Figure: A comparison of heliocentric and geocentric solar systems

Further explication

1. Image 1 Caption: The image shows a epicycle model for a planet in a geocentric solar system model. An epicycle model consists of a deferent (a large circle) and an epicycle that carries the planet directly.

   The motion of the planet on the epicycle is uniform circular motion and motion of the epicycle center on deferent is also unform circular motion.

   The compounded motion of the planet shown by the blue curve in the image is NOT uniform circular motion.

   Ancient Greek astronomers and almost all their heirs in the western Eurasian tradition of astronomy up to circa 1600 found non-uniform motions too difficult to treat mathematically by any other means than compounded uniform uniform motions.

2. Note, the compounded motion gives apparent retrograde motion which is when planet reverses for a short period its main direction of the motion.

   Planets do show apparent retrograde motion which is easily explained in the heliocentric solar system model. The planets do NOT reverse in 3-dimensional space, but merely in angle as seen from the Earth. Note, in astronomy, "apparent" does not mean false or seeming. It means as seen from the Earth.

   For the explication of apparent retrograde motion for the heliocentric solar system model, see File: Celestial sphere file: apparent_retrograde_motion.html

3. The mathematical astronomers made use of the epicycle models with many variations from the simplest kind for geocentric solar System. Epicycle models allowed the calculation of ephemerides (tables of astronomical predictions). Mathematical astronomers have always be tasked with producing ephemerides.

   However, many different epicycle models could all make the same accurate predictions to within ancient accuracy.

   The upshot was that some people interested in astronomy denied that any epicycle model was physically real and they were just non-unique decompositions of the planetary motions.

   Strict Aristotelians believed that Aristotelian cosmology was physically real qualitatively, but nature was too complex to use it for mathematical cosmology

4. Note, the classical planets for which epicycle models were used are in traditionally aussed order going outward from the Earth ⊕ are:
   Moon ☽, Mercury ☿, Venus ♀, Sun ☉, Mars ♂, Jupiter ♃, Saturn ♄.

   Note also, epicycle models are needed not just to account for apparent retrograde motion, but also all other deviations from simple unifrom circular motion by the planets. Thus, epicycle models were used for Sun and Moon even though they do not show apparent retrograde motion.

5. The most famous builder of epicycle models is Ptolemy (c.100--c.170 CE) whose complete geocentric solar system model is described in Ptolemy file: ptolemy_system.html.

   In fact, Ptolemy was such a clever builder of epicycle models that he must have understood the non-uniqueness problem, but perhaps he hoped that epicycle models were actually real and you just had to find the right one and that his system was close to being the right one.

   

6. Image 2 Caption: Image 2 shows a cartoon comparison of the heliocentric solar system model geocentric solar system model.

7. The images are not to-scale. In fact, geocentric models could not be put to-scale by the builders of epicyle models since they did not know distances to the classical planets, except that they did have a good distance for the Moon of about 60 Earth radii.

8. Ptolemy did mention that non-geocentric models were geometrically possible, but he believed they were physically unrealistic. He believed the Earth had to be at rest and being at rest was a distinct state from being in motion. He did not have a modern understanding of relative motion. In this regard though not in others, Ptolemy followed Aristotelian cosmology.

9. Aristarchos of Samos (c.310--c.230 BCE), another ancient Greek astronomer, is mentioned by the ancients as having proposed a heliocentric solar system model, but that is about all we do know. It is a reasonable guess that he did so for the same reason Nicolaus Copernicus (1473--1543) did 18 centuries later. However, Copernicus justly gets the credit for the heliocentric solar system model because he left in the historical record a strong argument for it and Aristarchos did not succeed in doing this.