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Heliocentric and
geocentric motion of the bright planets
| Planet | Sid. Orbital period |
Synodic period |
Multiple of syn. per. |
Multiple of sid. year |
Gap |
Eccentricity |
Orbital
Inclination
° |
| Mercury |
87.96934 d |
115.8776 d |
3 syn. per.
347.633 d
|
1 trop. year
365.25636 d
|
17.62 d 17.4° |
0.2056 |
7.004 |
| Venus |
224.70069 d | 583.9206 d | 5 syn. per. 2919.603 d |
8 trop. years
2922.051 d
|
2.45 d 2.4° |
0.0068 | 3.394 |
| Mars | 686.960 d | 779.9617 d |
7 syn. per. 5459.732 d |
15 trop. years
5478.845
d |
19.11 d 18.8° |
0.0935 | 1.850 |
| Jupiter |
4333.2867 d | 398.8781 d | 11 syn. per. 4387.659 d |
12 trop. years
4383.076
d |
-4.58 d -4.5° |
0.0489 | 1.308 |
| Saturn | 10756.1995 d | 378.0956 d | 28 syn. per. 10586.677 d |
29 trop. years
10.592.434
d |
5.76 d 5.7° |
0.0565 | 2.488 |
| Earth |
365.2564 d | 0.0167 |
0 |
| Ptolemy
explained the retrograde
motion of the planets by his
epicycle theory: the planets are assumed to move around a small circle (epicycle e), the center of which moves along a larger circle (deferent D). Both circles rotate counterclockwise and are roughly parallel to the Earth's plane of orbit (ecliptic). |
 |
| To improve the
agreement with observational data Ptolemy introduced the
concept of the equant: The equant
point (E) and the Earth are equidistant on either side of the
deferent
center (X). The center of the epicycle is rotating on the deferent
circle uniformly with respect to the equant. |
 |
 |
 |
| Mercury: 2008,
Jan 1 - Mar 28 elliptic orbit (e=0.2056) retrograde Jan 30 - Feb 19 |
Mercury
according to Ptolemy, assuming a circular orbit. |
Diagrams: geocentric longitude and
latitude
 |
 |
| Venus: 2009,
Jan 1 - Jun elliptic orbit (e=0.0068) retrograde Mar 8 - Apr 18 |
Venus according to
Ptolemy, assuming a circular orbit. |
Diagrams: geocentric longitude and latitude
Mercury:
Venus:
Mars:
Jupiter:
Saturn:
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The Origins of the
Pentagram and Hexagram Venus: Umlaufbahn und Resonanzen, Venus-Pentagramm (wikipedia) Venus, the Rose & the Heart Epicycle and Deferent Applet Retrograde Motion Ptolemy's Model Ptolemy's Epicycle Ptolemaic System Simulator Ptolemaic Model Applet Epicycloids and Hypocycloids (Eli Maor, PDF) page 9: illustration "The motion of Saturn Jupiter and Mars in respect of the Earth |
Updated:
2008, Nov 25