In the geocentric Ptolemaic model that described the apparent motions of planets against the background sky as viewed from a stationary Earth, at what distance with respect to its deferent is a particular planet on its epicycle when it appears to stop moving for a short period in its motion against the background?

Question

Quizplus · Accepted Answer

In the Ptolemaic model, a planet appears to stop moving against the background sky (a phenomenon known as retrograde motion) when it is at the points of its epicycle that are closest to the Earth, which means it is close to the deferent. This is because the planet's apparent motion is the result of both its movement on the epicycle and the epicycle's movement on the deferent. When the planet is closest to Earth, the combination of these motions makes it appear to stop and then move backward.

In the Geocentric Ptolemaic Model That Described the Apparent Motions