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<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;'>���� </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;'>���� </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;'>��������� </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;'>������������ </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;'>��������� </span><b><span
lang=EN-US>The Swiss Ephemeris</span></b><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="#_Toc335142931"><b><span lang=EN-US>2.</span></b><span lang=DE style='font-size:
12.0pt;color:windowtext;
text-decoration:none;'>��� </span><b><span
lang=EN-US>The Moshier Ephemeris</span></b><span
style='color:windowtext;display:none;text-decoration:none;'>� </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;'>��� </span><b><span
lang=EN-US>The full JPL Ephemeris</span></b><span
style='color:windowtext;display:none;text-decoration:none;'>� </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;'>������������ </span><span
lang=EN-US>Swiss Ephemeris and the Astronomical
Almanac</span><span style='color:windowtext;display:none;
text-decoration:none;'>� </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;'>������������ </span><span
lang=EN-US>Swiss Ephemeris and JPL Horizons
System</span><span style='color:windowtext;display:none;
text-decoration:none;'>�� </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;'>������������ </span><span
lang=EN-US>Differences between Swiss Ephemeris
1.70 and older versions</span><span style='color:windowtext;display:none;text-decoration:none;'>� </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;'>������������ </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;'>������������ </span><span
lang=EN-US>The details of coordinate
transformation</span><span style='color:windowtext;display:none;
text-decoration:none;'>� </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;'>������������ </span><span
lang=EN-US>The Swiss Ephemeris compression
mechanism</span><span style='color:windowtext;display:none;
text-decoration:none;'>�� </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;'>������������ </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;'>����� </span><span
lang=EN-US>Lunar and Planetary Nodes and
Apsides</span><span style='color:windowtext;display:none;
text-decoration:none;'>� </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;'>������������ </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;'>������������ </span><span
lang=EN-US>The 'True' Node</span><span
style='color:windowtext;display:none;text-decoration:none;'>� </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;'>������������ </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;'>������������ </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;'>������������ </span><span
lang=EN-US>Planetary Nodes and Apsides</span><span
style='color:windowtext;display:none;text-decoration:none;'>� </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;'>��������� </span><span
lang=EN-US>Asteroids</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="#_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>�Ceres� - 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;'>����� </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;'>����� </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;'>��������� </span><span
lang=EN-US>�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�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;'>������ </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;'>��������� </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;'>������ </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;'>����� </span><span
lang=EN-US>House Systems</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="#_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 (�topocentric�) 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;'>��������� </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;'>������������ </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;'>����� </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;'>��������� </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;'>���� </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;'>������ </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;'>������ </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;'>����� </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;'>����� </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>� </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>� 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>�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� +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����� 30-sept-1997</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.01����� 9-oct-1997����������� simplified
houses() and sidtime() functions, Vertex added.</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.02����� 16-oct-1997����������� houses() changed again</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.03����� 28-oct-1997���� minor fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.04����� 8-Dec-1997���� minor
fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.10����� 9-Jan-1998���� bug
fix, pushed to all licensees</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.11����� 12-Jan-98������� minor
fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.20����� 21-Jan-98������� <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����� 28-Jan-98� ����� Delphi
declarations and sample for Delphi 1.0</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.22����� 2-Feb-98����������� Asteroids moved to subdirectory.
Swe_calc() finds them there.</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.23����� 11-Feb-98� ����� two
minor bug fixes.</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.24����� 7-Mar-1998����������� Documentation for Borland C++
Builder added</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.25����� 4-June-1998���� sample for Borland Delphi-2 added</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.26����� 29-Nov-1998���� source added, Placalc API added</span></p>
<p class=MsoNormal><span lang=EN-US style='font-family:Arial;'>1.30����� 17-Dec-1998����������� </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����� 12-Jan-1999���� <span style='color:red'>NEW</span>: Eclipses</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.40����� 19-Apr-1999���� <span style='color:red'>NEW</span>: planetary phenomena</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.50����� 27-Jul-1999 ��� <span style='color:red'>NEW</span>: sidereal ephemerides</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.52�� �� 15-Feb-2000
��� Several <span style='color:red'>NEW</span>
features, minor bug fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.60����� 15-Feb-2000���� Major release with many new features and some minor bug fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.61����� 11-Sep-2000���� Minor release, additions to se_rise_trans(), swe_houses(),
ficitious planets</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.62����� 23-Jul-2001����� Minor release, fictitious earth satellites, asteroid numbers
> 55535 possible</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.63����� 5-Jan-2002���� Minor
