The retrograde motion of the planets is well modelled by both the Ptolemaic system and the Copernican system, and by the other models.
But the Copernican system explains it more simply because, for example, Mars's retrograde motion is caused simply when Mars is overtaken by the Earth, which goes more quickly round the Sun.
Thus an observer on the Earth sees Mars appearing to go 'backwards' on the ecliptic around the time of closest approach (opposition). This can be easily demonstrated by assuming simple circular orbits.
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Copernicus explained the retrograde motions of the planets by proposing that the Earth and the other planets revolve around the Sun in circular orbits. He suggested that the appearance of retrograde motion was a result of the varying speeds at which the planets orbited the Sun.
A major flaw of the Ptolemaic model was its complexity in explaining the retrograde motion of planets. Ptolemy introduced the concept of epicycles and deferents to account for this, which made the model overly complicated and not as accurate as later models, such as the heliocentric model proposed by Copernicus.
If you mean "retrograde rotation", they are Venus and Uranus.
Ancient astronomers found it difficult to explain apparent retrograde motion because they believed the Earth was at the center of the universe and all celestial bodies revolved around it in perfect circles. Retrograde motion conflicted with this geocentric model, leading to complex explanations involving epicycles and deferents. It wasn't until Copernicus proposed a heliocentric model that retrograde motion could be better understood as an illusion caused by the relative speeds and orbits of planets.
Copernicus proposed a heliocentric model, where planets revolve around the sun, while Ptolemy's geocentric model placed Earth at the center of the universe with planets orbiting around it. Copernicus' model helped to explain retrograde motion more simply than Ptolemy's epicycles.