Explain, according to both geocentric and heliocentric cosmologies, why we see retrograde motion of the planets.

Because of different orbital speed

Explanation:

Retrograde Motion: Retrograde motion is the apparent movement of the planet in the sky where it appears to move backwards in their orbit even though it is moving forward. It should be noted that in reality it moves forward in its orbit.

This apparent motion is seen because of the relative position of Earth and Planet. The orbital speed of Earth and planets are different which results in this retrograde motion. Even in the geocentric model this retrograde motion was observed because. Although the Earth was considered stationary different planets showed retrograde motion because of their respective orbital speed which was not same for all.