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 GeoAstro Applets |
 Astronomy |
 Chaos Game |
 Java |
 Miscel- laneous |
Heliocentric
and geocentric motion of the bright planets
At the left the applet is simulating the Copernican heliocentric model of the solar system,
whereas the simulation at the right is showing the motion from the geocentric point of view,
propagated by Tycho Brahe (Tychonic model).
Both models are equivalent, and both of them decscribe the phases of the Planets correctly.
| 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 |
The Ptolemaic Model
The phases of the planets as seen by Ptolemy's model are not correct.
| Ptolemy |  |
 |
 |
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| Copernicus | |
 |
 |
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| 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:
2023, Oct 04