release, house calculation added to swetest.c and swetest.exe</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.64����� 7-Apr-2002 ��� <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����� 12-Jun-2003���� Minor release, small code renovations for 64-bit compilation</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.66�� �� 10-Jul-2003���� <span style='color:red'>NEW:</span> Morinus
houses</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.67����� 31-Mar-2005���� Minor release: Delta-T updated, minor bug fixes</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.70
���� 2-Mar-2006���� IAU resolutions up to 2005 implemented; "interpolated"
lunar apsides</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.72����� 28-nov-2007���� Delta T calculation according to Morrison/Stephenson 2004</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.74����� 17-jun-2008���� License model changed to dual license, GNU GPL or Professional
License</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.76����� 31-mar-2009���� <span style='color:red'>NEW: </span>Heliacal events</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.77����� 25-jan-2011���� Delta T calculation updated acc. to Espenak/Meeus 2006, new fixed
stars file</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.78����� 2-aug-2012����������� Precession
calculation updated acc. to Vondr�k et alii 2012</span></p>
<p class=MsoEnvelopeReturn><span lang=EN-US>1.79����� 23-apr-2013���� 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 �hypothetical� 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.������� 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� system. The software
developer, who uses any part of Swiss Ephemeris� in his or her software, must choose between one of the two
license models, which are</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>� a) GNU public license version 2
or later</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>� 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� or her whole software project under
the GNU GPL or a compatible license.�
See http://www.gnu.org/licenses/old-licenses/gpl-2.0.html</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>If the developer choses the Swiss Ephemeris Professional license,� he must follow the instructions as found in
http://www.astro.com/swisseph/� and
purchase the Swiss Ephemeris Professional Edition from Astrodienst and sign the
corresponding license contract.</span></p>
<p class=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.-� 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.������� Descripition of the ephemerides</span></a></h1>
<h2 style='margin-left:0cm;text-indent:0cm;'><a
name="_Toc335142928"><span lang=EN-US>2.1�������� 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��� 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. ������� 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.� Using a sophisticated mechanism,
we succeeded in reducing JPL's 200 MB storage to only 18 MB. The agreement with
DE406 is� within 1 milli-arcsecond
(0.001�).� 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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 � 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� 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��������������� 2 Jan 5401 BC (jul. calendar)��������������� = JD�� -251291.5</span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
style='font-style:normal'>End date��������������� ��������������� 31
Dec 5399 AD (greg. Cal.) ������ = 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.�������� 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, �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�.
And:� �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. � (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.�������� 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 � 2160 there is a maximum difference of 0.1 � 0.2� 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� over that period. However, for the
period 1980 � 2000 the deviations between DE200 and DE406 are below 0.01� 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 � around 1600, and he says that these deviations
are due to the inherent uncertainty of extrapolating the orbits beyond the
period of accurate observational data.The uncertainty of Pluto exceeds
1� before 1910 and after 2010, and increases rapidly in more remote past or
future.</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>With the <i>moon</i>, there is an increasing difference of 0.9�/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'>��������������� 1980 � 2000������� all
planets�� ��������������� <
0.01�, </span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;text-indent:35.4pt'><span
lang=EN-US style='font-style:normal'>1600 � 1980������� Sun � Jupiter��� ��������������� a few 0.1�,</span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt;text-indent:35.4pt'><span
lang=EN-US style='font-style:normal'>1900 � 1980������� Saturn � Neptune��������������� ��������������� a
few 0.1�,</span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
style='font-style:normal'>�� ������������ 1600 � 1900������� Saturn � Neptune��������������� ��������������� a
few �,</span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
style='font-style:normal'>��������������� 1750 � 2169 ������ Moon���� ��������������� ��������������� a few �.</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>� 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'>��� start date��������������� 23
Feb 3001 BC (28 Jan greg.)���� = JD��� 625360.5,</span></p>
<p class=MsoBodyTextIndent style='margin-bottom:6.0pt'><span lang=EN-US
style='font-style:normal'>��� end date����������� � 3 Mar 3000 AD���� ��������������� ��������������� = JD� 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.� The conversions to apparent geocentric
ecliptical positions were done with the algorithms and constants of the
Astronomical Almanac as described in the �Explanatory Supplement to the
Astronomical Almanac�. 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,� 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����������� 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������� new - old</span></p>
<p class=MsoNormal><span lang=EN-US>2000������� -0.00108</span></p>
<p class=MsoNormal><span lang=EN-US>1995������� 0.02448</span></p>
<p class=MsoNormal><span lang=EN-US>1980������� 0.05868</span></p>
<p class=MsoNormal><span lang=EN-US>1970������� 0.10224</span></p>
<p class=MsoNormal><span lang=EN-US>1950������� 0.15768</span></p>
<p class=MsoNormal><span lang=EN-US>1900������� 0.30852</span></p>
<p class=MsoNormal><span lang=EN-US>1800������� 0.58428</span></p>
<p class=MsoNormal><span lang=EN-US>1799������� -0.04644</span></p>
<p class=MsoNormal><span lang=EN-US>1700������� -0.07524</span></p>
<p class=MsoNormal><span lang=EN-US>1500������� -0.12636</span></p>
<p class=MsoNormal><span lang=EN-US>1000������� -0.25344</span></p>
<p class=MsoNormal><span lang=EN-US>0������������� -0.53316</span></p>
<p class=MsoNormal><span lang=EN-US>-1000����� -0.85824</span></p>
<p class=MsoNormal><span lang=EN-US>-2000����� -1.40796</span></p>
<p class=MsoNormal><span lang=EN-US>-3000����� -3.33684</span></p>
<p class=MsoNormal><span lang=EN-US>-4000����� -10.64808</span></p>
<p class=MsoNormal><span lang=EN-US>-5000����� -32.68944</span></p>
<p class=MsoNormal><span lang=EN-US>-5400����� -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������� -0.00108</span></p>
<p class=MsoNormal><span lang=EN-US>2010������� -0.01620</span></p>
<p class=MsoNormal><span lang=EN-US>2050������� -0.14004</span></p>
<p class=MsoNormal><span lang=EN-US>2100������� -0.29448</span></p>
