Summarize the development of the greek geocentric model through ptolemy. how did the ptolemaic model account for apparent retrograde motion?

He assumed that planets move by making small circles, the epicircles, and making small circles (epicircles) they move along a larger circle, the deferent. Ptolemy called that Retrograde Motion.

Explanation:

In Ancient Times, Ancient Greek wise men, like Pythagoras and Aristotle each one at his own turn devised a cosmology to explain how the Heavenly bodies, i.e. planets, stars, move and behave in the universe.

Claudius Ptolemy had also developed a mathematical astronomical system assuming the Earth as the center of the universe. Moreover to that, our planet would be also a steady one. By that time, the Greek mathematician and polymath from Alexandria, registered his works in a book called Planetary Hypothesis, and on other work named Almagest, i.e The Great Book.

He  also assumed that planets move by making small circles,  epicircles, and making small circles (epicircles), they move along a larger circle, the deferent. Ptolemy called that Retrograde Motion.

Ptolemy in his book stood that the orbits of all heavenly bodies, moved in perfect circular orbits. Orbits that Newton, and Kepler much later proved through theoretical mathematical models working with proven laws such as gravitation, it to be elliptical.

Geocentric Model lasted 1500 years, and Kepler, and Copernicus and Galileo faced some resistance to contradict the Ptolemy Model. Mainly because:

•It was stood by many christians Joshua 10:13 "And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day." What misled many people to suppose to Geocentrism to be biblical prescribed.

•European Universities had been teaching Geocentric Models since the Middle Ages, and Ancient Times what defined a Cosmology like that. Despite the fact Heliocentrism was not a new thing

•Naked eye observation was reasonably accurate in some points to predict a position of Heavenly body.

landlessness of ordinary people

^^something like that^^^