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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 planet phase
venus phases
venis phase phase
synodic period
Copernicus planet phase greatest elongation
opposition
greatest elongation
synodic period


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).

epicycle
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.
ptolemy equant
mercury
                  heliocentric mercury
                  geocentric
Mercury: 2008, Jan 1 - Mar 28
elliptic orbit (e=
0.2056)
retrograde Jan 30 - Feb 19
Mercury according to Ptolemy,
assuming a circular orbit.

 
difference

Diagrams: geocentric longitude and latitude



venus
venus
Venus: 2009, Jan 1 - Jun
elliptic orbit (e=
0.0068)
retrograde Mar 8 - Apr 18

Venus according to Ptolemy,
assuming a circular orbit.


venus

Diagrams: geocentric longitude and latitude




Mercury:

Mercury

Venus:

Venus


Mars:

Mars

Jupiter:

Jupiter

Saturn:

Saturn


Web Links

Venus and the pentagram

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

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Updated: 2014, Dec 05