Celestial Mechanics - A Historical Perspective 

The Geocentric Solar System (Ptolemy): Problem: Why do some planets show retrograde motion?

Solution: Epicycles! (Orbits upon orbits)

But to accurately account for the planets motions, the epicycles need epicycles! Eventually the Ptolemaic model needed 16 levels of epicycles, plus off-center orbits for the Sun and planets...

...and it still didn't work very well.

We need a better model!

Development of the Heliocentric Solar System

Copernicus (1532): Earth and Planets orbit the Sun.

This model naturally accounts for retrograde motion in a simpler manner:

But Copernicus still used perfect circles, and there were discrepancies between the model and observations of the planets. To alleviate this, he had to fall back to adding epicycles.

Animated gifs of retrograde motion from the Dept of Physics and Astronomy, University of Tennessee, Knoxville.