LE200 (<i>L</i>unar <i>E</i>phemeris).</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The differences between DE200 and DE403 (DE406) can be summarized as
|
||
follows:</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1980 <20> 2000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> all
|
||
planets<EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <
|
||
0.01<EFBFBD>, </span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;text-indent:35.4pt'><span
|
||
lang=EN-US style='font-style:normal'>1600 <20> 1980<38><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Sun <20> Jupiter<65><72><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> a few 0.1<EFBFBD>,</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;text-indent:35.4pt'><span
|
||
lang=EN-US style='font-style:normal'>1900 <20> 1980<38><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Saturn <20> Neptune<6E><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> a
|
||
few 0.1<EFBFBD>,</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1600 <20> 1900<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Saturn <20> Neptune<6E><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> a
|
||
few <20>,</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1750 <20> 2169 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Moon<6F><6E><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> a few <20>.</span></p>
|
||
|
||
<p class=WW-EndnoteText><span lang=EN-US style='font-size:8.0pt;'>(see: E.M. Standish, X.X. Newhall, J.G. Williams, and W.M. Folkner, <i>JPL
|
||
Planetary and Lunar Ephemerides, DE403/LE403</i>, JPL Interoffice Memorandum
|
||
IOM 314.10-127, May 22, 1995, pp. 7f.)</span></p>
|
||
|
||
<p class=WW-EndnoteText><span lang=EN-US style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The DE406 is a 200 Megabyte file available for download from the JPL
|
||
server <u><span style='color:blue'>ftp://navigator.jpl.nasa.gov/ephem/export</span></u><EFBFBD> or on CD-ROM from the astronomical publisher
|
||
Willman-Bell, see <u><span style='color:blue'>http://www.willbell.com</span></u>.
|
||
<br>
|
||
Astrodienst has received permission from Dr. Standish to include the file on
|
||
the </span><span lang=EN-US style='font-size:11.0pt;font-family:"FuturaBlack BT";'>Swiss Ephemeris</span><span lang=EN-US
|
||
style='font-size:10.0pt;'> CD-ROM.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>There are several versions of the JPL Ephemeris. The version is
|
||
indicated by the DE-number. A higher number stands for a later update. SWISSEPH
|
||
should be able to read <i>any </i>JPL file from DE200 upwards.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The time range of this ephemeris (DE406) is:</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'><EFBFBD><EFBFBD><EFBFBD> start date<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 23
|
||
Feb 3001 BC (28 Jan greg.)<29><><EFBFBD><EFBFBD> = JD<4A><44><EFBFBD> 625360.5,</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-style:normal'><EFBFBD><EFBFBD><EFBFBD> end date<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> 3 Mar 3000 AD<41><44><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> = JD<4A> 2816848.5.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:11.0pt;font-family:
|
||
"FuturaBlack BT";'>Swiss Ephemeris</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> 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 18 Mb instead of 200 Mb. Therefore for most
|
||
applications it makes little sense to get the full JPL file, except to compare
|
||
the precision. Precision comparison can also be done at the Astrodienst web
|
||
server, because we have a test utility online which allows to compute planetary
|
||
positions for any date with any of the three ephemerides.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>For the extension of the JPL time range to 5400 BC - 5400 AD please see
|
||
section 2.5.1 below.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142933"><span lang=EN-US>2.1.2.1Swiss Ephemeris and the Astronomical Almanac</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The original JPL ephemeris gives barycentric equatorial Cartesian
|
||
positions of the equinox 2000. Moshier provides heliocentric positions.<2E> The conversions to apparent geocentric
|
||
ecliptical positions were done with 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 1995, 1996, and 1997 down to
|
||
the last digit. Editions of other years have not been checked.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Since 2003, 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, page B61-B63,<2C> to the last digit, i.e. to better than 0.001 arc second. (To
|
||
avoid confusion when checking this, 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.)</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142934"><span lang=EN-US>2.1.2.2Swiss Ephemeris and JPL Horizons System</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris, from Version 1.70 on, reproduces <i>astrometric</i> planetary positions of the
|
||
JPL Horizons System precisely. However, there are small differences with the <i>apparent</i> positions. The reason is that
|
||
the Horizons System still uses the old precession model IAU 1976 (Lieske) and
|
||
nutation IAU 1980 (Wahr). This was confirmed by Jon Giorgini from JPL in an
|
||
E-mail of 3 Feb. 2006.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Note on 2 August 2012. It seems that this is still true, according to
|
||
the documentation of the Horizons System at:
|
||
http://ssd.jpl.nasa.gov/?horizons_doc#longterm</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142935"><span lang=EN-US>2.1.2.3<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Differences between Swiss Ephemeris
|
||
1.70 and older versions</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- "Frame Bias" transformation from ICRS to J2000.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- Nutation IAU 2000B (could be switched to 2000A by the user)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The differences between the old and new <i>planetary positions</i> in ecliptic longitude (arc seconds) are:</span></p>
|
||
|
||
<p class=MsoFooter><span lang=EN-US>year<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> new - old</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00108</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1995<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.02448</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1980<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.05868</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1970<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.10224</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1950<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.15768</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1900<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.30852</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1800<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.58428</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1799<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.04644</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1700<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.07524</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1500<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.12636</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.25344</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>0<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.53316</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-1000<30><30><EFBFBD><EFBFBD><EFBFBD> -0.85824</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-2000<30><30><EFBFBD><EFBFBD><EFBFBD> -1.40796</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-3000<30><30><EFBFBD><EFBFBD><EFBFBD> -3.33684</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-4000<30><30><EFBFBD><EFBFBD><EFBFBD> -10.64808</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5000<30><30><EFBFBD><EFBFBD><EFBFBD> -32.68944</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5400<30><30><EFBFBD><EFBFBD><EFBFBD> -49.15188</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The discontinuity of the curve between 1800 and 1799 is explained by the
|
||
fact that the old 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 of that time range. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Note: In the literature there are no indications concerning the
|
||
long-term use of the precession model P03. It is said to be accurate to 0.00005
|
||
arc second for CE 1000-3000. However, there is no reason to trust alternative
|
||
models (e.g. Bretagnon 2003) more for the whole period of the Swiss Ephemeris. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The differences between version 1.70 and older versions for the future
|
||
are as follows:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00108</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2010<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.01620</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2050<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.14004</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2100<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.29448</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2200<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.61452</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2201<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.05940</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>3000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.27252</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>4000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.48708</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.47592</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5400<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.40032</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The discontinuity in 2200 has the same explanation as
|
||
the one in 1800.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span
|
||
lang=EN-US style='font-size:10.0pt;'>Jyotish / sidereal
|
||
ephemerides</span></i><span lang=EN-US style='font-size:10.0pt;'>:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The ephemeris changes by a constant value of about +0.3 arc second. This
|
||
is because all our ayanamsas have the start epoch 1900, for which epoch
|
||
precession was corrected by the same amount.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span
|
||
lang=EN-US style='font-size:10.0pt;'>Fictitious planets
|
||
/ Bodies from the orbital elements file seorbel.txt:</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The differences for ecliptic obliquity in arc seconds (new - old) are:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5400<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -1.71468</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -1.25244</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>4000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.63612</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>3000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.31788</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2100<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.06336</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.04212</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1900<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.02016</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1800<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.01296</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1700<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.04032</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1600<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.06696</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1500<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.09432</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.22716</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>0<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.51444</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-1000<30><30><EFBFBD><EFBFBD><EFBFBD> 1.07064</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-2000<30><30><EFBFBD><EFBFBD><EFBFBD> 2.62908</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-3000<30><30><EFBFBD><EFBFBD><EFBFBD> 6.68016</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-4000<30><30><EFBFBD><EFBFBD><EFBFBD> 15.73272</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5000<30><30><EFBFBD><EFBFBD><EFBFBD> 33.54480</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5400<30><30><EFBFBD><EFBFBD><EFBFBD> 44.22924</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The differences for <i>sidereal time </i>in
|
||
seconds (new - old) are:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5400<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -2.544</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>5000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -1.461</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>4000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.122</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>3000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.126</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2100<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.019</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.001</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1900<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.019</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.126</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>0<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.122</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-500<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.594</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-1000<30><30><EFBFBD><EFBFBD><EFBFBD> -1.461</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-2000<30><30><EFBFBD><EFBFBD><EFBFBD> -5.029</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-3000<30><30><EFBFBD><EFBFBD><EFBFBD> -12.355</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-4000<30><30><EFBFBD><EFBFBD><EFBFBD> -25.330</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5000<30><30><EFBFBD><EFBFBD><EFBFBD> -46.175</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>-5400<30><30><EFBFBD><EFBFBD><EFBFBD> -57.273</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142936"><span lang=EN-US>2.1.2.4<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Differences between Swiss Ephemeris
|
||
1.78 and 1.77</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Former versions of the Swiss Ephemeris had used the precession model by
|
||
Capitaine, Wallace, and Chapront of 2003 for the time range 1800-2200 and the
|
||
precession model J. G. Williams in Astron. J. 108, 711-724 (1994) for epochs
|
||
outside this time range. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Version 1.78 calculates precession and ecliptic obliquity according to
|
||
Vondr<EFBFBD>k, Capitaine, and Wallace, <20>New precession expressions, valid for long
|
||
time intervals<6C>, A&A 534, A22 (2011), which is good for +- 200 millennia. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This change has almost no effect for historical epochs. Planetary
|
||
positions and the obliquity of the ecliptic change by less than an arc minute
|
||
in 5400 BC. However, for research concerning the prehistoric cave paintings of
|
||
Lascaux, Altamira, etc, some of which may represent celestial constellations,
|
||
fixed star positions are required for 15<31>000 BC or even earlier (the Chauvet
|
||
cave was painted in 33<33>000 BC). 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 BC to 5400 AD.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Differences in precession (v. 1.78 <20> v. 1.77, test star was Aldebaran):</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Year<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Difference in arc sec</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-20000<30> -26715" </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-15000<30><30><EFBFBD> -2690"<EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-10000<30><30><EFBFBD><EFBFBD><EFBFBD> -256"<EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -5000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -3.95388"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -4000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -9.77904"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -7.00524"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -2000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -3.40560"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -1000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -1.23732"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.33948"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.05436"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1800<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00144"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1900<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00036"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.00000"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2100<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00036"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2200<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.00072"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.03528"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 4000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.59904"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 5000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2.90160"<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD>10000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 76"<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD>15001<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
227"<EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD>19000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
2839"<EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD>20000<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
5218"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>Differences in
|
||
ecliptic obliquity</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Year<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Difference in arc sec</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-20000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 11074.43664"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-15000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3321.50652"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-10000<30><30><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>632.60532"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> -5000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -33.42636"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.01008"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> 1000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.00972"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> 2000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.00000"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> 3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.01008"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> 4000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.05868"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> 10000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -72.91980"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> 15000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
-772.91712"</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD> 20000<30><30><EFBFBD><EFBFBD><EFBFBD>
|
||
-3521.23488<EFBFBD></span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142937"><span lang=EN-US>2.1.3<EFBFBD><EFBFBD><EFBFBD> The details of coordinate transformation</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The following conversions are applied to the coordinates after reading
|
||
the raw positions from the ephemeris files and before output:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Correction for light-time</span></i><span lang=EN-US
|
||
style='font-size:10.0pt;'>. 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 is 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<EFBFBD></span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Conversion from the solar system barycenter to the
|
||
geocenter</span></i><span lang=EN-US style='font-size:10.0pt;'>. 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=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Light deflection by the gravity of the sun</span></i><span
|
||
lang=EN-US style='font-size:10.0pt;'>. In gravitational
|
||
fields of the sun and the planets light rays are bent. However, within the
|
||
solar system only the sun has mass enough to deflect light significantly.
|
||
Gravity deflection is greatest for distant planets and stars, but never greater
|
||
than 1.8<EFBFBD>. When a planet disappears behind the sun, the <i>Explanatory
|
||
Supplement</i> recommends to set the deflection = 0. To avoid discontinuities,
|
||
we chose another procedure. See Appendix A.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'><EFBFBD>Annual<EFBFBD> aberration of light</span></i><span
|
||
lang=EN-US style='font-size:10.0pt;'>. 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=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Frame Bias (ICRS to J2000)</span></i><span lang=EN-US
|
||
style='font-size:10.0pt;'>. The JPL ephemeris
|
||
DE405/DE406 is referred to the International Celestial Reference System, a
|
||
time-independent, non-rotating reference system which was recommended 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=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Precession</span></i><span lang=EN-US
|
||
style='font-size:10.0pt;'>. The motion of the vernal
|
||
equinox, which is an effect of the influences of solar, lunar, and planetary
|
||
gravity 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 <i>date</i>. (From Swiss Ephemeris 1.78 on, we use the
|
||
precession model Vondr<64>k/Capitaine/Wallace 2011.)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Nutation (</span></i><span lang=EN-US
|
||
style='font-size:10.0pt;'>true<i> equinox of date)</i>.