<p class=MsoNormal><span lang=EN-US>2200������� -0.61452</span></p>
<p class=MsoNormal><span lang=EN-US>2201������� 0.05940</span></p>
<p class=MsoNormal><span lang=EN-US>3000������� 0.27252</span></p>
<p class=MsoNormal><span lang=EN-US>4000������� 0.48708</span></p>
<p class=MsoNormal><span lang=EN-US>5000������� 0.47592</span></p>
<p class=MsoNormal><span lang=EN-US>5400������� 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������� -1.71468</span></p>
<p class=MsoNormal><span lang=EN-US>5000������� -1.25244</span></p>
<p class=MsoNormal><span lang=EN-US>4000������� -0.63612</span></p>
<p class=MsoNormal><span lang=EN-US>3000������� -0.31788</span></p>
<p class=MsoNormal><span lang=EN-US>2100������� -0.06336</span></p>
<p class=MsoNormal><span lang=EN-US>2000������� -0.04212</span></p>
<p class=MsoNormal><span lang=EN-US>1900������� -0.02016</span></p>
<p class=MsoNormal><span lang=EN-US>1800������� 0.01296</span></p>
<p class=MsoNormal><span lang=EN-US>1700������� 0.04032</span></p>
<p class=MsoNormal><span lang=EN-US>1600������� 0.06696</span></p>
<p class=MsoNormal><span lang=EN-US>1500������� 0.09432</span></p>
<p class=MsoNormal><span lang=EN-US>1000������� 0.22716</span></p>
<p class=MsoNormal><span lang=EN-US>0������������� 0.51444</span></p>
<p class=MsoNormal><span lang=EN-US>-1000����� 1.07064</span></p>
<p class=MsoNormal><span lang=EN-US>-2000����� 2.62908</span></p>
<p class=MsoNormal><span lang=EN-US>-3000����� 6.68016</span></p>
<p class=MsoNormal><span lang=EN-US>-4000����� 15.73272</span></p>
<p class=MsoNormal><span lang=EN-US>-5000����� 33.54480</span></p>
<p class=MsoNormal><span lang=EN-US>-5400����� 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������� -2.544</span></p>
<p class=MsoNormal><span lang=EN-US>5000������� -1.461</span></p>
<p class=MsoNormal><span lang=EN-US>4000������� -0.122</span></p>
<p class=MsoNormal><span lang=EN-US>3000������� 0.126</span></p>
<p class=MsoNormal><span lang=EN-US>2100������� 0.019</span></p>
<p class=MsoNormal><span lang=EN-US>2000������� 0.001</span></p>
<p class=MsoNormal><span lang=EN-US>1900������� 0.019</span></p>
<p class=MsoNormal><span lang=EN-US>1000������� 0.126</span></p>
<p class=MsoNormal><span lang=EN-US>0������������� -0.122</span></p>
<p class=MsoNormal><span lang=EN-US>-500������� -0.594</span></p>
<p class=MsoNormal><span lang=EN-US>-1000����� -1.461</span></p>
<p class=MsoNormal><span lang=EN-US>-2000����� -5.029</span></p>
<p class=MsoNormal><span lang=EN-US>-3000����� -12.355</span></p>
<p class=MsoNormal><span lang=EN-US>-4000����� -25.330</span></p>
<p class=MsoNormal><span lang=EN-US>-5000����� -46.175</span></p>
<p class=MsoNormal><span lang=EN-US>-5400����� -57.273</span></p>
<h3 style='margin-left:0cm;text-indent:0cm;'><a
name="_Toc335142936"><span lang=EN-US>2.1.2.4����������� 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�k, Capitaine, and Wallace, �New precession expressions, valid for long
time intervals�, 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�000 BC or even earlier (the Chauvet
cave was painted in 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 � v. 1.77, test star was Aldebaran):</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Year������� 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� -26715" </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>-15000��� -2690"� </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>-10000����� -256"�� </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -5000��������� -3.95388"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -4000��������� -9.77904"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -3000��������� -7.00524"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -2000��������� -3.40560"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -1000��������� -1.23732"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�������� 0���������� -0.33948"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 1000���������� -0.05436"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 1800���������� -0.00144"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 1900���������� -0.00036"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 2000����������� 0.00000"�������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 2100���������� -0.00036"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 2200���������� -0.00072"������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 3000����������� 0.03528"�������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 4000����������� 0.59904"�������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�� 5000����������� 2.90160"�������
</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�10000��������� 76"���� </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�15001�������
227"��� </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�19000�����
2839"�� </span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>�20000�����
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������� 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������ 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�������� 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��� �������632.60532"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� -5000���������� -33.42636"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>��������� 0������������� 0.01008"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>��� 1000������������� 0.00972"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>��� 2000������������� 0.00000"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>��� 3000����������� -0.01008"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>��� 4000����������� -0.05868"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� 10000��������� -72.91980"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� 15000�������
-772.91712"</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt'><span
lang=EN-US style='font-size:10.0pt;'>� 20000�����
-3521.23488�</span></p>
<h3 style='margin-left:0cm;text-indent:0cm;'><a
name="_Toc335142937"><span lang=EN-US>2.1.3��� 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� in position, with the moon 0.5�</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�. 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;'>�Annual� 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�.</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�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�.
(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�/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� 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��� 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.� 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.�
