Celestial Mechanics - A Historical Perspective
The Geocentric Solar System
(Ptolemy):
-
The Earth is at the center of the Solar System.
-
The Sun and planets revolve around the Earth.
-
The Sun and planets move on perfect circular orbits.
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.