|
||
A short-period oscillation of the vernal equinox. It results from the moons
|
||
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 1.70 on, we use the nutation model IAU 2000. Older
|
||
versions used the nutation model IAU 1980 (Wahr).)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Transformation from equatorial to ecliptic coordinates.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>For <i>precise speed </i>of the planets and the moon, we had to make a
|
||
special effort, because the <i>Explanatory Supplement </i>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<EFBFBD>/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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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
|
||
speed precision is now better than 0.002<EFBFBD> for all planets, and the computation
|
||
is even much 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142938"><span lang=EN-US>2.1.4<EFBFBD><EFBFBD><EFBFBD> The Swiss Ephemeris compression mechanism</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>To make it simple, it works as follows:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The lunar and the inner planets ephemerides require by far the largest
|
||
part of the storage. A more sophisticated mechanism is needed for them than for
|
||
the outer planets.<2E> Instead of the
|
||
positions we store the differences between JPL and the mean orbits of the
|
||
analytical theory VSOP87. These differences are much smaller than the position
|
||
values, wherefore they require less storage.<2E>
|
||
They are stored in Chebyshew polynomials covering a period of an
|
||
anomalistic cycle each. (By the way, this is the reason, why Swiss Ephemeris
|
||
begins only with 4 Nov -3000 (instead of 23 Feb -3000 as JPL).<2E> This is the date, when the last of the inner
|
||
planets Mars has its first perihelion after the start date of DE406.)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the outer planets from Jupiter through Pluto we use a simpler
|
||
mechanism. We rotate the positions provided by DE406 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.<2E> (This is the reason, why Swiss Ephemeris stops in the year 2991
|
||
AD. 4000 days later is a date beyond 3000 AD)</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142939"><span lang=EN-US>2.1.5<EFBFBD><EFBFBD><EFBFBD> The extension of the time range to 10'800
|
||
years</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The JPL ephemeris covers the time range from 3000 BC to 3000 AD. While
|
||
this is an excellent range covering all precisely known historical events,
|
||
there are some types of astrological and historical research which would
|
||
welcome a longer time range. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>In December 1998 we have made an effort to extend the time range by 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The previous JPL ephemeris, the DE200, however has been reproduced by
|
||
Steve Moshier over a very long time range with his integration program, which
|
||
has been available to us. We have used this integration program with start
|
||
vectors taken at the end points of the DE406 time range. To test our numerical
|
||
integrator, we ran it upwards from 3000 BC to 600 BC 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 have varied the tidal coupling parameter (love number)
|
||
and the longitudinal libration phase at the start epoch until we found the best
|
||
agreement over the 2400 year test range between our integration and the JPL
|
||
data. We could reproduce the Moon's motion over a the 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With these modified parameters we ran the integration backward in time
|
||
from 3000 BC to 5400 BC. 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 border=0 cellspacing=0 cellpadding=0 style='margin-left:-.35pt;
|
||
border-collapse:collapse;'>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border:solid black .5pt;
|
||
border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>planet</span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border:solid black .5pt;
|
||
border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>max. error arcsec</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>avg. error arcec</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Mercury<EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>1.67</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.61</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Venus<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.14</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.03</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Earth<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>1.00</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.42</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Mars<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.21</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.06</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Jupiter<EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.85</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.38</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Saturn<EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.59</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.24</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Uranus<EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.20</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.09</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Neptune<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.12</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>0.06</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Pluto<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.12</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.04</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Moon<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>12.2</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>2.53</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Sun bary. </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>6.3</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>0.39</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='page-break-after:avoid'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The same procedure was applied
|
||
at the upper end of the DE406 range, to cover an extension period from 3000 AD
|
||
to 5400 AD. The maximum integration errors as determined in the test run 3000
|
||
AD down to 600 AD are given in the table below.</span></p>
|
||
|
||
<table border=0 cellspacing=0 cellpadding=0 style='margin-left:-.35pt;
|
||
border-collapse:collapse;'>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border:solid black .5pt;
|
||
border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>planet</span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border:solid black .5pt;
|
||
border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>max. error arcsec</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=ES>avg. error arcsec</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Mercury<EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>2.01</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.69</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Venus<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.06</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.02</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Earth<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.33</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.14</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Mars<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>1.69</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.82</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Jupiter<EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.09</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.05</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Saturn<EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.05</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.02</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Uranus<EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.16</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.07</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Neptune<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.06</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>0.03</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=FR>Pluto<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.11</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.04</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Moon<EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>8.89</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>3.43</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=99 valign=top style='width:74.4pt;border-top:none;border-left:solid black .5pt;
|
||
border-bottom:solid black .5pt;border-right:none;
|
||
padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='page-break-after:avoid;layout-grid-mode:char'><span
|
||
lang=EN-US>Sun bary. </span></p>
|
||
</td>
|
||
<td width=93 valign=top style='width:69.95pt;border-top:none;border-left:
|
||
solid black .5pt;border-bottom:solid black .5pt;border-right:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.61</span></p>
|
||
</td>
|
||
<td width=87 valign=top style='width:65.45pt;border:solid black .5pt;
|
||
border-top:none;padding:0cm 3.5pt 0cm 3.5pt'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>0.05</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>We expect that in some time a full integration program modeled after the
|
||
DE406 integrator will become available. At that time we will rerun our
|
||
integration and report any significant differences.</span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142940"><span lang=EN-US>2.2<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Lunar and Planetary Nodes and Apsides</span></a></h2>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142941"><span lang=EN-US>2.2.1<EFBFBD><EFBFBD><EFBFBD> Mean Lunar Node and Mean Lunar Apogee
|
||
('Lilith', 'Black Moon')</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Our mean node and mean apogee are computed from Moshier's lunar routine,
|
||
which adjusts the ELP2000-85 lunar theory of Chapront-Touz<75> and Chapront to fit
|
||
the JPL ephemeris on the interval from 3000 BC to 3000 AD. Its deviation from
|
||
Chapront's mean node is 0 for J2000 and keeps below 20 arc seconds for the
|
||
whole period. With the apogee, the deviation reaches 3 arc minutes at 3000 BC</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Lilith</span></i><span lang=EN-US style='font-size:
|
||
10.0pt;'> or the <i>Dark Moon </i>is either the apogee
|
||
(<28>aphelion<6F>) of the lunar orbital ellipse or, for some people, its empty focal
|
||
point.<2E> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Because the Earth is located in one of the two focuses of the ellipse,
|
||
it has also been argued that the second focal point ought to be called <20>Dark
|
||
Earth<EFBFBD> rather than <20>Dark Moon<6F> (Ernst Ott).</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The opposite point, the lunar perigee or orbital point closest to the Earth,
|
||
is also known as <i>Priapus</i>. However, if Lilith is understood as the second
|
||
focus, an opposite point makes no sense, of course. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:9.0pt;'>Originally, the term <20>Dark Moon<6F> was used for a hypothetical second body
|
||
that was believed to move around the earth. There are still ephemerides around
|
||
for such a body, but today<61>s observational skills and knowledge in celestial
|
||
mechanics clearly exclude the possibility of such an object. As a result of
|
||
confusion, the term <20>Dark Moon<6F> was later given to the lunar apogee. However,
|
||
from the astrological symbolism of the lunar apogee, the expression <20>Dark Moon<6F>
|
||
seems to be appropriate.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 has been
|
||
forgotten and therefore the book contains a false ephemeris. As a result of
|
||
this projection, we also provide an ecliptic latitude of the apogee, which will
|
||
be of importance if you work with declinations.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 it as the apogee, this
|
||
oscillation would be about +/- 40 arc minutes. If one defines it as the second
|
||
focus, the effect is much greater: +/- 6 degrees! However, we have neglected
|
||
this effect.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>[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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>In addition, computing topocentric positions of mean elements is also
|
||
meaningless and should not be done.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142942"><span lang=EN-US>2.2.2<EFBFBD><EFBFBD><EFBFBD> The 'True' Node</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The 'true' lunar node is usually considered to be 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The nodes are considered to be important because they are connected with
|
||
the 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 <i>the
|
||
momentary orbital plane of the sun.</i></span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This makes a difference! 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!<21> However, Swiss Ephemeris
|
||
computes the traditional version.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 true with the mean nodes.<2E> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>However, in the strict sense of the word, even the <20>true<75> 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 just a
|
||
hypothesis. They are founded on the idea that celestial orbits can be approximated
|
||
by elliptical elements. This works well with the planets, but not with the
|
||
moon, because its orbit is strongly perturbed by the sun. Another procedure,
|
||
which might be more reasonable, 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Precision of the true node:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The true node can be computed from all of our three ephemerides.<2E> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Maximum differences:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived node <20> Swiss-Ephemeris-derived node<64><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> ~ 0.1 arc second</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived node <20> Moshier-derived node<64><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> ~ 70<37><30> arc seconds</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>(PLACALC was not better either. Its error was often > 1 arc minute.)</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142943"><span lang=EN-US>2.2.3<EFBFBD><EFBFBD><EFBFBD> The Osculating Apogee (so-called 'True
|
||
Lilith' or 'True Dark Moon')</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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.<2E> 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,
|
||
but not of the lunar orbit which is strongly perturbed by the gravity of the
|
||
sun. <i>The lunar orbit is far away from being an ellipse!</i></span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>However, 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.<2E> In between those two points, the
|
||
value of the osculating apogee is pure imagination. The amplitude of the
|
||
oscillation of the <i>osculating</i> apogee around the mean apogee is +/- 25
|
||
degrees, while the <i>true</i> apogee's deviation from the mean one never
|
||
exceeds 5 degrees.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>It has also to be mentioned, that 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>. </span><span lang=FR
|
||
style='font-size:10.0pt;'>And he adds: <20>Nous constatons que
|
||
m<EFBFBD>me en utilisant ces 58 termes <i>correctifs</i>, l'erreur peut atteindre
|
||
0,5d!<21> </span><span lang=EN-US style='font-size:10.0pt;'>(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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Precision:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The osculating apogee can be computed from any one of the 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Maximum differences:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived apogee <20> Swiss-Ephemeris-derived apogee<65><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> ~ 0.9 arc second</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived apogee <20> Moshier-derived apogee<65><65> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> ~ 360<36><30> arc seconds<64><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> =
|
||
6<EFBFBD><EFBFBD> arc minutes!</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>There have been several other attempts to solve the problem of a 'true'
|
||
apogee. They are not included in the SWISSEPH package.<2E> All of them work with a correction table.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>However, this curve does not have exactly the shape of a sine, as is
|
||
assumed by all of those correction tables.<2E>
|
||
And most of them have an amplitude of more than 10 degrees, which is
|
||
much too high. The most realistic solution so far was the one proposed by Henry
|
||
Gouchon in <20>Dictionnaire Astrologique<75>, Paris 1992, which is based on an
|
||
amplitude of 5 degrees.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142944"><span lang=EN-US>2.2.4<EFBFBD><EFBFBD><EFBFBD> The Interpolated or Natural Apogee and
|
||
Perigee (Lilith and Priapus)</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>As has been said above, the osculating lunar apogee (so-called
|
||
"true Lilith") 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 <i>artifact</i> of the insufficient model, they
|
||
do not really show a motion of the apsides. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 squares 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This solution has been called the <i>"interpolated"</i>
|
||
or "realistic" apogee and perigee by Dieter Koch in his publications.
|
||
Juan Revilla prefers to call them the <i>"natural"
|
||
</i>apogee and perigee. Today, Dieter Koch would prefer the designation
|
||
"natural". The designation "interpolated" is a bit misleading,
|
||
because it associates something that astrologers used to do everyday in old
|
||
days, when they still used to work with printed ephemerides and house tables.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Note on implementation (from Swiss Ephemeris Version 1.70 on):</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Conventional interpolation algorithms do not work well in the case of
|
||
the lunar apsides. The supporting points are too far away from each other in
|
||
order to provide a good interpolation, the error estimation is greater than 1
|
||
degree for the perigee. Therefore, Dieter chose a different solution. He
|
||
derived an "interpolation method" from the analytical lunar theory
|
||
which we have in the form of moshier's lunar ephemeris. This
|
||
"interpolation method" has not only the advantage that it probably
|
||
makes more sense, but also that the curve and its derivation are both
|
||
continuous.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span style='font-size:10.0pt;'>Literature
|
||
(in German): </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span style='font-size:10.0pt;'>-
|
||
Dieter Koch, "Was ist Lilith und welche Ephemeride ist richtig", in:
|
||
Meridian 1/95</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span style='font-size:10.0pt;'>-
|
||
Dieter Koch and Bernhard Rindgen, "Lilith und Priapus",
|
||
Frankfurt/Main, 2000. (http://www.vdhb.de/Lilith_und_Priapus/lilith_und_priapus.html)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- Juan Revilla, "The Astronomical Variants of the Lunar Apogee -
|
||
Black Moon", http://www.expreso.co.cr/centaurs/blackmoon/barycentric.html</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142945"><span lang=EN-US>2.2.5 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Planetary Nodes and Apsides</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Note to specialists in
|
||
planetary nodes and apsides: If important publications or web sites concerning
|
||
this topic have been forgotten in this summary, your clue will be appreciated.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Methods written in small
|
||
characters are not supported by the Swiss Ephemeris software.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 much
|
||
greater differences in nodes and apsides.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Definitions of the nodes</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The lunar nodes indicate 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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>1)<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span><span
|
||
lang=EN-US style='font-size:10.0pt;'>They can be
|
||
understood as a <i>direction</i> or as an <i>axis</i> 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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:9.0pt;'>Note: However, as
|
||
Michael Erlewine points out in his elaborate web page on this topic
|
||
(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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:10.0pt;'>The ascending and
|
||
the descending node will, in this case, be in precise opposition.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>2)<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span><span
|
||
lang=EN-US style='font-size:10.0pt;'>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 <i>points</i> at
|
||
which a planetary orbit intersects with the ecliptic plane.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:10.0pt;'>For the lunar nodes
|
||
and heliocentric planetary nodes, this definition makes no difference from the
|
||
definition 1). However, it does make a difference for <i>geocentric</i>
|
||
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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:9.0pt;'>Note: There is
|
||
another possibility, not implemented in the Swiss ephemeris: E.g., instead of
|
||
considering the points of the Mars orbit that are located on the ecliptic
|
||
plane, one might consider the points of the <i>earth<EFBFBD>s</i> orbit that are
|
||
located on 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=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:9.0pt;'>3)<span
|
||
style='font:7.0pt "Times New Roman"'> </span></span><span
|
||
lang=EN-US style='font-size:9.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Possible definitions for apsides and focal points</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>One may consider either the
|
||
planetary <i>apsides</i>, i.e. the two points on a planetary orbit<69> that are closest to the sun and most distant
|
||
from the sun, resp. The former point is called the <i><EFBFBD>perihelion<EFBFBD></i> and the
|
||
latter one the <i><EFBFBD>aphelion<EFBFBD></i>. For a geocentric chart, these points could be
|
||
transformed from the heliocenter to the geocenter. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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<EFBFBD>. 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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The Swiss Ephemeris supports
|
||
both points of view.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'><EFBFBD></span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Special case: the Earth</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>There is no node of the earth
|
||
orbit itself. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:8.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Special case: the Sun</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>In addition to the Earth (EMB)
|
||
apsides, our software computes so-to-say "apsides" of the solar orbit
|
||
around the Earth, i.e. points on the orbit of the Sun where it is closest to
|
||
and where it is farthest from the Earth. These points form an opposition and are
|
||
used by some astrologers, e.g. by the Dutch astrologer George Bode or the Swiss
|
||
astrologer Liduina Schmed. The <20>perigee<65>, located at about 13 Capricorn, is
|
||
called the "Black Sun", the other one, in Cancer, is called the
|
||
<EFBFBD>Diamond<EFBFBD>.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>So, for a complete set of
|
||
apsides, one might want to calculate them for the Sun <i>and</i> the Earth and
|
||
all other planets. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'> </span></i></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Mean and osculating positions</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'> </span></i></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Mean positions</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><i><span lang=EN-US
|
||
style='font-size:10.0pt;'>Mean</span></i><span
|
||
lang=EN-US style='font-size:10.0pt;'> 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 can <i>not</i> be
|
||
calculated for Pluto and the asteroids, because there is no planetary theory
|
||
for them. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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. (http://ssd.jpl.nasa.gov/elem_planets.html,
|
||
<EFBFBD>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The differences between the
|
||
DE200 and the VSOP87 mean elements are considerable, though:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=FR style='font-size:10.0pt;'>Node<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Perihelion</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=FR style='font-size:10.0pt;'>Mercury <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3<><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 4<></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=FR style='font-size:10.0pt;'>Venus<EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3<><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 107<30></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Earth <20><><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -<2D><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 35<33></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Mars<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 74<37><34><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 4<></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Jupiter<EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 330<33><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1850<35></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Saturn<EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 178<37><38><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1530<33></span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Uranus<EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 806<30><36><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 6540<34> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'>Neptune<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 225<32><35><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 11600<30>
|
||
(>3 deg!)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;
|
||
text-align:justify'><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'><EFBFBD></span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>Osculating nodes and apsides</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 <i>if perturbations were to cease
|
||
instantaneously or if there were only two bodies (the sun and the planet)
|
||
involved in the motion from now on and the motion were an ideal ellipse</i>.
|
||
This ideal assumption makes it obvious that it would be misleading to call such
|
||
nodes or apsides "true". It is more appropriate to call them
|
||
"osculating". Osculating nodes and apsides are "true" only
|
||
at the precise moments, when the body passes through them, but for the times in
|
||
between, they are a mere mathematical construct, nothing to do with the nature
|
||
of an orbit.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:9.0pt;'>I have tried to solve the
|
||
problem by <i>interpolating</i> 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 make an
|
||
accurate interpolation possible. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>There is another problem about
|
||
heliocentric ellipses. E.g. Neptune's orbit has often two perihelia and two
|
||
aphelia within one revolution. As a result, there is a wild oscillation of the
|
||
osculating or "true" perihelion (and aphelion), which is not due to a
|
||
transformation of the orbital ellipse but rather due to the deviation of the
|
||
orbit from an elliptic shape. Neptune<6E>s orbit cannot be adequately represented
|
||
by a heliocentric ellipse. It makes no sense to use such points in astrology. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 much
|
||
faster than the motion of Neptune, and Neptune cannot react on 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 statement is also true, though less obvious, for
|
||
Saturn, Uranus and Pluto, but not for Jupiter and the inner planets.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>As a solution, it seems
|
||
reasonable to compute the osculating elements of <i>slow</i> 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 transsaturnian asteroids, this solution may be used
|
||
as a substitute for "mean" nodes and apsides. Note, however, that
|
||
there are considerable differences between barycentric osculating and mean
|
||
nodes and apsides for Saturn, Uranus, and Neptune. (A few degrees! But heliocentric
|
||
ones are worse.)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Anyway, neither the
|
||
heliocentric nor the barycentric ellipse is a perfect representation of the
|
||
nature of a planetary orbit. So, astrologers, do not expect anything very
|
||
reliable here either!</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The best choice of method will
|
||
probably be:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>For Mercury <20> Neptune: mean
|
||
nodes and apsides.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>For asteroids that belong to
|
||
the inner asteroid belt: osculating nodes/apsides from a heliocentric ellipse.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>For Pluto and transjovian
|
||
asteroids: osculating nodes/apsides from a barycentric ellipse.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><span lang=EN-US style='font-size:10.0pt;'>The modes of the Swiss Ephemeris function
|
||
swe_nod_aps()</span></i></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The<EFBFBD> function <i>swe_nod_aps()</i> can be run in the following modes:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>1) 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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>2) Osculating positions are
|
||
returned for nodes and apsides of all planets.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>3) Same as 2), but for planets
|
||
and asteroids beyond Jupiter, a barycentric ellipse is used.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>4) Same as 1), but for Pluto
|
||
and asteroids beyond Jupiter, a barycentric ellipse is used.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>For the reasons given above,
|
||
Dieter Koch would prefer method 4) as making most sense. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>In all of these modes, the second focal point of the ellipse can be
|
||
computed instead of the aphelion.</span></p>
|
||
|
||
<p class=MsoPlainText style='text-align:justify'><span lang=EN-US> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142946"><span lang=EN-US>2.3.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Asteroids</span></a></h2>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142947"><span lang=EN-US>Asteroid
|
||
ephemeris files</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The standard distribution of SWISSEPH includes the <i>main</i> asteroids
|
||
Ceres, Pallas, Juno, Vesta, as well as Chiron, and Pholus. To compute them, you
|
||
must<EFBFBD> have the main-asteroid ephemeris
|
||
files in your ephemeris directory. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The names of these files are of the following form:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>seas_18.se1</span><span lang=EN-US
|
||
style='font-size:10.0pt;'><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> main asteroids
|
||
for 600 years from 1800 - 2400</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The size of such a file is about 200 kb.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>All other asteroids are available in separate files. The names of
|
||
additional asteroid files look like:</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
|
||
style='font-size:12.0pt;font-family:"Courier New";
|
||
font-style:normal'>se00433.se1</span><span lang=EN-US style='font-size:12.0pt;font-style:normal'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> the file of asteroid No. 433 (=
|
||
Eros)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>These files cover the period 3000 BC - 3000 AD.<br>
|
||
A short version for the years 1500 <20> 2100 AD has the file name with an 's'
|
||
imbedded, </span><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New";'>se00433s.se1</span><span lang=EN-US style='font-size:
|
||
10.0pt;'>.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The numerical integration of the all officiall numbered asteroids is an
|
||
ongoing effort. In December 1998, 8000 asteroids were numbered, and their
|
||
orbits computed by the devlopers of Swiss Ephemeris. In January 2001, the list
|
||
of numbered asteroids has reached 20957, and is growing very fast.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><b><span lang=EN-US style='font-size:10.0pt;'>Availability of asteroid files:</span></b></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:35.4pt;text-indent:-35.4pt;'><span lang=EN-US style='font-size:10.0pt;'>-<2D><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> all short files
|
||
(over 200000) are available for free download at our ftp server <u><span
|
||
style='color:blue'>ftp.astro.ch/pub/swisseph</span></u>.<br>
|
||
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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>-<2D><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> for all named
|
||
asteroids also a long<6E> (6000 years) file
|
||
is available in the download area.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142948"><span lang=EN-US>How the
|
||
asteroids were computed</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <20>Horizons<6E> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>(However, the Swisseph asteroid ephemerides <i>do</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Sources of errors are:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>-<2D><><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US style='font-size:10.0pt;'>Only some of the
|
||
minor planets are known to better than an arc second for recent decades. (See
|
||
also informations below on Ceres, Chiron, and Pholus.) </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>-<2D><><EFBFBD><EFBFBD><EFBFBD> </span><span
|
||
lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The orbits of some asteroids are extremely sensitive to perturbations by
|
||
major planets. E.g. 1862 Apollo becomes chaotic before the year 1870 AD 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142949"><span lang=IT>Ceres, Pallas,
|
||
Juno, Vesta</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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<EFBFBD> (AA 1985 <20> 1997). But the tables in AA are based on
|
||
older computations, whereas we used recent orbital elements. </span><span
|
||
lang=FR style='font-size:10.0pt;'>(s. AA 1997, page L14)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 AD and a few arc minutes in 3000 BC. </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142950"><span lang=EN-US>Chiron</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Positions of Chiron can be well computed for the time between 700
|
||
AD<EFBFBD> and 4650 AD. As a result of close
|
||
encounters with Saturn in Sept. 720 AD and in 4606 AD we cannot trace its orbit
|
||
beyond this time range. Small uncertainties in today's orbital elements have <i>chaotic</i>
|
||
effects before the year 700.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Do not rely on earlier Chiron ephemerides supplying a Chiron for Cesar's,
|
||
Jesus', or Buddha's birth chart. They are completely meaningless.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142951"><span lang=EN-US>Pholus</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 AD through
|
||
now. Outside the 20th century it will probably have to be corrected by several
|
||
arc minutes during the coming years.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142952"><span lang=EN-US><EFBFBD>Ceres<EFBFBD> -
|
||
an application program for asteroid astrology</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Dieter Koch has written the application program <i>Ceres</i> 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=Textkrper-Einzug><span lang=FR style='font-size:10.0pt;'>- natal positions, synastries/transits, composite charts, progressions,
|
||
primary directions etc. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- geocentric, heliocentric, topocentric, house horoscopes</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- lists sorted by position in zodiac, by asteroid name, by declination
|
||
etc.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The program is on the asteroid short files CD-ROM and the standard Swiss
|
||
Ephemeris CD-ROM.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142953"><span lang=EN-US>2.4<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Comets</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris does not provide ephemerides of comets yet.</span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142954"><span lang=EN-US>2.5<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Fixed stars and Galactic Center</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>A database of fixed stars is included with Swiss Ephemeris. It contains
|
||
about 800 stars, which can be computed with the swe_fixstar() function. The
|
||
precision is about 0.001<EFBFBD>.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Our data are based on the star catalogue of Steve Moshier. It can be
|
||
easily extended if more stars are required.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The database was improved 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 (http://simbad.u-strasbg.fr/Simbad).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In Jan.