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).� 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.� (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��� 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�� </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���� </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���� </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����� ��� </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�� </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��� </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��� </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��������������� </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����� </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���� </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�� </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���� </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���� </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����� ��� </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�� </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��� </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��� </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��������������� </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����� </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���� </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�������� 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��� 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� 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
(�aphelion�) of the lunar orbital ellipse or, for some people, its empty focal
point.� As seen from the geocenter, this
makes no difference. Both of them are located in exactly the same direction.
But the definition makes a difference for topocentric ephemerides.</span></p>
<p class=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 �Dark
Earth� rather than �Dark Moon� (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 �Dark Moon� 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�s observational skills and knowledge in celestial
mechanics clearly exclude the possibility of such an object. As a result of
confusion, the term �Dark Moon� was later given to the lunar apogee. However,
from the astrological symbolism of the lunar apogee, the expression �Dark Moon�
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�lle de
Gravelaine in her book �Lilith, der schwarze Mond� (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��� 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!� 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.� </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 �true� 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 �true� 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.� 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 � Swiss-Ephemeris-derived node��������������� ~ 0.1 arc second</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived node � Moshier-derived node������� ��������������� ~ 70�� 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��� 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.� 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.� 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�e moyen'
published by Chapront and Chapront-Touz�. </span><span lang=FR
style='font-size:10.0pt;'>And he adds: �Nous constatons que
m�me en utilisant ces 58 termes <i>correctifs</i>, l'erreur peut atteindre
0,5d!� </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 � Swiss-Ephemeris-derived apogee��������������� ~ 0.9 arc second</span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>JPL-derived apogee � Moshier-derived apogee�� ��������������� ~ 360�� arc seconds��������������� =
6�� 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.� 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.�
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 �Dictionnaire Astrologique�, 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 �Meridian� 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, �Meridian� 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��� 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 ����������� 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�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� that are closest to the sun and most distant
from the sun, resp. The former point is called the <i>�perihelion�</i> and the
latter one the <i>�aphelion�</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 �black stars� or the �black suns of the
planets�. 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;'>�</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 �perigee�, located at about 13 Capricorn, is
called the "Black Sun", the other one, in Cancer, is called the
�Diamond�.</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 �true�.</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 � 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 � 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,
�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�)</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;'>��������������� ��������������� </span><span
lang=FR style='font-size:10.0pt;'>Node����� ��������������� 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 ��������������� 3������������ ��������������� 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��� ��������������� 3������������ ��������������� 107�</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 ���� ��������������� -������������� ��������������� 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;'>Mars����� ��������������� 74���������� ��������������� 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��� ��������������� 330�������� ��������������� 1850�</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��� ��������������� 178�������� ��������������� 1530�</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�� ��������������� 806�������� ��������������� 6540� </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��������������� 225�������� ��������������� 11600�
(>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;'>�</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�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�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 � 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� 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.�������� 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� 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;'>� ��������������� 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'>������ ����������� 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 � 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;'>-������������� 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;'>-������������� for all named
asteroids also a long� (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�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�s on-line ephemeris system �Horizons� 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;'>-����� </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;'>-����� </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, �into infinity�,
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� (AA 1985 � 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� 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>�Ceres� -
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�������� 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�������� 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�.</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�������� �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 � 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
�hypothetical� 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�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.�
Some of them are perfect circles � 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�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.� 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.� 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.� 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.� 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 �Die Sterne� 3/1952, p. 70.
