If the Earth Were the Center of the Universe and the Moon

Essay

If the earth were the center of the universe and the Moon, planets, and Sun all moved around the earth, logic would say that all of these celestial objects should move in the same direction across the sky, and relative to the celestial background. The Sun and Moon both follow this pattern, but the other planets have periods of retrograde motion. How did the Ptolemaic model explain retrograde motion and how is it more easily explained by the heliocentric model.