|
||
2011 (Version 1.77) a new fixed stars file sefstars.txt was created from the
|
||
SIMBAD database.</span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142955"><span lang=EN-US>2.6<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20>Hypothetical' bodies</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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
|
||
<EFBFBD>hypothetical<EFBFBD> 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142956"><span lang=DA>Uranian Planets
|
||
(Hamburg Planets: Cupido, Hades, Zeus, Kronos, Apollon, Admetos, Vulkanus,
|
||
Poseidon)</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>On the other hand, if one looks at their orbital elements, it is obvious
|
||
that these orbits are highly unrealistic.<2E>
|
||
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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 20</span><sup><span lang=EN-US
|
||
style='font-size:8.0pt;'>th</span></sup><span
|
||
lang=EN-US style='font-size:10.0pt;'> century, and
|
||
greater errors for earlier centuries.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142957"><span lang=EN-US>Transpluto
|
||
(Isis)</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>However, this theory has been superseded by other attempts during the
|
||
following decades, which proceeded from better observational data.<2E> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>In telescope observations, no hint could be discovered that this planet
|
||
actually existed. Rumors that claim the opposite are wrong.<2E> Moreover, all of the transneptunian bodies
|
||
that have been discovered since 1992 are very different from Isis-Transpluto.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Even if Sevin's computation were correct, it could only provide a rough
|
||
position. To rely on arc minutes would be illusory.<2E> Neptune was more than a degree away from its theoretical position
|
||
predicted by Leverrier and Adams.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Moreover, Transpluto's position is computed from a simple Kepler
|
||
ellipse, disregarding the perturbations by other planets' gravities.<2E> Moreover, Sevin gives no orbital
|
||
inclination. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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.<2E> Therefore, we fitted it to the Astron
|
||
ephemeris which apparently uses the equinox of 1945 (which, however, is rather
|
||
unusual!).</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142958"><span lang=EN-US>Harrington</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This is another attempt to predict Planet X's orbit and position from
|
||
perturbations in the orbits of<6F> 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142959"><span lang=EN-US>Nibiru</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>A highly speculative planet derived from the theory of Zecharia Sitchin,
|
||
who is an expert in ancient Mesopotamian history and a <20>paleoastronomer<65>.<2E> The elements have been supplied by Christian
|
||
Woeltge, Hannover.<2E> 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.<2E> In
|
||
spite of its retrograde motion, it <i>seems</i> 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142960"><span lang=EN-US>Vulcan</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142961"><span lang=EN-US>Selena/White
|
||
Moon</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142962"><span lang=EN-US>Dr.
|
||
Waldemath<EFBFBD>s Black Moon</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This is another hypothetical second moon of the earth, postulated by a
|
||
Dr. Waldemath in the <i>Monthly Wheather Review</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142963"><span lang=EN-US>The
|
||
Planets X of Leverrier, Adams, Lowell and Pickering</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>These are the hypothetical planets that have lead to the discovery of
|
||
Neptune and Pluto or at least have been brought into connection with them.<2E> 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 <i>swetest</i> as follows:</span></p>
|
||
|
||
<p class=WW-Heading6 style='margin-left:0cm;text-indent:0cm'><span lang=EN-US>$ swetest -p8 -dU -b1.1.1770 -n8 -s7305 -hel
|
||
-fPTLBR -head </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>(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 <u><span style='color:blue'>swetest.htm</span></u>. The
|
||
output will be:)</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
01.01.1770<EFBFBD> -18<31> 0'52.3811<EFBFBD><EFBFBD><EFBFBD> 0<>55' 0.0332<EFBFBD><EFBFBD> -6.610753489</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
01.01.1790<EFBFBD><EFBFBD> -8<>42' 9.1113<EFBFBD><EFBFBD><EFBFBD> 1<>42'55.7192<EFBFBD><EFBFBD> -4.257690148</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
02.01.1810<EFBFBD><EFBFBD> -3<>49'45.2014<EFBFBD><EFBFBD><EFBFBD> 1<>35'12.0858<EFBFBD><EFBFBD> -2.488363869</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
02.01.1830<EFBFBD><EFBFBD> -1<>38' 2.8076<EFBFBD><EFBFBD><EFBFBD> 0<>35'57.0580<EFBFBD><EFBFBD> -2.112570665</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
02.01.1850<EFBFBD><EFBFBD><EFBFBD> 1<>44'23.0943<EFBFBD><EFBFBD> -0<>43'38.5357<EFBFBD><EFBFBD> -3.340858070</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
02.01.1870<EFBFBD><EFBFBD><EFBFBD> 9<>17'34.4981<EFBFBD><EFBFBD> -1<>39'24.1004<EFBFBD><EFBFBD> -5.513270186</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
02.01.1890<EFBFBD><EFBFBD> 21<32>20'56.6250<EFBFBD><EFBFBD> -1<>38'43.1479<EFBFBD><EFBFBD> -7.720578177</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
|
||
03.01.1910<EFBFBD><EFBFBD> 36<33>27'56.1314<EFBFBD><EFBFBD> -0<>41'59.4866<EFBFBD><EFBFBD> -9.265417529</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD> (difference in<69><6E><EFBFBD> (difference in<69><6E>
|
||
(difference in</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD> longitude)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> latitude)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
solar distance)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>One can see that the error is in the range of 2 degrees between 1830 and
|
||
1850 and grows very fast beyond that period.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142964"><span lang=EN-US>2.7
|
||
Sidereal Ephemerides</span></a></h2>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142965"><span lang=EN-US>Sidereal
|
||
Calculations</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sidereal
|
||
astrology has a complicated history, and we (the developers of Swiss Ephemeris)
|
||
are actually tropicalists. Any suggestions how we could improve our sidereal
|
||
calculations are welcome!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For deeper
|
||
studies of the problem, read:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Raymond
|
||
Mercier, <20>Studies in the Medieval Conception of Precession<6F>, </span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>in 'Archives
|
||
Internationales d'Histoire des Sciences', (1976) 26:197-220 (part I), and
|
||
(1977) 27:33-71 (part II)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Thanks to
|
||
Juan Ant. Revilla, San Jose, Costa Rica, who gave us this precious
|
||
bibliographic hint.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142966"><span lang=EN-US>The
|
||
problem of defining the zodiac</span></a></h3>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US> </span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One of the
|
||
main differences between the western and the eastern tradition of astrology is
|
||
the definition of the zodiac. Western astrology uses the so-called <i>tropical
|
||
zodiac</i> in which 0 Aries is defined as the vernal point (the celestial point
|
||
where the sun stands at the beginning of spring). The <i>tropical zodiac </i>is a division of the ecliptic into 12 <i>zodiac
|
||
signs</i> that are all of equal size, i. e. 30<33>. Astrologers call these signs
|
||
after some constellations that are found along the ecliptic, but they are
|
||
actually independent of these constellations. Because the vernal point slowly
|
||
moves through the constellations and completes its cycle once in 26000 years,
|
||
tropical Aries moves through all constellations along the ecliptic, staying in
|
||
each one for roughly 2160 years. Currently, the vernal point, and the beginning
|
||
of tropical Aries, is located in sidereal Pisces. In a few hundred years, it will
|
||
enter Aquarius, which is the reason why the more impatient ones among us are
|
||
already preparing for the <20>Age of Aquarius<75>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
so-called <i>sidereal zodiac </i>also consists of 12 equal-sized zodiac signs,
|
||
but it is tied to the fixed stars. These sidereal signs, which are used in
|
||
Hindu astrology but also by some western Neo-Babylonian and Neo-Hellenistic
|
||
astrologers, only roughly coincide with the sidereal constellations, which are
|
||
of variable size.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>While the
|
||
definition of the tropical zodiac is clear and never questioned, sidereal
|
||
astrology has quite some problems in defining its zodiac. There are many
|
||
different definitions of the sidereal zodiac, and they differ by several
|
||
degrees. At a first glance, all of them look arbitrary, 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 all of them stem from
|
||
only one sidereal zodiac. On the other hand, this does not mean that it be
|
||
simple to give a precise definition of it.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sidereal
|
||
planetary positions are usually computed from an equation similar to:</span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US>sidereal_position
|
||
= tropical_position <20> ayanamsha,</span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>where <i>ayanamsha</i>
|
||
is the difference between the two zodiacs and changes with time. (Sanskrit <i>ayan<EFBFBD>msha</i>
|
||
means <20>part of a path<74>; the Hindi form of the word is <i>ayanamsa</i> with an <i>s</i>
|
||
instead of <i>sh</i>.) <20></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The value
|
||
of the <i>ayanamsha</i> of date is computed from the <i>ayanamsha</i> value at
|
||
a start date (e.g. 1 Jan 1900) and the speed of the vernal point, the so-called
|
||
<i>precession rate</i> in ecliptic longitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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='margin-left:35.4pt;text-indent:35.4pt'><i><span
|
||
lang=EN-US>sidereal Aries = tropical Aries <20>
|
||
ayanamsha</span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>and by a
|
||
date for which this equation is true.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The Swiss
|
||
Ephemeris allows for about twenty different <i>ayanamshas</i>, but the user can
|
||
also define his or her own <i>ayanamsha</i>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142967"><span lang=EN-US>The
|
||
Babylonian tradition and the Fagan/Bradley ayanamsha</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<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 from some
|
||
sidereally fixed reference point. The main problem in fixing the zero point is
|
||
the inaccuracy of ancient observations. Around 1900 <i>F.X. Kugler </i>found
|
||
that the Babylonian star positions fell into three groups: </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US><EFBFBD> </span><span lang=FR>9) <i>ayanamsha</i> = -3<>22<32>, t0 = -100</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>10) <i>ayanamsha</i>
|
||
= -4<>46<34>, t0 = -100<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Spica at 29 vi 26</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>11) <i>ayanamsha</i>
|
||
= -5<>37<33>, t0 = -100<30> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(9 <20> 11 =
|
||
Swiss Ephemeris <i>ayanamsha</i> numbers)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 1958, <i>Peter
|
||
Huber </i>reviewed the topic in the light of new material and found:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=IT>12) <i>ayanamsha</i>
|
||
= -4<>34<33> +/- 20<32>, t0 = <20>100<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
Spica at 29 vi 14</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> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 1977 <i>Raymond
|
||
Mercier </i>noted that the zero point might have been defined as the ecliptic
|
||
point that culminated simultaneously with the star <i>eta Piscium</i> (Al
|
||
Pherg). For this possibility, we compute:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=IT>13) <i>ayanamsha</i>
|
||
= -5<>04<30>46<34>, t0 = <20>129<32><39><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Spica at 29 vi 21</span></p>
|
||
|
||
<p class=MsoNormal><span lang=IT> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Around
|
||
1950, <i>Cyril Fagan</i>, 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 <20>rigorous statistical investigation<6F>
|
||
(astrological!) of solar and lunar ingress charts, <i>Donald Bradley </i>decided
|
||
that the sidereal longitude of the vernal point must be computed from Spica at
|
||
29 vi 06'05" <i>disregarding its proper motion</i>. Fagan and Bradley
|
||
defined their <20>synetic vernal point<6E> as:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>0) <i>ayanamsha</i>
|
||
= 24<32>02<30>31.36<EFBFBD><EFBFBD> for 1 Jan. 1950<35><30> with Spica at 29 vi 06'05" (without
|
||
aberration)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(For the
|
||
year <20>100, this <i>ayanamsha</i> places Spica at 29 vi 07<30>32<33>.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Fagan and
|
||
Bradley said that the difference between P. Huber<65>s zodiac and theirs was only
|
||
1<EFBFBD>. But actually (if Mercier<65>s value for the Huber <i>ayanamsha</i> is correct)
|
||
it was 7<>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>According
|
||
to a text by Fagan (found on the internet), Bradley <20>once opined in print prior
|
||
to "New Tool" that it made more sense to consider Aldebaran and
|
||
Antares, at 15 degrees of their respective signs, as prime fiducials than it
|
||
did to use Spica at 29 Virgo<67>. Such statements raise the question if the
|
||
sidereal zodiac ought to be tied up to one of those stars. Today, we know that
|
||
the fixed stars have a proper motion, wherefore such definitions are not a good
|
||
idea, if an absolute coordinate system independent on moving bodies is
|
||
intended. But the Babylonians considered them to be fixed. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>For this
|
||
possibility, Swiss Ephemeris gives an Aldebaran <i>ayanamsha</i>:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>14) <i>ayanamsha</i>
|
||
with Aldebaran at 15ta00<30>00<30> and Antares at 15sc00<30>17<31> around the year <20>100.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
difference between this <i>ayanamsha</i> and the Fagan/Bradley one is 1<>06<30>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142968"><span lang=EN-US>The
|
||
Hipparchan tradition</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US>Raymond
|
||
Mercier</span></i><span lang=EN-US> has shown
|
||
that all of the ancient Greek and the medieval Arabic astronomical works
|
||
located the zero point of the ecliptic somewhere <i>between 10 and 22 arc
|
||
minutes east of the star zeta Piscium</i>. This definition goes back to the
|
||
great Greek astronomer <i>Hipparchus</i>. How did he choose that point?