The article does not say which equinox they are referred to.� Therefore, we fitted it to the Astron
ephemeris which apparently uses the equinox of 1945 (which, however, is rather
unusual!).</span></p>
<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� 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 �paleoastronomer�.� The elements have been supplied by Christian
Woeltge, Hannover.� This planet is
interesting because of its bizarre orbit. It moves in clockwise direction and
has a period of 3600 years. Its orbit is extremely eccentric. It has its
perihelion within the asteroid belt, whereas its aphelion lies at about 12
times the mean distance of Pluto.� In
spite of its retrograde motion, it <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 �hypothetical� planet inside the orbit of Mercury (not
identical to the �Uranian� planet Vulkanus). Orbital elements according to L.H.
Weston. Note that the speed of this �planet� 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 �hypothetical� second moon of the earth (or a third one, after
the �Black Moon�) 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�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�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�s ephemeris either, which is obviously inconsistent
with Waldemath�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�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.� 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� -18� 0'52.3811��� 0�55' 0.0332�� -6.610753489</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
01.01.1790�� -8�42' 9.1113��� 1�42'55.7192�� -4.257690148</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
02.01.1810�� -3�49'45.2014��� 1�35'12.0858�� -2.488363869</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
02.01.1830�� -1�38' 2.8076��� 0�35'57.0580�� -2.112570665</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
02.01.1850��� 1�44'23.0943�� -0�43'38.5357�� -3.340858070</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
02.01.1870��� 9�17'34.4981�� -1�39'24.1004�� -5.513270186</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
02.01.1890�� 21�20'56.6250�� -1�38'43.1479�� -7.720578177</span></p>
<p class=MsoPlainText><span lang=EN-US>Nep-Lev
03.01.1910�� 36�27'56.1314�� -0�41'59.4866�� -9.265417529</span></p>
<p class=MsoNormal><span lang=EN-US> </span></p>
<p class=MsoPlainText><span lang=EN-US>� (difference in��� (difference in��
(difference in</span></p>
<p class=MsoPlainText><span lang=EN-US>� longitude)������� latitude)�������
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, �Studies in the Medieval Conception of Precession�, </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�. 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 �Age of Aquarius�.</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 � from a mere astronomical point of view � 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 � 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�msha</i>
means �part of a path�; the Hindi form of the word is <i>ayanamsa</i> with an <i>s</i>
instead of <i>sh</i>.) �</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 �
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>� </span><span lang=FR>9) <i>ayanamsha</i> = -3�22�, t0 = -100</span></p>
<p class=MsoNormal><span lang=FR>10) <i>ayanamsha</i>
= -4�46�, t0 = -100������������������������������� Spica at 29 vi 26</span></p>
<p class=MsoNormal><span lang=FR>11) <i>ayanamsha</i>
= -5�37�, t0 = -100� </span></p>
<p class=MsoNormal><span lang=FR> </span></p>
<p class=MsoNormal><span lang=EN-US>(9 � 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� +/- 20�, t0 = �100�����������������
Spica at 29 vi 14</span></p>
<p class=MsoNormal><span lang=EN-US>The
standard deviation was 1�08�</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�46�, t0 = �129���������������������������� 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�00 Virgo. As a result of �rigorous statistical investigation�
(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 �synetic vernal point� as:</span></p>
<p class=MsoNormal><span lang=EN-US> </span></p>
<p class=MsoNormal><span lang=EN-US>0) <i>ayanamsha</i>
= 24�02�31.36�� for 1 Jan. 1950�� with Spica at 29 vi 06'05" (without
aberration)</span></p>
<p class=MsoNormal><span lang=EN-US>(For the
year �100, this <i>ayanamsha</i> places Spica at 29 vi 07�32�.)</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�s zodiac and theirs was only
1�. But actually (if Mercier�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 �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�. 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�00� and Antares at 15sc00�17� around the year �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�.</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�, the latitude of the
island of Rhodos, which Hipparchus� 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� 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�
geographical latitude of 36�. 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� ��� 27 June �128 (jd
1674484)��� zePsc 29pi33�49���������������� Hipparchos</span></p>
<p class=MsoNormal><span lang=EN-US> </span></p>
<p class=MsoNormal><span lang=EN-US>(According
to Mercier�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� 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� � 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�13� for 27 June �128 (jd 1674484) and zePsc would be found at 29pi12�,
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�rya Sidd�nta</i>, the star <i>zeta Piscium</i> (in
Sanskrit <i>Revat�</i>) has almost the same position as in the Greek sidereal
zodiac, i.e. 29�50� in Pisces. On the other hand, however, Spica (in Sanskrit <i>Citra</i>)
is given the longitude 30� Virgo. This is a contradiction, either Spica or
Revat� 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�rya Sidd�nta </i>is used to compute an <i>ayanamsha</i>
for the date of Hipparchus, it will turn out to be �9�14�01�, which is very
close to the Hipparchan value. The same calculation can be done with the <i>�rya
Sidd�nta</i>, and the <i>ayanamsha</i> for Hipparchos� date will be �9�14�55�.