|
||
Hipparchus said that the beginning of Aries rises when Spica sets. This
|
||
statement was meant for a geographical latitude of 36<33>, the latitude of the
|
||
island of Rhodos, which Hipparchus<75> descriptions of rises and settings are
|
||
referred to. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However,
|
||
there seems to be more behind it. Mercier points out that according to
|
||
Hipparchus<EFBFBD> star catalogue the stars <i>alpha Arietis, beta Arietis, zeta
|
||
Piscium, </i>and <i>Spica </i>are located in precise alignment on a great
|
||
circle which goes through that zero point near <i>zeta Piscium</i>. Moreover,
|
||
this great circle was identical with the horizon once a day at Hipparchus<75>
|
||
geographical latitude of 36<33>. In other words, the zero point rose at the same
|
||
time when the three mentioned stars in Aries and Pisces rose and at the same
|
||
time when Spica set. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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 <i>assumed</i> to be
|
||
so.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier
|
||
gives the following <i>ayanamsha</i>s for <i>Hipparchus</i> and <i>Ptolemy</i>
|
||
(who used the same star catalogue as Hipparchus):</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>16) <i>ayanamsha</i>
|
||
= -9<>20<32> <20><><EFBFBD> 27 June <20>128 (jd
|
||
1674484)<29><><EFBFBD> zePsc 29pi33<33>49<34><39><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Hipparchos</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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 <i>ayanamsha</i>, as given
|
||
by Mercier, has actually the zero point 26<32> east of zePsc. This comes from the
|
||
fact that Mercier refers to the <i>Hipparchan</i> position of zeta Piscium, which
|
||
was at least rounded to 10<31> <20> if otherwise correct.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If we used
|
||
the explicit statement of Hipparchus that <i>Aries rose when Spica set </i>at a
|
||
geographical latitude of 36 degrees, the precise <i>ayanamsha</i> 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> </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 <i>S<EFBFBD>rya Sidd<64>nta</i>, the star <i>zeta Piscium</i> (in
|
||
Sanskrit <i>Revat<EFBFBD></i>) 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 <i>Citra</i>)
|
||
is given the longitude 30<33> Virgo. This is a contradiction, either Spica or
|
||
Revat<EFBFBD> must be considered wrong.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover,
|
||
if the precession model of the <i>S<EFBFBD>rya Sidd<64>nta </i>is used to compute an <i>ayanamsha</i>
|
||
for the date of Hipparchus, it will turn out to be <20>9<EFBFBD>14<31>01<30>, which is very
|
||
close to the Hipparchan value. The same calculation can be done with the <i><EFBFBD>rya
|
||
Sidd<EFBFBD>nta</i>, and the <i>ayanamsha</i> for Hipparchos<6F> date will be <20>9<EFBFBD>14<31>55<35>.
|
||
For the <i>Sidd<EFBFBD>nta Shiromani</i> the zero point turns out to be Revat<61> itself.
|
||
By the way, this is also the zero point chosen by <i>Copernicus</i>! So, there
|
||
is an astonishing agreement between Indian and Western traditions!</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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 <i>Ush<EFBFBD>shash<EFBFBD>
|
||
ayanamsha</i> which is still in use. It differs from the Hipparchan one by only
|
||
11 arc minutes.</span></p>
|
||
|
||
<p class=MsoEndnoteText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>4) <i>ayanamsha</i>
|
||
= 18<31>39<33>39.46<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1 Jan. 1900<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Ush<73>shash<68><EEA0A0><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:70.8pt;text-indent:35.4pt'><span
|
||
lang=EN-US>zePsc (Revat<61>) 29pi50<35> (today),
|
||
29pi45<EFBFBD> (Hipparchus<75> epoch)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
Greek-Arabic-Hindu <i>ayanamsha</i> was zero around 560 AD. The tropical and
|
||
the sidereal zero points were at exactly the same place. Did astronomers or
|
||
astrologers react on that event? They did! Under the Sassanian ruler Khusrau
|
||
An<EFBFBD>shirw<EFBFBD>n, in the year 556, the astronomers of Persia met to correct their
|
||
astronomical tables, the so-called <i>Z<EFBFBD>j al-Sh<53>h</i>. 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> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One of the
|
||
most important cycles in Persian astronomy/astrology was the one of Jupiter,
|
||
which started and ended with the conjunctions of Jupiter with the sun. This
|
||
cycle happened to end <i>in the year 564</i>, and the conjunction of Jupiter
|
||
with the Sun took place only one day after the spring equinox. And <i>the
|
||
spring equinox took place precisely 10 arcmin east of zePsc</i>. 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><EFBFBD></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Mercier
|
||
also shows that in the precession model used in that epoch 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 today<61>s knowledge, but they
|
||
show how important that date was considered to be. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>16) <i>ayanamsha</i>
|
||
= 0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 18 Mar 564, 7:53:23 UT (jd /ET 1927135.8747793)<29><><EFBFBD> Sassanian</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:283.2pt;text-indent:35.4pt'><span
|
||
lang=FR><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span><span lang=EN-US>zePsc<EFBFBD> 29pi49'59"</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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<EFBFBD>rizmian tables, the S<>rya Siddh<64>nta, and the Ush<73>shash<73> <i>ayanamsha</i>.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>(Besides
|
||
the synchronicity of the Sun-Jupiter conjunction and the coincidence of the two
|
||
zodiacs, it is funny to note that the cosmos helped the inaccuracy of ancient
|
||
astronomy by <20>rounding<6E> the position of the star zePsc to precisely 10 arc
|
||
minutes east of the zero point! All Ptolemean star positions were rounded to 10
|
||
arc minutes.)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><span
|
||
lang=EN-US>Suryasiddhanta and Aryabhata</span></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US>The explanations 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 style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><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 18<sup>th</sup> February 3102 BC,
|
||
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 era <20>K0a<30>. </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US>Now, Aryabhata mentioned that he was
|
||
23 years old when exactly 3600 years had passed 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 21<sup>st</sup> March, 499 AD, 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 derive an ayanamsha from this
|
||
information. There are two possible solutions, though:</span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US>1. 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=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US>2. As 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 style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><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 style='text-autospace:ideograph-numeric ideograph-other'><span
|
||
lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='text-autospace:ideograph-numeric ideograph-other'><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).<2E><><EFBFBD> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142969"><span lang=EN-US>The
|
||
Spica/Citra tradition and the Lahiri ayanamsha</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There is
|
||
another ayanamsha tradition that assumes the star Spica (in Sanskrit Citra) at
|
||
0<EFBFBD> Libra. This ayanamsha definition is the most common one in modern Hindu astrology.
|
||
It was first proposed by the astronomy historian S. B. Dixit (also written
|
||
Dikshit), who in 1896 published his important work <i>History of Indian
|
||
Astronomy</i> (=<i> Bharatiya Jyotih
|
||
Shastra</i>; bibliographical details further below). Dixit came to the
|
||
conclusion that, given the prominence that Vedic religion gave to the cardinal
|
||
points of the tropical year, the Indian calendar, which is based on the zodiac,
|
||
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 <i>Grahalaghava</i>, a work by the 16th century
|
||
astronomer <i>Ganeśa Daivaj<61>a</i> that
|
||
was still used in the 20<sup>th</sup> century by Indian calendar makers. (op.
|
||
cit., Part II, p. 323ff.). This view was taken over by the <i>Indian Calendar Reform Committee</i> on the occasion of the Indian
|
||
calendar reform</span><span lang=EN-US style='font-family:SimSun;'> in 1956</span><span
|
||
lang=EN-US>, when the ayanamsha based on the
|
||
star Spica/Citra was declared the Indian standard. This standard is mandatory
|
||
not only for astrology but also for astronomical ephemerides and almanacs and
|
||
calendars published in India. 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, who was a member of the Reform
|
||
Committee. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>However, as
|
||
has been said, it was Dixit who first propagated this solution to the ayanamsha
|
||
problem. Besides, the Suryasiddhanta, the most important work of ancient Hindu
|
||
astronomy, which was written in the first centuries AD, but reworked several
|
||
times, already assumes Spica/Citra at 180<38> (although this statement has caused
|
||
a lot of controversy because it is in contradiction with the positions of other
|
||
stars, and in particular with zeta Piscium/Revati at 359<35>50<35>). And last but not
|
||
least, the same ayanamsha definition seems to have been used in Babylon and
|
||
Greece, as well. While the information given above in the chapters about the
|
||
Babylonian and the Hipparchan traditions are based on analyses of old star
|
||
catalogues and planetary theories, a study by Nick Kollerstrom of 22 ancient
|
||
Greek and 5 Babylonian birth charts has lead to a different conclusion: they
|
||
fit better with Spica at 0 Libra (= Lahiri), than with Aldebaran at 15 Taurus
|
||
and Spica at 29 Virgo (= Fagan/Bradley). </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
standard definition of the Indian ayanamsha (<28>Lahiri<72> ayanamsha) was originally
|
||
introduced in 1955 by the Indian <i>Calendar
|
||
Reform Committee</i> (23<32>15' 00" on the 21 March 1956, 0:00 Ephemeris
|
||
Time). The definition was corrected in <i>Indian
|
||
Astronomical Ephemeris</i> 1989, page 556, footnote: </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>"According
|
||
to new determination of the location of equinox this initial value has been
|
||
revised to and used in computing the mean ayanamsha with effect from
|
||
1985'."</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The mention
|
||
of <20>mean ayanamsha<68> is misleading though. The value 23<32>15' 00".658 is true
|
||
ayanamsha, i. e. it includes nutation and is relative to the true equinox of
|
||
date.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>1) true
|
||
ayanamsha = 23<32>15' 00".658<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 21 March 1956, 0:00 TDT<44><54><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Lahiri, Spica roughly at 0 Libra</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-GB>The Lahiri
|
||
standard position of Spica is 179<37>59<35>04 in the year 2000, and 179<37>59<35>08 in
|
||
1900. In the year 285, when the star was conjunct the autumnal equinox, its
|
||
position was 180<38>00<30>16. It was in the year 667 AD that its position was
|
||
precisely 180<38>. The motion of the star is a result partly of its proper motion
|
||
and partly of planetary precession, which has the ecliptic slightly change its
|
||
orientation. But what method exactly was used to define this ayanamsha?
|
||
According to the Indian pundit AK Kaul, an expert in Hindu calendar and
|
||
astrology, Lahiri wanted to place the star at 180<38>, but at the same time arrive
|
||
at an ayanamsha that was in agreement with the Grahalaghava, an important work
|
||
for traditional Hindu calendar calculation that was written in the 16<sup>th</sup>
|
||
century. (e-mail from Mr. Kaul to Dieter Koch on 1 March 2013)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-GB> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In 1967, 12
|
||
years after the standard definition of the Lahiri ayanamsha had been published
|
||
by the Calendar Reform Committee, Lahiri published another ayanamsha in his
|
||
Bengali book <i>Panchanga Darpan</i>. There,
|
||
the value of <20>mean ayanamsha<68> is given as 22<32>26<32>45<34>.50 in 1900, whereas the
|
||
official value is 22<32>27<32>37<33>.76. The idea behind this modification was obviously
|
||
that he wanted to have the star exactly at 180<38> for recent years, whereas with
|
||
the standard definition the star is <20>wrong<6E> by almost an arc minute. It
|
||
therefore seems that Lahiri did not follow the Indian standard himself but was
|
||
of the opinion that Spica had to be at exactly 180<38> (true chitrapaksha
|
||
ayanamsha). At the moment, the Swiss only supports the official standard.
|
||
However, it is rather trivial to calculate the positions of a planet and the
|
||
star and then subtract the star from the planet.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-GB> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Swiss
|
||
Ephemeris versions below 1.78.01, had a slightly different definition of the
|
||
Lahiri ayanamsha that had been taken from Robert Hand's astrological software
|
||
Nova. It made a difference of only 0.01 arc sec.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Many thanks
|
||
to Vinay Jha, Narasimha Rao, and Avtar Krishen Kaul for helping us to better
|
||
understand the complicated matter. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If the
|
||
reader finds errors in this documentation or is able to contribute important
|
||
information, his or her feedback will be greatly appreciated. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Sources:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Burgess,
|
||
E., <i>The Surya Siddanta. A Text-book of Hindu Astronomy</i>, Delhi, 2000
|
||
(MLBD).</span></p>
|
||
|
||
<p class=MsoBodyText style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-GB>Dikshit, S(ankara) B(alkrishna), <i>Bharatiya Jyotish Sastra (History of Indian Astronomy)</i> (Tr.
|
||
from Marathi), Govt. of India, 1969, part I & II. </span></p>
|
||
|
||
<p class=MsoBodyText style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US>Kollerstrom, Nick, <20></span><span
|
||
lang=EN-GB>The Star Zodiac of Antiquity<74>, in: <i>Culture
|
||
& Cosmos</i></span><span lang=EN-US>, Vol.
|
||
1, No.2, 1997).</span></p>
|
||
|
||
<p class=MsoBodyText style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=IT>Lahiri, N. C., <i>Panchanga Darpan </i>(in Bengali), Calcutta, 1967 (Astro Research
|
||
Bureau).</span></p>
|
||
|
||
<p class=MsoBodyText style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-GB>Lahiri,
|
||
N. C., <i>Tables of the Sun</i>, Calcutta, 1952 (Astro Research Bureau).</span></p>
|
||
|
||
<p class=MsoBodyText style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-GB>Saha, M.
|
||
N., and Lahiri, N. C., <i>Report of the Calendar Reform Committee</i></span><span
|
||
lang=EN-GB>, C.S.I.R., New Delhi, 1955.</span></p>
|
||
|
||
<p class=MsoBodyText><i><span lang=EN-US>The
|
||
Indian astronomical ephemeris for the year</span></i><span lang=EN-US> <i>1989</i>,
|
||
Delhi (Positional Astronomy Centre, India Meteorological Department)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142970"><span lang=EN-US>The
|
||
sidereal zodiac and the Galactic Center</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As said
|
||
before, there is a very precise definition for the tropical ecliptic. It starts
|
||
at one of the two intersection points of the ecliptic and the celestial
|
||
equator. Similarly, we have a very precise definition for the house circle
|
||
which is said to be an analogy of the zodiac. It starts at one of the two
|
||
intersection points of the ecliptic and the local horizon. Unfortunately there
|
||
is no such definition for the sidereal zodiac. Or can a fixed star like Spica
|
||
be important enough to play the role of an anchor star? </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One could
|
||
try to make the sidereal zero point agree with the Galactic Center. The Swiss
|
||
astrologer Bruno Huber has pointed out that the Galactic Center enters a new
|
||
tropical sign always around the same time when the vernal point enters the next
|
||
sidereal sign. Around the time, when the vernal point will go into Aquarius,
|
||
the Galactic Center will change from Sagittarius to 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 Jupiter,
|
||
will be Saturn in a few hundred years). </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A
|
||
correction of the Fagan <i>ayanamsha</i> by about 2 degrees or a correction of
|
||
the Lahiri <i>ayanamsha</i> by 3 degrees would place the Galactic Center at 0
|
||
Sagittarius. Astrologically, this would obviously make some sense. Therefore,
|
||
we add an <i>ayanamsha</i> fixed at the Galactic Center:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>17)
|
||
Galactic Center at 0 Sagittarius</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The other
|
||
possibility <20> in analogy with the tropical ecliptic and the house circle <20>
|
||
would be to start the sidereal ecliptic at the intersection point of the
|
||
ecliptic and the galactic plane. At present, this point is located near 0
|
||
Capricorn. However, defining this point 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> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142971"><span lang=EN-US>Other
|
||
ayanamshas</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>There are a
|
||
few more <i>ayanamshas</i>, whose provenance is not known to us. They were
|
||
given to us by Graham Dawson (<28>Solar Fire<72>), who took them over from Robert
|
||
Hand<EFBFBD>s Program <20>Nova<76>:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>2) De Luce</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>3) Raman</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR>5) Krishnamurti</span></p>
|
||
|
||
<p class=MsoNormal><span lang=FR> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=FR style='font-family:"Times New Roman";'>David Cochrane adds</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=FR style='font-family:"Times New Roman";'> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=FR style='font-family:"Times New Roman";'>7) Yukteshvar</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=FR style='font-family:"Times New Roman";'>8) JN Bhasin</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=FR style='font-family:"Times New Roman";'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Graham
|
||
Dawson adds the following one:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>6) Djwhal
|
||
Khul</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US style='font-family:"Times New Roman";'> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US style='font-family:"Times New Roman";'>He comments it as follows: <20>The "Djwhal
|
||
Khul" ayanamsha originates from information in an article in the Journal
|
||
of Esoteric Psychology, Volume 12, No 2, pp91-95, Fall 1998-1999 publ. Seven
|
||
Ray Institute). It is based on an inference that the Age of Aquarius starts in
|
||
the year 2117. I decided to use the 1st of July simply to minimise the possible
|
||
error given that an exact date is not given.<2E></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142972"><span lang=EN-US>Conclusions</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>We have
|
||
found that there are basically three definitions, not counting the manifold
|
||
variations:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>1.<2E><><EFBFBD><EFBFBD> the Babylonian zodiac with Spica at 29
|
||
Virgo or Aldebaran at 15 Taurus:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt'><span lang=EN-US>a) P. Huber, b) Fagan/Bradley c) refined with <b>Aldebaran</b>
|
||
at 15 Tau</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>2.<2E><><EFBFBD><EFBFBD> the Greek-Arabic-Hindu zodiac with the zero
|
||
point between 10 and 20<32> east of <i>zeta Piscium</i>:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt'><span lang=EN-US>a) Hipparchus, b) Ush<73>shash<73>, c) <b>Sassanian</b></span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>3.<2E><><EFBFBD><EFBFBD> the Greek-Hindu astrological zodiac with
|
||
Spica at 0 Libra</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt'><span lang=EN-US>a) <b>Lahiri</b></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The
|
||
differences are: </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>between 1)
|
||
and 3) is about 1 degree</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>between 1)
|
||
and 2) is about 5 degrees</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>between 2)
|
||
and 3) is about 4 degrees</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>It is
|
||
obvious that all of them stem from the same origin, but it is difficult to say
|
||
which one should be preferred for sidereal astrology.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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. Aldebaran at 15 Tau might be one. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>3) has the
|
||
most striking reference point, the bright star Spica at 0 Libra. But this
|
||
definition is so clear and simple that, had it really been intended by the
|
||
inventors of the sidereal ecliptic, it would certainly not have been forgotten
|
||
or given up by the Greek and Arabic tradition.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>2) is the
|
||
only definition independent on a star <20> especially, if we take the Sassanian
|
||
version. This is an advantage, because all stars have a proper motion and
|
||
cannot really define a fixed coordinate system. Also, it is the only <i>ayanamsha</i>
|
||
for which there is historical evidence that it was observed and recalibrated at
|
||
the time when it was 0. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>On the
|
||
other hand, the point 10<31> East of zePsc has no astronomical significance at
|
||
all, and the great difference between this zero point and the Babylonian one
|
||
raises the question: Did Hipparchus<75> definition result from a misunderstanding
|
||
of the Babylonian definition, or was it an attempt to improve the Babylonian
|
||
zodiac?</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142973"><span lang=EN-US>In search
|
||
of correct algorithms</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>A second
|
||
problem in sidereal astrology <20> after the definition of the zero point <20> is the
|
||
precession algorithm to be applied. We can think of five possibilities:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>1)<29><><EFBFBD><EFBFBD> <i>the traditional algorithm (implemented in
|
||
Swiss Ephemeris as default mode)</i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>In all
|
||
software known to us, sidereal planetary positions are computed from an
|
||
equation mentioned before:</span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US>sidereal_position
|
||
= tropical_position <20> ayanamsha,</span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The <i>ayanamhsa</i>
|
||
is computed from the <i>ayanamsha(t0) </i>at a starting date (e.g. 1 Jan 1900)
|
||
and the speed of the vernal point, the so-called <i>precession rate</i>. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This
|
||
algorithm is unfortunately too simple. At best, it can be considered as an
|
||
approximation. The precession of the equinoxes is not only a matter of
|
||
ecliptical longitude, but is a more complex phenomenon. It has two components:</span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US> </span></i></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>a) The <i>soli-lunar</i>
|
||
<i>precession</i>: The combined gravitational pull of the Sun and the Moon on
|
||
the equatorial bulge of the earth causes the earth to spin like a top. As a
|
||
result of this movement, the vernal point moves around the ecliptic with a
|
||
speed of about 50<35>. This cycle lasts about 26000 years.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>b) The <i>planetary
|
||
precession</i>: The earth orbit itself is not fixed. The gravitational
|
||
influence from the planets causes it to wobble. As a result, the obliquity of
|
||
the ecliptic currently decreases by 47<34> per century, and this movement has an
|
||
influence on the position of the vernal point, as well. (This has nothing to do
|
||
with the precessional motion of the earth rotation axis; the equator holds an
|
||
almost stable angle against the ecliptic of a fixed date, e.g. 1900, with a
|
||
change of only a couple of 0.06<EFBFBD> cty-2). </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Because the
|
||
ecliptic is not fixed, it cannot be correct just to subtract an <i>ayanamsha</i>
|
||
from the tropical position in order to get a sidereal position. Let us take,
|
||
e.g., the Fagan/Bradley <i>ayanamsha</i>, which is defined by:</span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=FR>ayanamsha =
|
||
24<EFBFBD>02<EFBFBD>31.36<EFBFBD> + d(t</span></i><span lang=FR>)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>24<EFBFBD>02<EFBFBD>...
|
||
is the value of the <i>ayanamsha</i> on 1 Jan 1950. It is obviously measured on
|
||
<i>the ecliptic of 1950</i>. </span></p>
|
||
|
||
<p class=MsoNormal><i><span lang=EN-US>d(t) </span></i><span
|
||
lang=EN-US>is the distance of the vernal point
|
||
at epoch <i>t</i> from the position of the vernal point on 1 Jan 1950. This
|
||
value is also measured on the ecliptic of 1950. But the whole <i>ayanamsha</i>
|
||
is subtracted from a planetary position which is referred to the <i>ecliptic of
|
||
the epoch t</i>. This does not make sense. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>As an
|
||
effect of this procedure, objects that do not move sidereally, e.g. the
|
||
Galactic Center, seem to move. If we compute its precise tropical position for
|
||
several dates and then subtract the Fagan/Bradley <i>ayanamsha</i> for the same
|
||
dates in order to get its sidereal position, these positions will all be
|
||
slightly different:</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><i><span lang=EN-US>Date</span></i><span
|
||
lang=EN-US><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <i>Longitude</i><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
<i>Latitude</i></span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>01.01.-5000<30> 2 sag 07'57.7237<EFBFBD><EFBFBD> -4<>41'34.7123 (without aberration)</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>01.01.-4000<30> 2 sag 07'32.9817<EFBFBD><EFBFBD> -4<>49' 4.8880</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>01.01.-3000<30> 2 sag 07'14.2044<EFBFBD><EFBFBD> -4<>56'47.7013</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>01.01.-2000<30> 2 sag 07' 0.4590<EFBFBD><EFBFBD> -5<> 4'39.5863</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>01.01.-1000<30> 2 sag 06'50.7229<EFBFBD><EFBFBD> -5<>12'36.9917</span></p>
|
||
|
||
<p class=MsoPlainText>01.01.0<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2 sag 06'44.2492<EFBFBD><EFBFBD> -5<>20'36.4081</p>
|
||
|
||
<p class=MsoPlainText>01.01.1000<EFBFBD><EFBFBD> 2 sag 06'40.7813<EFBFBD><EFBFBD> -5<>28'34.3906</p>
|
||
|
||
<p class=MsoPlainText>01.01.2000<EFBFBD><EFBFBD> 2 sag 06'40.5661<EFBFBD><EFBFBD> -5<>36'27.5619</p>
|
||
|
||
<p class=MsoPlainText>01.01.3000<EFBFBD><EFBFBD> 2 sag 06'44.1743<EFBFBD><EFBFBD> -5<>44'12.6886</p>
|
||
|
||
<p class=MsoPlainText>01.01.4000<EFBFBD><EFBFBD> 2 sag 06'52.1927<EFBFBD><EFBFBD> -5<>51'46.6231</p>
|
||
|
||
<p class=MsoPlainText>01.01.5000<EFBFBD><EFBFBD> 2 sag 07' 4.8942<EFBFBD><EFBFBD> -5<>59' 6.3665</p>
|
||
|
||
<p class=MsoNormal> </p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>The effect
|
||
can be much greater for bodies with greater ecliptical latitude.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Exactly the
|
||
same kind of thing happens to sidereal planetary positions, if one calculates
|
||
them in the traditional way. It is only because planets move that we are not
|
||
aware of it. </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoBodyTextIndent><span lang=EN-US style='
|
||
font-style:normal'>The traditional method of computing sidereal positions is
|
||
geometrically not sound and can never achieve the same degree of accuracy as
|
||
tropical astrology is used to.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>2)<29><><EFBFBD><EFBFBD> <i>fixed-star-bound ecliptic (not
|
||
implemented in Swiss Ephemeris)</i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>One could
|
||
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 has to be noted, that this system is not
|
||
really fixed either, because it is still based on the moving ecliptic, and
|
||
moreover the fixed stars have a small proper motion, as well.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>3)<29><><EFBFBD><EFBFBD> <i>projection onto the ecliptic of t0
|
||
(implemented in Swiss Ephemeris as an option)</i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Another
|
||
possibility would be to project the planets onto the reference ecliptic of the <i>ayanamsha</i>
|
||
<EFBFBD> for Fagan/Bradley, e.g., this would be the ecliptic of 1950 <20> by a correct <i>coordinate
|
||
transformation</i> and then subtract 24.042<EFBFBD>, the initial value of the <i>ayanamsha</i>.
|
||
</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>If we
|
||
follow this method, the position of the galactic center will always be the same
|
||
(2 sag 06'40.4915<EFBFBD><EFBFBD> -5<>36' 4.0652<EFBFBD><EFBFBD><EFBFBD><EFBFBD> (without aberration))</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This method
|
||
is geometrically sounder than the traditional one, but still it has a problem.
|
||
For, if we want everything referred to the ecliptic of a fixed date t0, we will
|
||
have to choose that date very carefully. Its ecliptic ought to be of special
|
||
importance. The ecliptic of 1950 or the one of 1900 are obviously meaningless
|
||
and not suitable as a reference plane. And how about that 18 March 564, on
|
||
which the tropical and the sidereal zero point coincided? Although this may be
|
||
considered as a kind of cosmic anniversary (the Sassanians did so), the
|
||
ecliptic plane of that time does not have an <20>eternal<61> value. It is different
|
||
from the ecliptic plane of the previous anniversary around the year 26000 BC,
|
||
and it is also different from the ecliptic plane of the next cosmic anniversary
|
||
around the year 26000 AD.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This
|
||
algorithm is supported by the Swiss Ephemeris, too. However, it <i>must not be
|
||
used with the Fagan/Bradley definition </i>or with other definitions that were
|
||
calibrated with the traditional method of <i>ayanamsha</i> subtraction. It can
|
||
be used for computations of the following kind:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>a)<29><><EFBFBD><EFBFBD> Astronomers may want to calculate <i>positions
|
||
referred to a standard equinox </i>like J2000, B1950, or B1900, or to any other
|
||
equinox. </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>b)<29><><EFBFBD> Astrologers may be interested in the
|
||
calculation of <i>precession-corrected transits</i>. See explanations in the
|
||
next chapter.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>c)<29><><EFBFBD><EFBFBD> The algorithm can be applied to the <i>Sassanian</i>
|
||
<i>ayanamsha</i> or to any user-defined sidereal mode, if the ecliptic of its
|
||
reference date is considered to be astrologically significant.</span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>d)<29><><EFBFBD> The algorithm makes the problems of the
|
||
traditional method visible. It shows the dimensions of the inherent inaccuracy
|
||
of the traditional method.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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> </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> </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, <i>not</i> with the ecliptic
|
||
of date. Here, there are greater deviations from the traditional procedure. If <i>t</i>
|
||
is 2000 years from <i>t0</i> the difference between the ascendant positions
|
||
might well be 1/2 degree.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>4)<29><><EFBFBD><EFBFBD> <i>The long-term mean Earth-Sun plane (not
|
||
implemented in Swiss Ephemeris)</i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>To avoid
|
||
the problem of choice of a reference ecliptic, we might watch out for a kind of
|
||
<EFBFBD>average ecliptic<69>. As a matter of fact, there are some possibilities in this
|
||
direction. The mechanism of the planetary precession mentioned above works in a
|
||
similar way as the mechanism of the luni-solar precession. The movement 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
|
||
<EFBFBD>long-term mean Earth-Sun plane<6E> is not really stable, either, and therefore
|
||
not suitable as a fixed reference frame.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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 at the moment about 1<>33<33>, but it changes
|
||
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> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>5)<29><><EFBFBD><EFBFBD> <i>The solar system rotation plane
|
||
(implemented in Swiss Ephemeris as an option)</i></span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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 probably the only convincing candidate
|
||
for a fixed zodiac plane.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>This
|
||
algorithm must not be applied to any of the predefined sidereal modes, except
|
||
the Sassanian one. You can use this algorithm, if you want to research on a
|
||
better-founded sidereal astrology, experiment with your own sidereal mode, and
|
||
calibrate it as you like.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142974"><span lang=EN-US>More
|
||
benefits from our new sidereal algorithms: standard equinoxes and
|
||
precession-corrected transits</span></a></h3>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<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=MsoNormal><span lang=EN-US>18) J2000</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>19) J1900</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>20) B1950</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US>Moreover,
|
||
it is possible to compute <i>precession-corrected transits or synastries</i>
|
||
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 <i>precession-corrected</i>
|
||
transits. This is more precise than just correcting for the precession in
|
||
longitude (see details in the programmer's documentation <i>swephprg.doc</i>,
|
||
ch. 8.1).</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142975"><span lang=EN-US>3. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Apparent versus true planetary positions</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss ephemeris provides the calculation of <i>apparent</i> or <i>true</i>
|
||
planetary positions. Traditional astrology works with apparent positions.
|
||
<EFBFBD>Apparent<EFBFBD> means that the position where we <i>see </i>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<EFBFBD>, light-time and aberration) Astronomers therefore make a
|
||
difference between <i>apparent </i>and<i> true </i>positions. However, this
|
||
effect is below 1 arc minute. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Most astrological ephemerides provide <i>apparent</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Moreover, the Swiss Ephemeris supports so-called <i>astrometric</i>
|
||
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>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142976"><span lang=EN-US>4. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Geocentric versus topocentric and
|
||
heliocentric positions</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <i>more than a
|
||
degree </i>with the moon! Such a position referred to the birth place is called
|
||
the <i>topocentric</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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<EFBFBD>. The
|
||
altitudes are referred to the approximate earth ellipsoid. Local irregularities
|
||
of the geoid have been neglected. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Our topocentric lunar positions differ from the NASA positions (s. the <i>Horizons
|
||
Online Ephemeris System </i>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 <i>Horizons</i> <i>System</i>,
|
||
it is written that: "The Earth is assumed to be a rigid body. ... These
|
||
Earth-model approximations result in topocentric station location errors, with
|
||
respect to the reference ellipsoid, of less than 500 meters."</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss ephemeris also allows the computation of apparent or true <i>topocentric
|
||
</i>positions.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the lunar nodes and apogees, Swiss Ephemeris does not make a
|
||
difference between topocentric and geocentric positions. There are manyfold
|
||
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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Moreover, the Swiss Ephemeris supports the calculation of <i>heliocentric</i>
|
||
and <i>barycentric</i> planetary positions. Heliocentric positions are
|
||
positions as seen from the center of the sun rather than from the center of the
|
||
earth. Barycentric 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.</span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142977"><span lang=EN-US>5.
|
||
Heliacal Events, Eclipses, Occultations, and Other Planetary Phenomena</span></a></h1>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142978"><span
|
||
lang=EN-US>5.1. Heliacal Events of the Moon,
|
||
Planets and Stars</span></a></h2>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142979"><span
|
||
lang=EN-US>5.1.1. Introduction</span></a></h3>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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.<2E> 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 style='margin-bottom:6.0pt'><span lang=EN-US>The heliacal events that can be determined are:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:42.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Inferior
|
||
planets</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Heliacal
|
||
rising (morning first)</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Heliacal
|
||
setting (evening last)</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Evening
|
||
first</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
6.0pt;margin-left:77.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:
|
||
Symbol;'><EFBFBD></span><span
|
||
lang=EN-US>Morning last</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:42.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Superior
|
||
planets and stars</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Heliacal
|
||
rising</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
6.0pt;margin-left:77.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:
|
||
Symbol;'><EFBFBD></span><span
|
||
lang=EN-US>Heliacal setting</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
6.0pt;margin-left:60.1pt'><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:42.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Moon</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Evening
|
||
first</span></p>
|
||
|
||
<p class=MsoNormal style='margin-top:0cm;margin-right:5.95pt;margin-bottom:
|
||
0cm;margin-left:78.0pt;margin-bottom:.0001pt;text-indent:-17.85pt;'><span lang=EN-US
|
||
style='font-family:Symbol;'><EFBFBD></span><span lang=EN-US>Morning
|
||
last</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </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> </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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=MsoNormal style='margin-right:5.95pt;
|
||
margin-left:41.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Position
|
||
celestial objects <br>
|
||
like the position and magnitude of the Sun, Moon and the studied celestial object,
|
||
</span></p>
|
||
|
||
<p class=MsoNormal style='margin-right:5.95pt;
|
||
margin-left:41.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Location
|
||
and optical properties observer <br>
|
||
like his/her location (longitude, latitude, height), age, acuity and possible
|
||
magnification of optical instruments (like binoculars)</span></p>
|
||
|
||
<p class=MsoNormal style='margin-right:5.95pt;
|
||
margin-left:41.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Meteorological
|
||
circumstances <br>
|
||
mainly expressed in the astronomical extinction coefficient, which is
|
||
determined by temperature, air pressure, humidity, visibility range (air
|
||
quality).</span></p>
|
||
|
||
<p class=MsoNormal style='margin-right:5.95pt;
|
||
margin-left:41.95pt;text-indent:-17.85pt;'><span lang=EN-US style='font-family:Symbol;'><EFBFBD><span style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US>Contrast
|
||
between studied object and sky background <br>
|
||
The observer<65>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 style='margin-bottom:6.0pt'><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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142980"><span
|
||
lang=EN-US>5.1.2. Aspect determining visibility</span></a></h3>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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='margin-left:0cm;text-indent:0cm'><a name="_Toc335142981"><span
|
||
lang=EN-US>5.1.2.1. Position of celestial
|
||
objects</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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='margin-left:0cm;text-indent:0cm'><a name="_Toc335142982"><span
|
||
lang=EN-US>5.1.2.2. Geographic location</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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='margin-left:0cm;text-indent:0cm'><a name="_Toc335142983"><span
|
||
lang=EN-US>5.1.2.3. Optical properties of
|
||
observer</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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 used optical instruments (like
|
||
binocular or telescope).</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142984"><span
|
||
lang=EN-US>5.1.2.4. Meteorological
|
||
circumstances</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>The meteorological circumstances are very
|
||
important for determining the visibility of the celestial object. These
|
||
circumstances influence the transparency of the airmass (due to
|
||
Rayleigh&aerosol scattering and ozone&water absorption) between the
|
||
celestial object and the observer<65>s eye. This result in the astronomical
|
||
extinction coefficient (AEC: k<sub>tot</sub>). 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 style='margin-bottom:6.0pt'><span lang=EN-US>The parameters are stored in the datm (Pressure
|
||
[mbar], Temperature [C], Relative humidity [%], AEC [-]) array.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142985"><span
|
||
lang=EN-US>5.1.2.5. Contrast between object and
|
||
sky background</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>All the above aspects influence the perceived
|
||
brightnesses 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142986"><span
|
||
lang=EN-US>5.1.3. Functions to determine the
|
||
heliacal events</span></a></h3>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>Two functions are seen as the spill of
|
||
calculating the heliacal events: </span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142987"><span
|
||
lang=EN-US>5.1.3.1. Determining the contrast
|
||
threshold (swe_vis_limit_magn)</span></a><span lang=EN-US> </span></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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='margin-left:0cm;text-indent:0cm'><a name="_Toc335142988"><span
|
||
lang=EN-US>5.1.3.2. Iterations to determine
|
||
when the studied object is really visible (swe_heliacal_ut)</span></a><span
|
||
lang=EN-US> </span></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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 swe_vis_limit_magn function).</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142989"><span
|
||
lang=EN-US>5.1.3.3. Geographic limitations of
|
||
swe_heliacal_ut() and strange behavior of planets in high geographic latitudes</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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.<2E> We found cases
|
||
of strange planetary behavior even at 55N. </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>An example:</span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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 style='margin-bottom:6.0pt'><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<6F> 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 style='margin-bottom:6.0pt'><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='margin-left:0cm;text-indent:0cm'><a name="_Toc335142990"><span
|
||
lang=EN-US>5.1.3.4. Visibility of Venus and the
|
||
Moon during day</span></a></h4>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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 style='margin-bottom:6.0pt'><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.<2E> (Whoever does not believe me, please read
|
||
the article by H.B. Curtis listed under <20>References<65>.)<29> 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>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142991"><span
|
||
lang=EN-US>5.1.4. Future developments</span></a></h3>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><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<EFBFBD>s criterion [1928], Hoffman<61>s overview [2005] and
|
||
Caldwall&Laney criterion [2005].</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm'><a name="_Toc335142992"><span
|
||
lang=EN-US>5.1.5. References</span></a></h3>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Caldwell, J.A.R., Laney, C.D., First
|
||
visibility of the lunar crescent, </span><span lang=DE><a
|
||
href="http://www.saao.ac.za/public-info/sun-moon-stars/moon-index/lunar-crescent-visibility/first-visibility-of-lunar-crescent/"
|
||
target="_blank"><span lang=EN-US>http://www.saao.ac.za/public-info/sun-moon-stars/moon-index/lunar-crescent-visibility/first-visibility-of-lunar-crescent/</span></a></span><span
|
||
lang=EN-US>, 2005, viewed March, 30<sup>th</sup>,
|
||
2009 </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- H.B. Curtis, <i>Venus Visible at inferior
|
||
conjunction</i>, in : <i>Popular Astronomy</i> vol. 18 (1936), p. 44;
|
||
online at <a
|
||
href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1936PA.....44...18C&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf">http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1936PA.....44...18C&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf</a></span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Hoffman, R.E., Rational design of
|
||
lunar-visibility criteria, <i>The observatory</i>, Vol. 125, June 2005, No.