For the <i>Sidd�nta Shiromani</i> the zero point turns out to be Revat� 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� is also used by the so-called <i>Ush�shash�
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�39�39.46��������������� 1 Jan. 1900��������������� Ush�shash������� </span></p>
<p class=MsoNormal style='margin-left:70.8pt;text-indent:35.4pt'><span
lang=EN-US>zePsc (Revat�) 29pi50� (today),
29pi45� (Hipparchus� 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�shirw�n, in the year 556, the astronomers of Persia met to correct their
astronomical tables, the so-called <i>Z�j al-Sh�h</i>. These tables are no
longer extant, but they were the basis of later Arabic tables, the ones of
al-Khw�rizm� 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>�</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 �the movement of Jupiter, the calendar marker of the night sky,
in its relation to the Sun, the time keeper of the daily sky�. Such theories
were of course wrong, from the point of view of today�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������������� ��������������� 18 Mar 564, 7:53:23 UT (jd /ET 1927135.8747793)��� Sassanian</span></p>
<p class=MsoNormal style='margin-left:283.2pt;text-indent:35.4pt'><span
lang=FR>����
</span><span lang=EN-US>zePsc� 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�rizmian tables, the S�rya Siddh�nta, and the Ush�shash� <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 �rounding� 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 �K0s�. 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 �K0a�. </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, �Numerical expressions for precession formulae and
mean elements for the Moon and the planets�, in: Astron. Astrophys. 282,663-683
(1994).��� </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� 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�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 �Lahiri ayanamsha�. 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� (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�50�). 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 (�Lahiri� ayanamsha) was originally
introduced in 1955 by the Indian <i>Calendar
Reform Committee</i> (23�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 �mean ayanamsha� is misleading though. The value 23�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�15' 00".658���������������������������� 21 March 1956, 0:00 TDT������� 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�59�04 in the year 2000, and 179�59�08 in
1900. In the year 285, when the star was conjunct the autumnal equinox, its
position was 180�00�16. It was in the year 667 AD that its position was
precisely 180�. 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�, 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 �mean ayanamsha� is given as 22�26�45�.50 in 1900, whereas the
official value is 22�27�37�.76. The idea behind this modification was obviously
that he wanted to have the star exactly at 180� for recent years, whereas with
the standard definition the star is �wrong� 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� (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, �</span><span
lang=EN-GB>The Star Zodiac of Antiquity�, 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 � in analogy with the tropical ecliptic and the house circle �
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 (�Solar Fire�), who took them over from Robert
Hand�s Program �Nova�:</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: �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.�</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.���� 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.���� the Greek-Arabic-Hindu zodiac with the zero
point between 10 and 20� east of <i>zeta Piscium</i>:</span></p>
<p class=MsoNormal style='margin-left:18.0pt'><span lang=EN-US>a) Hipparchus, b) Ush�shash�, c) <b>Sassanian</b></span></p>
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;'><span lang=EN-US>3.���� 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 � 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� 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� 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 � after the definition of the zero point � 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)���� <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 � 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�. 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� 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� 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�02�31.36� + d(t</span></i><span lang=FR>)</span></p>
<p class=MsoNormal><span lang=EN-US>24�02�...
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>�������� <i>Longitude</i>�������
<i>Latitude</i></span></p>
<p class=MsoPlainText><span lang=EN-US>01.01.-5000� 2 sag 07'57.7237�� -4�41'34.7123 (without aberration)</span></p>
<p class=MsoPlainText><span lang=EN-US>01.01.-4000� 2 sag 07'32.9817�� -4�49' 4.8880</span></p>
<p class=MsoPlainText><span lang=EN-US>01.01.-3000� 2 sag 07'14.2044�� -4�56'47.7013</span></p>
<p class=MsoPlainText><span lang=EN-US>01.01.-2000� 2 sag 07' 0.4590�� -5� 4'39.5863</span></p>
<p class=MsoPlainText><span lang=EN-US>01.01.-1000� 2 sag 06'50.7229�� -5�12'36.9917</span></p>
<p class=MsoPlainText>01.01.0����� 2 sag 06'44.2492�� -5�20'36.4081</p>
<p class=MsoPlainText>01.01.1000�� 2 sag 06'40.7813�� -5�28'34.3906</p>
<p class=MsoPlainText>01.01.2000�� 2 sag 06'40.5661�� -5�36'27.5619</p>
<p class=MsoPlainText>01.01.3000�� 2 sag 06'44.1743�� -5�44'12.6886</p>
<p class=MsoPlainText>01.01.4000�� 2 sag 06'52.1927�� -5�51'46.6231</p>
<p class=MsoPlainText>01.01.5000�� 2 sag 07' 4.8942�� -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)���� <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)���� <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>
� for Fagan/Bradley, e.g., this would be the ecliptic of 1950 � by a correct <i>coordinate
transformation</i> and then subtract 24.042�, 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�� -5�36' 4.0652���� (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 �eternal� 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)���� 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)��� 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)���� 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)��� 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)���� <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
�average ecliptic�. 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
�long-term mean Earth-Sun plane� 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�, 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)���� <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�44� 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. ������� 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.