|
||
1186, pp 156-168. </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Reijs, V.M.M., Extinction angle and heliacal events,
|
||
</span><span lang=DE><a href="http://www.iol.ie/%7Egeniet/eng/extinction.htm"
|
||
target="_blank"><span lang=EN-US>http://www.iol.ie/~geniet/eng/extinction.htm</span></a></span><span
|
||
lang=EN-US>, 2003, viewed March, 30<sup>th</sup>,
|
||
2009 </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Schaefer, B., Astronomy and the limit of
|
||
vision, <i>Vistas in astronomy</i>, 36:311, 1993 </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Schaefer, B., New methods and techniques for
|
||
historical astronomy and archaeoastronomy, <i>Archaeoastronomy</i>, Vol. XV,
|
||
2000, page 121-136 </span></p>
|
||
|
||
<p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US>- Schoch, K., Astronomical and calendrical
|
||
tables in Langdon. S., Fotheringham, K.J., <i>The Venus tables of Amninzaduga:
|
||
A solution of Babylonian chronology by means of Venus observations of the first
|
||
dynasty</i>, Oxford, 1928.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142993"><span lang=EN-US>5.2.
|
||
Eclipses, occultations, risings, settings, and other planetary phenomena</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris also includes functions for many calculations
|
||
concerning solar and lunar eclipses. You can:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- search for eclipses or occultations, globally or for a given
|
||
geographical position</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- compute global or local circumstances of eclipses or occultations</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- compute the geographical position where an eclipse is central</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Moreover, you can compute for all planets and asteroids:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- risings and settings (also for stars)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- midheaven and lower heaven transits (also for stars)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- height of a body above the horizon (refracted and true, also for
|
||
stars)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- phase angle</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- phase (illumined fraction of disc)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- elongation (angular distance between a planet and the sun)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- apparent diameter of a planetary disc</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- apparent magnitude.</span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335142994"><span lang=EN-US>6. <20><><EFBFBD> AC, MC, Houses, Vertex</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The Swiss Ephemeris package
|
||
also includes a function that computes the Ascendant, the MC, the houses, the
|
||
Vertex, and the Equatorial Ascendant (sometimes called "East Point").</span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335142995"><span lang=EN-US>6.1.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> House Systems</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The following house methods
|
||
have been implemented so far:</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335142996"><span lang=EN-US>6.1.1.
|
||
Placidus</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 11</span><span lang=EN-US
|
||
style='font-size:8.0pt;'>th</span><span lang=EN-US
|
||
style='font-size:10.0pt;'>
|
||
cusp is the point on the ecliptic that has completed 2/3 of its semidiurnal
|
||
arc, the 12</span><span lang=EN-US style='font-size:8.0pt;'>th</span><span lang=EN-US style='font-size:10.0pt;'> cusp the point that has completed 1/3 of it.
|
||
The 2</span><span lang=EN-US style='font-size:8.0pt;'>nd</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> cusp has completed 2/3 of its seminocturnal arc, and the 3</span><span
|
||
lang=EN-US style='font-size:8.0pt;'>rd</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> cusp 1/3.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335142997"><span lang=EN-US>6.1.2.
|
||
Koch/GOH</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>This system is called after
|
||
the German astrologer Walter Koch (1895-1970). Actually it was invented by
|
||
Fiedrich Zanzinger and Heinz Specht, but it was made known by Walter Koch. In
|
||
German-speaking countries, it is also called the
|
||
"Geburtsorth<EFBFBD>usersystem" (GOHS), i.e. the "Birth place house
|
||
system". Walter Koch thought that this system was more related to the
|
||
birth place than other systems, because all house cusps are computed with the "polar
|
||
height of the birth place", which has the same value as the geographic
|
||
latitude. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335142998"><span lang=EN-US>6.1.3.
|
||
Regiomontanus</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Named after the Johannes
|
||
M<EFBFBD>ller (called "Regiomontanus", because he stemmed from K<>nigsberg)
|
||
(1436-1476). </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335142999"><span lang=IT>6.1.4. Campanus</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=IT
|
||
style='font-size:10.0pt;'>Named after Giovanni di Campani
|
||
(1233-1296).</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143000"><span lang=EN-US>6.1.5.
|
||
Equal System</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The zodiac is divided into 12
|
||
houses of 30 degrees each starting from the Ascendant.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143001"><span lang=EN-US>6.1.6
|
||
Vehlow-equal System</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Equal houses with the
|
||
Ascendant positioned in the middle of the first house.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143002"><span lang=EN-US>6.1.7.
|
||
Axial Rotation System</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Also called the "Meridian
|
||
house system". 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 1<sup>st</sup>
|
||
house cusp.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143003"><span lang=EN-US>6.1.8.
|
||
The Morinus System</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 1<sup>st</sup> cusp, and the MC is different from the 10<sup>th</sup> cusp.
|
||
</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143004"><span lang=EN-US>6.1.9.
|
||
Horizontal system</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143005"><span lang=EN-US>6.1.10.
|
||
The Polich-Page (<28>topocentric<69>) system</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 11<sup>th</sup> house is the
|
||
tangens of the geo. latitude divided by 3. (2/3 of it are taken for the 12<sup>th</sup>
|
||
house cusp.) The philosophical reasons for this algorithm are obscure. Nor is this
|
||
house system more <20>topocentric<69> (i.e. birth-place-related) than any other house
|
||
system. (c.f. the misunderstanding with the <20>birth place system<65>.) The
|
||
<EFBFBD>topocentric<EFBFBD> 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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143006"><span lang=EN-US>6.1.11.
|
||
Alcabitus system</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 the few remaining examples of ancient Greek
|
||
horoscopes. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The MC and ASC are
|
||
respectively 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>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143007"><span lang=EN-US>6.1.12.
|
||
Gauquelin sectors</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>This is the <20>house<73> system
|
||
used by the Gauquelins 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=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>Up to 36 <20>sectors<72> (or house cusps) are used instead of 12 houses.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>The sectors are counted in clockwise direction. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>-<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-align:justify'><span
|
||
lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143008"><span lang=EN-US>6.1.13.
|
||
Krusinski/Pisa/Goelzer system</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This house system was first published in 1994/1995 by three different
|
||
authors independently of each other:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>- by Bogdan
|
||
Krusinski (Poland)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:10.0pt;'>- by Milan Pisa
|
||
(Czech Republic) under the name <20>Amphora house system<65>. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- by Georg Goelzer (Switzerland) under the name <20>Ich-Kreis-H<>usersystem<65>
|
||
(<28>I-Circle house system<65>).. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:8.0pt;'>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 style='font-size:8.0pt;'>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 style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>Bogdan Krusinski first published the house
|
||
system at an astrological congress in Poland, the <20></span><span lang=EN-GB
|
||
style='font-size:8.0pt;'>"XIV
|
||
Szkola Astrologii Humanistycznej" held by Dr Leszek Weres, which took
|
||
place between 15.08.1995 and 28.08.1995 in<69>
|
||
Pogorzelica at cost of the Baltic Sea.<2E> </span><span lang=EN-US
|
||
style='font-size:8.0pt;'>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 http://www.ci.uw.edu.pl/~bogdan/astrol.htm (now at
|
||
http://www.astrologia.pl/main/domy.html) 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 style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>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 style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>By March 2006, when the house system was
|
||
included in the Swiss Ephemeris under the name<6D>
|
||
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><span lang=EN-US style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>Conclusion: It seems that the house system was
|
||
first <20>discovered<65> and published by<62>
|
||
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>
|
||
|
||
<p class=MsoFooter><span lang=EN-US> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-align:justify;text-indent:0cm;'><a
|
||
name="_Toc335143009"><span lang=EN-US>6.2.
|
||
Vertex, Antivertex, East Point and Equatorial Ascendant, etc.</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The <i>Vertex</i> is the point
|
||
of the ecliptic that is located precisely in western direction. The <i>Antivertex</i>
|
||
is the opposition point and indicates the precise east in the horoscope. It is
|
||
identical to the first house cusp in the <i>horizon house system</i>.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>There is a lot of confusion
|
||
about this, because there is also another point which is called the "<i>East
|
||
Point</i>" but is usually <i>not </i>located in the east. In celestial
|
||
geometry, the expression "East Point" means the point on the horizon
|
||
which is in precise eastern direction. The equator goes through this point as
|
||
well, at a right ascension which is equal to ARMC + 90 degrees. On the other
|
||
hand, what some astrologers call the "East Point" is the point on the
|
||
ecliptic whose right ascension is equal to ARMC + 90 (i.e. the right ascension
|
||
of the horizontal East Point). This point can deviate from eastern direction by
|
||
23.45 degrees, the amount of the ecliptic obliquity. For this reason, the
|
||
term<EFBFBD> "East Point" is not very
|
||
well-chosen for this ecliptic point, and some astrologers (M. Munkasey) prefer
|
||
to call it the <i>Equatorial Ascendant</i>. This, because it is identical to
|
||
the Ascendant at a geographical latitude 0.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The Equatorial Ascendant is
|
||
identical to the first house cusp of the <i>axial rotation system</i>.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Note: If a projection of the
|
||
horizontal East Point on the ecliptic is wanted, it might seem more reasonable
|
||
to use a projection rectangular to the ecliptic, not rectangular to the equator
|
||
as is done by the users of the "East Point". The planets, as well,
|
||
are not projected on the ecliptic in a right angle to the ecliptic.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The Swiss Ephemeris supports
|
||
three more points connected with the house and angle calculation. They are part
|
||
of Michael Munkasey's system of the 8 <i>Personal Sensitive Points</i> (PSP).
|
||
The PSP include the <i>Ascendant</i>, the <i>MC</i>, the <i>Vertex</i>, the <i>Equatorial</i>
|
||
<i>Ascendant</i>, the <i>Aries</i> <i>Point</i>, the <i>Lunar</i> <i>Node</i>,
|
||
and the "<i>Co-Ascendant</i>" and the "<i>Polar</i> <i>Ascendant</i>".</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The term
|
||
"Co-Ascendant" seems to have been invented twice by two different
|
||
people, and it can mean two different things. The one "Co-Ascendant"
|
||
was invented by Walter Koch (?). To calculate it, one has to take the ARIC as
|
||
an ARMC and compute the corresponding Ascendant for the birth place. The
|
||
"Co-Ascendant" is then the opposition to this point.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The second
|
||
"Co-Ascendant" stems from Michael Munkasey. It is the Ascendant
|
||
computed for the natal ARMC and a latitude which has the value 90<39> -
|
||
birth_latitude. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>The "Polar
|
||
Ascendant" finally was introduced by Michael Munkasey. It is the
|
||
opposition point of Walter Koch's version of the "Co-Ascendant".
|
||
However, the "Polar Ascendant" is not the same as an Ascendant
|
||
computed for the birth time and one of the geographic poles of the earth. At
|
||
the geographic poles, the Ascendant is always 0 Aries or 0 Libra. This is not
|
||
the case for Munkasey's "Polar Ascendant".</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143010"><span lang=EN-US>6.3.<2E><><EFBFBD><EFBFBD><EFBFBD> House cusps beyond the polar circle</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Beyond the polar circle, we proceed as follows:</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>1)<29><><EFBFBD> </span><span
|
||
lang=EN-US style='font-size:10.0pt;'>We make sure that
|
||
the ascendant is always in the eastern hemisphere.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>2)<29><><EFBFBD> </span><i><span
|
||
lang=EN-US style='font-size:10.0pt;'>Placidus</span></i><span
|
||
lang=EN-US style='font-size:10.0pt;'> and <i>Koch </i>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=Textkrper-Einzug style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>3)<29><><EFBFBD> </span><span
|
||
lang=EN-US style='font-size:10.0pt;'>Beyond the polar
|
||
circles, the MC is sometimes below the horizon. The geometrical definition of
|
||
the <i>Campanus</i> and <i>Regiomontanus</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>There are similar problems with the <i>Vertex</i> and the <i>horizon
|
||
house system</i> for birth places in the tropics. The <i>Vertex</i> 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 <i>Antivertex</i>.
|
||
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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Of course, there are no problems in the calculation of the <i>Equatorial
|
||
Ascendant </i>for any place on earth.</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143011"><span lang=EN-US>6.3.1.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Implementation in other calculation
|
||
modules:</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>a) PLACALC</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <i>priority</i> to the Ascendant, choosing it always as the
|
||
eastern rising point of the ecliptic and <i>accepting an MC below the horizon</i>,
|
||
whereas Placalc gave <i>priority</i> to the MC. The MC was always chosen as the
|
||
intersection of the meridian with the ecliptic <i>above the horizon</i>. 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>b) ASTROLOG program as written by Walter Pullen </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>c) ASTROLOG on our website</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>d) other astrology programs</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143012"><span lang=EN-US>6.4.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> House position of a planet</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <b><i>house horoscope</i></b>. (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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 11 th or
|
||
10 th) 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Although it is not possible to compute <i>Placidus</i> house <i>cusps</i>
|
||
beyond the polar circle, this function will also provide Placidus house
|
||
positions for polar regions. The situation is as follows: </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <20>midnight<68> 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 11 th house cusp did not exist, but there were <i>two </i>12th
|
||
house cusps.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The <i>Koch</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Note that Koch planets do strange jumps when the 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</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143013"><span lang=EN-US>6.5.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Gauquelin sector position of a planet</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>Three different algorithms
|
||
have been used by Gauquelin and others to determine the sector position of a
|
||
planet.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>1.<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>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></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>2.<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>We can take the true planetary position (taking into account ecliptical
|
||
latitude) for the same calculation.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-left:36.0pt;text-align:justify;
|
||
text-indent:-18.0pt;'><span
|
||
lang=EN-US style='font-size:10.0pt;'>3.<span
|
||
style='font:7.0pt "Times New Roman"'>
|
||
</span></span><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>All three methods are
|
||
supported by the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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 <20>midnight<68> and <20>midday<61> culminations are used to define its semidiurnal and
|
||
seminocturnal arcs.</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='text-align:justify'><span lang=EN-US
|
||
style='font-size:10.0pt;'>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>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143014"><span style='font-family:Times;'>7.<2E><><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></a><span lang=EN-US style='font-family:Symbol;'>D</span>T (Delta T)</h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The computation of planets uses the so called <i>Ephemeris Time </i>(ET)
|
||
which is a completely regular time measure. Computations of sidereal time and
|
||
houses, on the other hand, depend on the rotation of the earth, which is not
|
||
regular at all. The time used for such purposes is called <i>Universal Time </i>(UT)
|
||
or <i>Terrestrial Dynamic Time</i> (TDT). It is an irregular time measure, and
|
||
is roughly identical to the time indicated by our clocks (if time zones are
|
||
neglected). The difference between ET and UT is called </span><span lang=EN-US
|
||
style='font-size:10.0pt;font-family:Symbol;'>D</span><span
|
||
lang=EN-US style='font-size:10.0pt;'>T (<28>Delta T<>), and
|
||
is defined as </span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span lang=EN-US style='font-size:10.0pt;'>T = ET <20> UT.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The earth's rotation decreases slowly, currently at the rate of about
|
||
0.5 <20> 1 second per year. Even worse, this decrease is irregular itself. It
|
||
cannot precisely predicted but only derived from star observations. The values
|
||
of </span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span lang=EN-US style='font-size:10.0pt;'>T achieved like this must be tabulated. However, this
|
||
table, which is published yearly by the Astronomical Almanac, starts only at
|
||
1620, about the time when the telescope was invented. For more remote
|
||
centuries, </span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span lang=EN-US style='font-size:10.0pt;'>T must be estimated from old eclipse records. The
|
||
uncertainty is in the range of hours for the year 3000 B.C. For future times, </span><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span
|
||
lang=EN-US style='font-size:10.0pt;'>T is estimated from
|
||
the current and the general changing rate, depending on whether a short-term or
|
||
a long-term extrapolation is intended.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><b><span
|
||
lang=EN-US style='font-size:10.0pt;color:red;'>NOTE:</span></b><span lang=EN-US style='font-size:10.0pt;'>The </span><span lang=EN-US style='font-size:10.0pt;
|
||
font-family:Symbol;'>D</span><span lang=EN-US
|
||
style='font-size:10.0pt;'>T algorithms have been
|
||
improved with the Swiss Ephemeris release 1.64 (Stephenson 1997), with release
|
||
1.72 (Morrison/Stephenson 2004) and 1.77 (Espenak & Meeus). These changes
|
||
result in significant changes of the ephemeris for remote historical dates, if
|
||
Universal Time is used.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The Swiss Ephemeris computes </span><span lang=EN-US style='font-size:
|
||
10.0pt;font-family:Symbol;'>D</span><span lang=EN-US
|
||
style='font-size:10.0pt;'>T as follows.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>1633 - today + a
|
||
couple of years:</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The tabulated values of </span><span lang=EN-US style='font-size:10.0pt;
|
||
font-family:Symbol;'>D</span><span lang=EN-US
|
||
style='font-size:10.0pt;'>T, in hundredths of a second,
|
||
were taken from the Astronomical Almanac page K8 and K9 and are yearly updated.