�Apparent� 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 �The details of coordinate
transformation�, 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 �effects�
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. ������� 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�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�. 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.� 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;'>�<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;'>�</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;'>�</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;'>�</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;'>�</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;'>�<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;'>�</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;'>�</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;'>�<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;'>�</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;'>�</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;'>�<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;'>�<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;'>�<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;'>�<span style='font:7.0pt "Times New Roman"'>
</span></span><span lang=EN-US>Contrast
between studied object and sky background <br>
The observer�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�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�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�s eye. This result in the astronomical
extinction coefficient (AEC: k<sub>tot</sub>). As this is a complex
environment, it is sometimes �easier� 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�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.� 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 �morning last� 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 �morning lasts� of Mars and
following �second heliacal risings�. The function only provides the heliacal
rising of� 25 Nov. 1957 and the next
ordinary heliacal rising in its ordinary synodic cycle which took place on 11
June 1960.</span></p>
<p class=MsoNormal 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.� (Whoever does not believe me, please read
the article by H.B. Curtis listed under �References�.)� 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�s criterion [1928], Hoffman�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. ��� 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.�������� 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�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�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 (�topocentric�) 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 �topocentric� (i.e. birth-place-related) than any other house
system. (c.f. the misunderstanding with the �birth place system�.) The
�topocentric� 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 �house� 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 �sectors� (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 (�) 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 � 3, 9 � 12, 19 � 21, 28 � 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 �Amphora house system�. </span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>- by Georg Goelzer (Switzerland) under the name �Ich-Kreis-H�usersystem�
(�I-Circle house system�).. </span></p>
<p class=Textkrper-Einzug><span lang=EN-US style='font-size:10.0pt;'>Krusinski
defines the house system as �� 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.�
(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 �stolen� 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 (�Algoritmy noveho systemu
astrologickych domu�). 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�s
first publication on the house system happened in spring 1997 in �Konstelace�
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 �</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�
Pogorzelica at cost of the Baltic Sea.� </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� and floppy disks with house tables for latitudes 0-90�. In
1996, he offered his program code to Astrodienst for implementation of this
house system into Astrodienst�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 �Der Ich-Kosmos�, 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 �9 April 1993� 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�
of �Krusinski houses�, 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 �discovered� and published by�
Goelzer, but that Pisa and Krusinski also �discovered� 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� "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� -
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.����� 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)��� </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)��� </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)��� </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.����������� 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�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 �wrong� 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�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.�������� 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 �traditional� 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 �midnight� 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 �hand calculation� 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.�������� 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�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 �midnight� and �midday� 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�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.����� �������� </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 (�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 � 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 � 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;'>��� year����������
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;'>� -3000���������������� 3</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>� -2000�� ����������
�� 2</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>� -1100��������� ���
�� 1</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>� -1001��������� ���
29</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>��� -900��������� ���
-45</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>��� -800��������� ���
-57</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>��� -700��������� ���
���� -696� (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;'>��� -500��������� ���
-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 ������� 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 ��������� 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 ��������� 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 ������� 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 ������� 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 ������� 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 ������ ���������������������� 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 ������ �������������������� 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 �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;'>��� year����������
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;'>� -3000������������������ -4127</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>� -2000�� ����������
���� -2130</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>� -1000��������� ���
���� -760</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�������� 0������������� -20</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1000������������� -30</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1600�������������� 10</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1619������������� 0.5</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1620���������������� 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;'>��� year����������
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;'>� -3000���������� 2900</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�������� 0���������� 1200</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1600�������������� 29</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1619�������������� 60</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1620�������������� -0.6</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1700�������������� -0.4</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1800�������������� -0.1</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1900�������������� -0.02</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1940�������������� -0.001</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 1950 ���������������0</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 2000��������������� 0</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 2020��������������� 2</span></p>
<p class=Textkrper-Einzug style='margin-bottom:0cm;margin-bottom:.0001pt;'><span lang=EN-US style='font-size:10.0pt;'>�� 2100������������� 23</span></p>
<p class=Textkrper-Einzug><span
lang=EN-US style='font-size:10.0pt;'>�� 3000���������� -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, �Five-millennium Catalog of Lunar
Eclipses �1900 to +3000�, 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, �Historical
Values of the Earth�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�, 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.������� 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 ��������������� (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� (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� 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. ������� Swiss Ephemeris Functions</span></a></h1>
<h2 style='margin-left:0cm;text-indent:0cm;'><a
name="_Toc335143017"><span lang=EN-US>9.1�������� 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();��� </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";'>�* 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>;����������� </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();���������� </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();��� </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();���� </span></p>
<h4 style='margin-left:0cm;text-indent:0cm;'><span
lang=EN-US style='font-family:"Courier New";'>����� </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();��� </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";'>�* 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();� </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>�* 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>�* 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� * 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>�* 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>�* 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>�* 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>�* 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>�* 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>�* 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� </span></p>
<p class=MsoPlainText><span lang=EN-US>�* 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>�* 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�������� 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� 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 �sees� when it passes close by or �through� 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�, 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�) 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.� 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,� 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;'>#�� 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;'>#�� 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;'>� </span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>1��� Ceres������� # 913 km� 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��� Pallas������ # 523 km� 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��� Vesta������� # 501 km� 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�� Hygiea������ # 429 km� 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� Davida������
# 324 km� 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� Interamnia��
# 338 km� "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;'>����������������� #�������� 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�� Cybele������ # 308 km� 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�� Europa������ # 292 km� 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�� Sylvia������ # 282 km� </span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>451� Patientia���
# 280 km� 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�� Euphrosyne�� # 270 km� 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�� Eunomia����� # 260 km� 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� Bamberga����
# 252 km� 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��� Juno�������� # 248 km� 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�� Psyche������ # 248 km�
"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;'>#�� 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;'>#�� 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;'>#�� 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;'>#�� 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;'>#�� (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;'>#�� 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�������� # 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��� # 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;'>����������������� # 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������ # 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������ # 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;'>����������������� # 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;'>����������������� # 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���� # 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;'>������������� ����# 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;'>����������������� # 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�������� # 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� Eros��������
# 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������ 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� Hungaria����
# 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;'>�</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>8��� Flora������� # 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�� Phocaea����� # 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� Koronis�����
# 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� Eos���������
# 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�� Themis������ # 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� Hilda�������
# 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� Thule�������
# 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� Hector������
# 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;'>����������������� # 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� Achilles����
# 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
�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� 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� # 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;'>����������������� # 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� Hidalgo�����
# 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;'>����������������� # 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���� # 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;'>����������������� # 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������ # 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;'>����������������� # 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������ # 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;'>����������������� # 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�� ����# 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;'>����������������� # 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��� # 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;'>����������������� </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 ��# 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�� Isis�������� # 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;'>����������������� # 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� Cupido������
# 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;'>����������������� # 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���� # 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;'>����������������� # 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����� # 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;'>���� �������������# 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;'>����������������� # 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�������� # 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;'>����������������� # 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������ # 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;'>����������������� # 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� Admete������
# 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;'>����������������� # "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������ # 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;'>����������������� # 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���� # 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;'>����������������� # 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;'>����������������� # 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;'>����������������� # 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;'>����������������� # 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��� Astraea����� # 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��� Hebe�������� # 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��� Iris�������� # 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��� Flora������� # 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��� Metis������� # 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�� Hygiea������ # 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�� Irene������� # 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�� Psyche������ # "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�� Fortuna����� # 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�� Diana</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>170� Maria</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>234� Barbara</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>375� Ursula������
</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=EN-US style='font-size:9.0pt;'>412� 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� 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� Sophrosyne��
# 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� Arete�������
# 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� 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� Sophia������
# 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� Aletheia����
# 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� Sapientia���
# 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� Desiderata</span></p>
<p class=MsoPlainText style='margin-left:1.0cm;line-height:9.0pt;'><span lang=IT style='font-size:9.0pt;'>433� 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� 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� 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�������������� </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�������� # Indian 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;'>1388
Aphrodite��� # 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������� # 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�� # 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�� Melpomene��� 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�� Kalliope���� 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�� Thalia��
����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�� Euterpe����� 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�� Urania������ 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�� Polyhymnia�� 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�� Erato������� 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�� Terpsichore� 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�� Klio�������� 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�� Fortuna����� # 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� 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������� # 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� 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� 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)���������� 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������������������������ 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)���������� 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������������������ 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���������� 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)��������� 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��� 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����������������������������� 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������� 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����������������� 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������� 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������� 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����� 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������������� 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����������� 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����������������� 101</span></p>
<p class=MsoPlainText style='text-indent:1.0cm'><span lang=EN-US
style='font-size:9.0pt;'># Plants, trees, animals��������������� 63</span></p>
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