|
||
</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The </span><span lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span lang=EN-US style='font-size:10.0pt;'>T function adjusts for a value of secular tidal
|
||
acceleration ndot = -25.826 arcsec per century squared, the value contained in
|
||
JPL's lunar ephemeris LE405/6. ELP2000 (and DE200) used the value -23.8946. </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>To change ndot, one can either redefine SE_TIDAL_DEFAULT in swephexp.h
|
||
or use the routine swe_set_tid_acc() before calling the Swiss Ephemeris.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Bessel's interpolation formula was implemented to obtain fourth order
|
||
interpolated values at intermediate times.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>-before 1633:</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>For dates before 1600, the polynomials published by Espenak and Meeus
|
||
(2006) are used, with linear interpolation. They are based on an assumed value
|
||
of ndot = -26. The program adjusts for ndot = -25.826. These formulae include
|
||
the long-term formula by Morrison/Stephenson (2004, p. 332), which is used for
|
||
epochs before -500.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>future:</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>For the time after the last tabulated value, we use the formula of
|
||
Stephenson (1997; p. 507), with a modification that avoids a jump 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. (Need not be updated, when
|
||
table will be enlarged.)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>Differences between
|
||
the old and new algorithms (before and after release 1.77):</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US
|
||
style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> year<61><72><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
difference in seconds (new - old)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -2000<30><30> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
<EFBFBD><EFBFBD> 2</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -1100<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
<EFBFBD><EFBFBD> 1</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -1001<30><31><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
29</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> -900<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
-45</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> -800<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
-57</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> -700<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD> -696<39> (is a maximum!)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> -500<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
-14</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until -200 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3
|
||
> diff > -25</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 100 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3
|
||
> diff > -15</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 500 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 3
|
||
> diff > -3</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 1600 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 4
|
||
> diff > -16</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 1630 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1
|
||
> diff > -30</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 1700 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.1
|
||
|diff|</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 1900 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.01</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>until 2100 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.001</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>The differences for <20>1000 to + 1630 are explained as
|
||
follows: </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>Espenak & Meeus ignore Morrison & Stephenson's
|
||
values for -700 and -600, whereas the former Swiss Ephemeris versions used
|
||
them. For -500 to +1600 Espenak & Meeus use polynomials whereas the former
|
||
Swiss Ephemeris versions used a linear interpolation between Morrison /
|
||
Stephenson's tabulated values.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'> </span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>Differences between
|
||
the old and new algorithms (before and after release 1.72):</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US
|
||
style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> year<61><72><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
difference in seconds (new - old)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -4127</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -2000<30><30> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD> -2130</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -1000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD>
|
||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD> -760</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -20</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -30</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1600<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 10</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1619<31><39><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0.5</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1620<32><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0</span></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'> </span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><i><u><span
|
||
lang=EN-US style='font-size:10.0pt;'>Differences between
|
||
the old and new algorithms (before and after release 1.64):</span></u></i></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US
|
||
style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD> year<61><72><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
difference in seconds (new - old)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD> -3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2900</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1200</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1600<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 29</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1619<31><39><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 60</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1620<32><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.6</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1700<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.4</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1800<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.1</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1900<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.02</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1940<34><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -0.001</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 1950 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>0</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 0</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2020<32><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 2100<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 23</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span
|
||
lang=EN-US style='font-size:10.0pt;'><EFBFBD><EFBFBD> 3000<30><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> -400</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>In 1620, where the </span><span lang=EN-US style='font-size:10.0pt;
|
||
font-family:Symbol;'>D</span><span lang=EN-US
|
||
style='font-size:10.0pt;'>T table of the Astronomical
|
||
Almanac starts, there was a jump of a whole minute in the old algorithms. The
|
||
new algorithms has no jumps anymore.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The smaller differences for the period 1620-1955, where we still use the
|
||
same data as before, is 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 </span><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:Symbol;'>D</span><span
|
||
lang=EN-US style='font-size:10.0pt;'>T calculations.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>References:</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'> </span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- Borkowski, K. M., "ELP2000-85 and the Dynamical Time - Universal
|
||
Time relation," <i>Astronomy and
|
||
Astrophysics </i>205, L8-L10 (1988)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- Chapront-Touze, Michelle, and Jean Chapront, <i>Lunar Tables and Programs from 4000 B.C. to A.D. 8000</i>, Willmann-Bell
|
||
1991</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- Espenak, Fred, and Jean Meeus, <20>Five-millennium Catalog of Lunar
|
||
Eclipses <20>1900 to +3000<30>, 2009, p. 18ff., </span><span lang=EN-US
|
||
style='font-size:8.0pt;'>http://eclipse.gsfc.nasa.gov/5MCSE/TP2009-214174.pdf.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- <i>Explanatory Supplement of the
|
||
Astronomical Almanach</i>, University Science Books, 1992, Mill Valley, CA, p.
|
||
265ff.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- Morrison, L. V. and F. R. Stephenson, <i>Sun and Planetary System</i>, vol 96,73 eds. </span><span
|
||
style='font-size:8.0pt;'>W. Fricke, G. Teleki, Reidel,
|
||
Dordrecht (1982)</span></p>
|
||
|
||
<p class=MsoBodyTextIndent><span lang=EN-US style='font-size:8.0pt;font-style:normal'>- Morrison, L. V., and F.R. Stephenson, <20>Historical
|
||
Values of the Earth<74>s Clock Error </span><span lang=EN-US style='font-size:
|
||
8.0pt;font-family:Symbol;font-style:normal'>D</span><span
|
||
lang=EN-US style='font-size:8.0pt;font-style:normal'>T
|
||
and the Calculation of Eclipses<65>, JHA xxxv (2004), pp.327-336</span></p>
|
||
|
||
<p class=MsoBodyTextIndent><span lang=EN-US style='font-size:8.0pt;font-style:normal'>- Stephenson, F. R., and L. V. Morrison,
|
||
"Long-term changes in the rotation of the Earth: 700 BC to AD 1980", </span><span
|
||
lang=EN-US style='font-size:8.0pt;'>Philosophical Transactions of the Royal Society of London</span><span
|
||
lang=EN-US style='font-size:8.0pt;font-style:normal'>,
|
||
Series A 313, 47-70 (1984)</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'>- Stephenson, F. R., and M. A. Houlden, <i>Atlas of Historical Eclipse Maps</i>, Cambridge U. Press (1986)</span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:8.0pt;'>- Stephenson, F.R. & Morrison, L.V., "Long-Term Fluctuations in
|
||
the Earth's Rotation: 700 BC to AD 1990", in: <i>Philosophical Transactions of the Royal Society of London</i>, Ser. A,
|
||
351 (1995), 165-202. </span></p>
|
||
|
||
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
|
||
lang=EN-US style='font-size:8.0pt;'>- Stephenson, F. Richard, <i>Historical
|
||
Eclipses and Earth's Rotation</i>, Cambridge U. Press (1997)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:8.0pt;'>- For a comprehensive collection of
|
||
publications and formulae, see R.H. van Gent at
|
||
http://www.phys.uu.nl/~vgent/astro/deltatime.htm.</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US style='font-size:8.0pt;'> </span></p>
|
||
|
||
<h1 style='margin-left:35.25pt;text-indent:0cm;'><a
|
||
name="_Toc335143015"><span lang=EN-US>8.<2E><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Programming Environment</span></a></h1>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>To build the DLLs, we use Microsoft Visual C++ version 5.0 (for 32-bit).</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>The DLL has been successfully used in the following programming
|
||
environments:</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Visual C++ 5.0 <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (sample
|
||
code included in the distribution)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Visual Basic 5.0<EFBFBD> (sample code
|
||
and VB declaration file included)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Delphi 2 and Delphi 3 (32-bit, declaration file included)</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>As the number of<6F> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Earlier version up to version 1.61 supported 16-bit Windows programming.
|
||
Since then, 16-bit support has been dropped.</span></p>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143016"><span lang=EN-US>9. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Swiss Ephemeris Functions</span></a></h1>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143017"><span lang=EN-US>9.1<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Swiss Ephemeris API</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 </span><span lang=EN-US style='font-size:10.0pt;
|
||
font-family:"Courier New";'>swephprg.doc</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> which is
|
||
distributed together with the file you are reading.</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143018"><span lang=EN-US>Calculation
|
||
of planets and stars</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* planets, moon, asteroids, lunar
|
||
nodes, apogees, fictitious bodies */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_calc();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* fixed stars */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_fixstar();<3B><><EFBFBD> </span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143019"><span lang=EN-US>Date and
|
||
time conversion</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* delta t from Julian day number </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'><EFBFBD>* Ephemeris time (ET) = Universal time (UT) + swe_deltat(UT)*/</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_deltat();</span></p>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* Julian day number from year, month,
|
||
day, hour, */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_date_conversion (<b>)</b>;<3B><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* Julian day number from year, month,
|
||
day, hour */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_julday();<3B><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* year, month, day, hour from Julian
|
||
day number */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_revjul ();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* UTC to Julian day number */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_utc_to_jd ();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* Julian day number TT to UTC */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_jdet_to_utc ();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* Julian day number UT1 to UTC */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_jdut1_to_utc ();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* utc to time zone or time zone to
|
||
utc*/</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_utc_time_zone ();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* get tidal acceleration used in
|
||
swe_deltat() */ </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_get_tid_acc(); </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* set tidal acceleration to be used in
|
||
swe_deltat() */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_set_tid_acc();</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143020"><span lang=EN-US>Initialization,
|
||
setup, and closing functions</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* set directory path of ephemeris files
|
||
*/</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_set_ephe_path();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* set name of JPL ephemeris file */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_set_jpl_file();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* close Swiss Ephemeris */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_close();</span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143021"><span lang=EN-US>House
|
||
calculation</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* sidereal time */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_sidtime();<3B><><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* house cusps, ascendant, MC, armc,
|
||
vertex */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_houses();<3B><><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<h4 style='margin-left:0cm;text-indent:0cm;'><span
|
||
lang=EN-US style='font-family:"Courier New";'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><a name="_Toc335143022"><span
|
||
lang=EN-US>Auxiliary functions</span></a></h4>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* coordinate transformation, from
|
||
ecliptic to equator or vice-versa. */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_cotrans();<3B><><EFBFBD> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* coordinate transformation of position
|
||
and speed, </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'><EFBFBD>* from ecliptic to equator or vice-versa*/</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_cotrans_sp();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* get the name of a planet */</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_get_planet_name();<3B> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>/* normalization of any degree number to
|
||
the range 0 ... 360 */ </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'>swe_degnorm();</span></p>
|
||
|
||
<h3 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143023"><span lang=EN-US>Other
|
||
functions that may be useful</span></a></h3>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=MsoPlainText><span lang=EN-US>/*
|
||
normalize argument into interval [0..DEG360] </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: csnorm() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_csnorm();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
distance in centisecs p1 - p2 normalized to [0..360[ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: difcsn() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_difcsn
|
||
();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
distance in degrees<65> * former function
|
||
name: difdegn() */ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_difdegn
|
||
();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
distance in centisecs p1 - p2 normalized to [-180..180[ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: difcs2n() */ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_difcs2n();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
distance in degrees</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: difdeg2n() */ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_difdeg2n();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/* round
|
||
second, but at 29.5959 always down </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: roundsec() */ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_csroundsec();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
double to long with rounding, no overflow check </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: d2l() */ </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_d2l();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
Monday = 0, ... Sunday = 6 </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: day_of_week() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_day_of_week();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
centiseconds -> time string</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: TimeString() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_cs2timestr();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/*
|
||
centiseconds -> longitude or latitude string<6E> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: LonLatString() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_cs2lonlatstr();</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US> </span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>/* centiseconds
|
||
-> degrees string</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US><EFBFBD>* former function name: DegreeString() */</span></p>
|
||
|
||
<p class=MsoPlainText><span lang=EN-US>swe_cs2degstr();</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;font-family:
|
||
"Courier New";'> </span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143024"><span lang=EN-US>9.2<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Placalc API</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>This interface (</span><span lang=EN-US style='font-size:10.0pt;
|
||
font-family:"Courier New";'>swepcalc.c</span><span
|
||
lang=EN-US style='font-size:10.0pt;'> and </span><span
|
||
lang=EN-US style='font-size:10.0pt;font-family:"Courier New";'>swepcalc.h</span><span lang=EN-US style='font-size:10.0pt;'>) 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>
|
||
|
||
<h1 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143025"><span lang=EN-US>Appendix</span></a></h1>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143026"><span lang=EN-US>A. The
|
||
gravity deflection for a planet passing behind the Sun</span></a></h2>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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>
|
||
|
||
<table border=0 cellspacing=0 cellpadding=0 style='margin-left:.4pt;border-collapse:
|
||
collapse;'>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Planet</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>number of passes behind the Sun</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>Mercury</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>1723</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>Venus</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>456</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=FR>Mars</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>412</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Jupiter</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>793</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Saturn</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>428</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Uranus</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>1376</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Neptune</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>543</span></p>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td width=88 valign=top style='width:65.8pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>Pluto</span></p>
|
||
</td>
|
||
<td width=196 valign=top style='width:146.85pt;padding:0cm 0cm 0cm 0cm'>
|
||
<p class=MsoNormal style='layout-grid-mode:char'><span lang=EN-US>57</span></p>
|
||
</td>
|
||
</tr>
|
||
</table>
|
||
|
||
<p class=MsoNormal><span lang=EN-US> </span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Strictly speaking, there is no <i>apparent</i> 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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<EFBFBD> an aspect of the planet.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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 <i>apparent</i> positions also for occulted
|
||
planets.</span></p>
|
||
|
||
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>For a remote planet just at the edge of the Solar disk the gravity
|
||
deflection is about 1.8<EFBFBD>, 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=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>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=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>.. it
|
||
seems that your approach is</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>entirely
|
||
reasonable and can be easily justified as long</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>as you
|
||
choose a reasonable model for the density of </span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>the
|
||
sun.<2E> The solution may become more
|
||
difficult if an</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>ellipsoidal
|
||
sun is considered,<2C> but certainly that
|
||
is</span></p>
|
||
|
||
<p class=MsoBodyTextIndent style='margin-left:1.0cm'><span lang=EN-US
|
||
style='font-family:Courier;font-style:normal'>an
|
||
additional refinement which can not be crucial.</span></p>
|
||
|
||
<p class=MsoSalutation><span lang=EN-US> </span></p>
|
||
|
||
<h2 style='margin-left:0cm;text-indent:0cm;'><a
|
||
name="_Toc335143027"><span lang=EN-US>B. The
|
||
list of asteroids</span></a></h2>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
====================================</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># At
|
||
the same time a brief introduction into asteroids</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
====================================================</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># As
|
||
of the year 2010, there is no longer any CDROM. All</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
parts of Swiss Ephemeris can be downloaded in the download area.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Literature:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Lutz D. Schmadel, Dictionary of Minor Planet Names,</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> Springer, Berlin, Heidelberg, New York</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Charles T. Kowal, Asteroids. Their Nature and Utilization,</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> Whiley & Sons, 1996, Chichester,
|
||
England</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
What is an asteroid?</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Asteroids are small planets. Because there are too many </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># of
|
||
them and because most of them are quite small, </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
astronomers did not like to call them "planets", but </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
invented names like "asteroid" (Greek "star-like",</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
because through telescopes they did not appear as planetary</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
discs but as star like points) or "planetoid" (Greek </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
"something like a planet"). However they are also often</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
called minor planets.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># The
|
||
minor planets can roughly be divided into two groups.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
There are the inner asteroids, the majority of which</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
circles in the space between Mars and Jupiter, and</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
there are the outer asteroids, which have their realm</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
beyond Neptune. The first group consists of rather </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
dense, earth-like material, whereas the Transneptunians</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
mainly consist of water ice and frozen gases. Many comets</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># are
|
||
descendants of the "asteroids" (or should one say</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
"comets"?) belt beyond Neptune. The first Transneptunian</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
objects (except Pluto) were discovered only after 1992 </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># and
|
||
none of them has been given a name as yet.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># The
|
||
largest asteroids</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
---------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Most asteroids are actually only debris of collisions</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># of
|
||
small planets that formed in the beginning of the </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
solar system. Only the largest ones are still more</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># or
|
||
less complete and round planets.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1<EFBFBD><EFBFBD><EFBFBD> Ceres<65><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 913 km<6B> goddess of
|
||
corn and harvest</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2<EFBFBD><EFBFBD><EFBFBD> Pallas<61><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 523 km<6B> goddess of
|
||
wisdom, war and liberal arts </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4<EFBFBD><EFBFBD><EFBFBD> Vesta<74><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 501 km<6B> goddess of
|
||
the hearth fire</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>10<EFBFBD><EFBFBD> Hygiea<65><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 429 km<6B> goddess of
|
||
health</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>511<EFBFBD> Davida<64><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# 324 km<6B> after an astronomer
|
||
David P. Todd</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>704<EFBFBD> Interamnia<69><61>
|
||
# 338 km<6B> "between
|
||
rivers", ancient name of </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> #<23><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> its discovery place Teramo </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>65<EFBFBD><EFBFBD> Cybele<6C><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 308 km<6B> Phrygian
|
||
Goddess, = Rhea, wife of Kronos-Saturn</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>52<EFBFBD><EFBFBD> Europa<70><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 292 km<6B> beautiful
|
||
mortal woman, mother of Minos by Zeus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>87<EFBFBD><EFBFBD> Sylvia<69><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 282 km<6B> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>451<EFBFBD> Patientia<69><61><EFBFBD>
|
||
# 280 km<6B> patience</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>31<EFBFBD><EFBFBD> Euphrosyne<6E><65> # 270 km<6B> one of the
|
||
three Graces, benevolence</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>15<EFBFBD><EFBFBD> Eunomia<69><61><EFBFBD><EFBFBD><EFBFBD> # 260 km<6B> one of the
|
||
Hours, order and law</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>324<EFBFBD> Bamberga<67><61><EFBFBD><EFBFBD>
|
||
# 252 km<6B> after a city in Bavaria</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3<EFBFBD><EFBFBD><EFBFBD> Juno<6E><6F><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 248 km<6B> wife of
|
||
Zeus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>16<EFBFBD><EFBFBD> Psyche<68><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # 248 km<6B>
|
||
"soul", name of a nymph</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Asteroid families</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
-----------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Most asteroids live in families. There are several kinds</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># of
|
||
families. </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># -
|
||
There are families that are separated from each other </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> by orbital resonances with Jupiter or other
|
||
major planets.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># -
|
||
Other families, the so-called Hirayama families, are the </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> relics of asteroids that broke apart long
|
||
ago when they</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> collided with other asteroids. </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># -
|
||
Third, there are the Trojan asteroids that are caught </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> in regions 60 degrees ahead or behind a
|
||
major planet </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> (Jupiter or Mars) by the combined
|
||
gravitational forces </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#<23><> of this planet and the Sun.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Near Earth groups:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Aten family: they cross Earth; mean distance from Sun is less than Earth </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2062
|
||
Aten<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # an Egyptian Sun god</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2100
|
||
Ra-Shalom<6F><6D><EFBFBD> # Ra is an Egyptian Sun
|
||
god, Shalom is Hebrew "peace"</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # was discovered during Camp
|
||
David mid-east peace conference</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Apollo family: they cross Earth; mean distance is greater than Earth </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1862
|
||
Apollo<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Greek Sun god</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1566
|
||
Icarus<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # wanted to fly to the sky,
|
||
fell into the ocean</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Icarus crosses Mercury,
|
||
Venus, Earth, and Mars</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # and has his perihelion
|
||
very close to the Sun</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3200
|
||
Phaethon<EFBFBD><EFBFBD><EFBFBD><EFBFBD> # wanted to drive the solar
|
||
chariot, crashed in flames</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD># Phaethon crosses Mercury, Venus, Earth, and Mars</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # and has his perihelion
|
||
very close to the Sun</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Amor family: they cross Mars, approach Earth</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1221
|
||
Amor<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Roman love god</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>433<EFBFBD> Eros<6F><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# Greek love god</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'># Mars
|
||
Trojans:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'>#
|
||
-------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'>5261
|
||
Eureka<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> a mars Trojan</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Main belt families:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
-------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Hungarias: asteroid group at 1.95 AU </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>434<EFBFBD> Hungaria<69><61><EFBFBD><EFBFBD>
|
||
# after Hungary</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Floras: Hirayama family at 2.2 AU</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD></span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>8<EFBFBD><EFBFBD><EFBFBD> Flora<72><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of flowers</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Phocaeas: asteroid group at 2.36 AU</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>25<EFBFBD><EFBFBD> Phocaea<65><61><EFBFBD><EFBFBD><EFBFBD> # maritime town in Ionia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Koronis family: Hirayama family at 2.88 AU</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>158<EFBFBD> Koronis<69><73><EFBFBD><EFBFBD><EFBFBD>
|
||
# mother of Asklepios by Apollo</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># Eos
|
||
family: Hirayama family at 3.02 AU</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>221<EFBFBD> Eos<6F><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# goddess of dawn</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># Themis
|
||
family: Hirayama family at 3.13 AU</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>24<EFBFBD><EFBFBD> Themis<69><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of justice</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Hildas: asteroid belt at 4.0 AU, in 3:2 resonance with Jupiter</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------------------------------------------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># The
|
||
Hildas have fairly eccentric orbits and, at their</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
aphelion, are very close to the orbit of Jupiter. However,</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># at
|
||
those times, Jupiter is ALWAYS somewhere else. As</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Jupiter approaches, the Hilda asteroids move towards</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
their perihelion points.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>153<EFBFBD> Hilda<64><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# female first name, means "heroine"</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># a
|
||
single asteroid at 4.26 AU, in 4:3 resonance with Jupiter</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>279<EFBFBD> Thule<6C><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# mythical center of Magic in the uttermost north </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Jupiter Trojans:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
----------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Only the Trojans behind Jupiter are actually named after Trojan heroes,</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># whereas
|
||
the "Trojans" ahead of Jupiter are named after Greek heroes that</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
participated in the Trojan war. However there have been made some mistakes,</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
i.e. there are some Trojan "spies" in the Greek army and some Greek
|
||
"spies"</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># in
|
||
the Trojan army.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># Greeks
|
||
ahead of Jupiter:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>624<EFBFBD> Hector<6F><72><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# Trojan "spy" in the Greek army, by far the greatest </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Trojan hero and the
|
||
greatest Trojan asteroid</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>588<EFBFBD> Achilles<65><73><EFBFBD><EFBFBD>
|
||
# slayer of Hector</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1143
|
||
Odysseus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Trojans behind Jupiter:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1172
|
||
<EFBFBD>neas</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3317
|
||
Paris</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>884<EFBFBD> Priamus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Jupiter-crossing asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
---------------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3552
|
||
Don Quixote<74> # perihelion near Mars,
|
||
aphelion beyond Jupiter;</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # you know Don Quixote,
|
||
don't you?</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>944<EFBFBD> Hidalgo<67><6F><EFBFBD><EFBFBD><EFBFBD>
|
||
# perihelion near Mars, aphelion near Saturn;</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # after a Mexican national
|
||
hero</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>5335
|
||
Damocles<EFBFBD><EFBFBD><EFBFBD><EFBFBD> # perihelion near Mars,
|
||
aphelion near Uranus;</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # the man sitting below a
|
||
sword suspended by a thread</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Centaurs:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
---------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2060
|
||
Chiron<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # perihelion near Saturn,
|
||
aphelion near Uranus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # educator of heros,
|
||
specialist in healing and war arts</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>5145
|
||
Pholus<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # perihelion near Saturn,
|
||
aphelion near Neptune</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # seer of the gods, keeper
|
||
of the wine of the Centaurs</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>7066
|
||
Nessus<EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD># perihelion near Saturn, aphelion in Pluto's mean distance</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # ferryman, killed by
|
||
Hercules, kills Hercules</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Plutinos:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
---------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
These are objects with periods similar to Pluto, i.e. objects</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
that resonate with the Neptune period in a 3:2 ratio.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
There are no Plutinos included in Swiss Ephemeris so far, but</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
PLUTO himself is considered to be a Plutino type asteroid!</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Cubewanos:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
----------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
These are non-Plutiono objects with periods greater than Pluto.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># The
|
||
word "Cubewano" is derived from the preliminary designation</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># of
|
||
the first-discovered Cubewano: 1992 QB1</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>20001
|
||
1992 QB1<42><31><EFBFBD> # will be given the name of
|
||
a creation deity </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span><span lang=FR
|
||
style='font-size:9.0pt;'># (fictitious catalogue number
|
||
20001!)</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
other Transplutonians:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>20001
|
||
1996 TL66 <20><># mean solar distance 85 AU,
|
||
period 780 years</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Asteroids that challenge hypothetical planets astrology</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
-------------------------------------------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>42<EFBFBD><EFBFBD> Isis<69><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # not identical with "Isis-Transpluto"</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Egyptian lunar goddess</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>763<EFBFBD> Cupido<64><6F><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# different from Witte's Cupido</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Roman god of sexual desire</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4341
|
||
Poseidon<EFBFBD><EFBFBD><EFBFBD><EFBFBD> # not identical with
|
||
Witte's Poseidon</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Greek name of Neptune</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4464
|
||
Vulcano<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # compare Witte's Vulkanus </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD># and intramercurian hypothetical Vulcanus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Roman fire god</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>5731
|
||
Zeus<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # different from Witte's
|
||
Zeus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Greek name of Jupiter</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1862
|
||
Apollo<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # different from Witte's
|
||
Apollon</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Greek god of the Sun</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>398<EFBFBD> Admete<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# compare Witte's Admetos</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # "the untamed
|
||
one", daughter of Eurystheus</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Asteroids that challenge Dark Moon astrology</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------------------------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1181
|
||
Lilith<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # not identical with Dark
|
||
Moon 'Lilith'</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # first evil wife of Adam</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3753
|
||
Cruithne<EFBFBD><EFBFBD><EFBFBD><EFBFBD> # often called the
|
||
"second moon" of earth;</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # actually not a moon, but
|
||
an asteroid that </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # orbits around the sun in a
|
||
certain resonance </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # with the earth.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # After the first Celtic
|
||
group to come to the British Isles.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Also try the two points 60 degrees in front of and behind the</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Moon, the so called Lagrange points, where the combined</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
gravitational forces of the earth and the moon might imprison</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
rocks and stones. There have been some photographic hints</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
that there are clouds of such material around these points.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
They are called the Kordylewski clouds.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
other asteroids</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
---------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>5<EFBFBD><EFBFBD><EFBFBD> Astraea<65><61><EFBFBD><EFBFBD><EFBFBD> # a goddess of justice</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>6<EFBFBD><EFBFBD><EFBFBD> Hebe<62><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of youth</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>7<EFBFBD><EFBFBD><EFBFBD> Iris<69><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # rainbow goddess, messenger of the gods</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>8<EFBFBD><EFBFBD><EFBFBD> Flora<72><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of flowers and gardens</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>9<EFBFBD><EFBFBD><EFBFBD> Metis<69><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of prudence</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>10<EFBFBD><EFBFBD> Hygiea<65><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of health</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>14<EFBFBD><EFBFBD> Irene<6E><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # goddess of peace</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'>16<EFBFBD><EFBFBD> Psyche<68><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # "soul", a nymph</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>19<EFBFBD><EFBFBD> Fortuna<6E><61><EFBFBD><EFBFBD><EFBFBD> # goddess of fortune</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Some frequent names:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
There are thousands of female first names in the asteroids list.</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Very interesting for relationship charts!</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>78<EFBFBD><EFBFBD> Diana</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>170<EFBFBD> Maria</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>234<EFBFBD> Barbara</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>375<EFBFBD> Ursula<6C><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>412<EFBFBD> Elisabetha</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>542<EFBFBD> Susanna</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Wisdom asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
-----------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>134<EFBFBD> Sophrosyne<6E><65>
|
||
# equanimity, healthy mind and impartiality</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>197<EFBFBD> Arete<74><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# virtue</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>227<EFBFBD> Philosophia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>251<EFBFBD> Sophia<69><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
||
# wisdom (Greek)</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>259<EFBFBD> Aletheia<69><61><EFBFBD><EFBFBD>
|
||
# truth </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>275<EFBFBD> Sapientia<69><61><EFBFBD>
|
||
# wisdom (Latin)</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'># Love
|
||
asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>#
|
||
---------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>344<EFBFBD> Desiderata</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>433<EFBFBD> Eros</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>499<EFBFBD> Venusia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>763<EFBFBD> Cupido </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1221
|
||
Amor<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1387
|
||
Kama<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Indian god of sexual
|
||
desire<EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD></span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1388
|
||
Aphrodite<EFBFBD><EFBFBD><EFBFBD> # Greek love Goddess</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1389
|
||
Onnie<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # what is this, after 1387
|
||
and 1388 ?</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1390
|
||
Abastumani<EFBFBD><EFBFBD> # and this?</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># The
|
||
Nine Muses</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>18<EFBFBD><EFBFBD> Melpomene<6E><65><EFBFBD> Muse of tragedy</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>22<EFBFBD><EFBFBD> Kalliope<70><65><EFBFBD><EFBFBD> Muse of heroic poetry</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>23<EFBFBD><EFBFBD> Thalia<69><61>
|
||
<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Muse of comedy</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>27<EFBFBD><EFBFBD> Euterpe<70><65><EFBFBD><EFBFBD><EFBFBD> Muse of music and lyric poetry</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>30<EFBFBD><EFBFBD> Urania<69><61><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Muse of astronomy and astrology</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>33<EFBFBD><EFBFBD> Polyhymnia<69><61> Muse of singing and rhetoric</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>62<EFBFBD><EFBFBD> Erato<74><6F><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Muse of song and dance</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>81<EFBFBD><EFBFBD> Terpsichore<72> Muse of choral dance and song</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>84<EFBFBD><EFBFBD> Klio<69><6F><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> Muse of history</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Money and big busyness asteroids</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
--------------------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>19<EFBFBD><EFBFBD> Fortuna<6E><61><EFBFBD><EFBFBD><EFBFBD> # goddess of fortune</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>904<EFBFBD> Rockefellia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1338
|
||
Duponta </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3652
|
||
Soros </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Beatles asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4147
|
||
Lennon</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4148
|
||
McCartney</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>4149
|
||
Harrison</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'>4150 Starr</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=FR style='font-size:9.0pt;'># Composer
|
||
Asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
-------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2055
|
||
Dvorak</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1814
|
||
Bach</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1815
|
||
Beethoven</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1034
|
||
Mozartia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3941
|
||
Haydn</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>And
|
||
there are many more...</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Astrodienst asteroids:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
----------------------</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
programmers group:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>3045
|
||
Alois</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2396
|
||
Kochi</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>2968
|
||
Iliya<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> # Alois' dog</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
artists group:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>412<EFBFBD> Elisabetha</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
production family:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>612<EFBFBD> Veronika</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1376
|
||
Michelle</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1343
|
||
Nicole</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1716
|
||
Peter</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
children group</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>105
|
||
Artemis</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1181
|
||
Lilith</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
special interest group</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>564
|
||
Dudu</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>349
|
||
Dembowska</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>484
|
||
Pittsburghia</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># By
|
||
the year 1997, the statistics of asteroid names looked as follows:</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'> </span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'># Men
|
||
(mostly family names)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 2551</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Astronomers<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 1147</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Women (mostly first names)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 684</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Mythological terms<6D><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 542</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Cities, harbours buildings<67><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 497</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Scientists (no astronomers)<29><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 493</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Relatives of asteroid discoverers<72><73><EFBFBD> 277</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Writers<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 249</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Countries, provinces, islands<64><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 246</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Amateur astronomers<72><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 209</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Historical, political figures<65><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 176</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Composers, musicians, dancers<72><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 157</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Figures from literature, operas<61><73><EFBFBD><EFBFBD><EFBFBD> 145</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Rivers, seas, mountains<6E><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 135</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Institutes, observatories<65><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 116</span></p>
|
||
|
||
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>#
|
||
Painters, sculptors<72><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 101</span></p>
|
||
|
||
<p class=MsoPlainText style='text-indent:1.0cm'><span lang=EN-US
|
||
style='font-size:9.0pt;'># Plants, trees, animals<6C><73><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 63</span></p>
|
||
|
||
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|
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||
</body>
|
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