One of the problems with this fix, however, was that it only worked in hindsight: Ptolemy could explain previous instances of retrograde motion, but not make predictions about when or where we should expect to see them again. And of course, there was no suggestion of a mechanism that would be responsible for such odd behavior... until a chap by the name of Copernicus, you might have heard of him, came up with a revolutionary new way to understand the problem: the apparent retrograde motion of the planets can be understood as an illusion if we simply assume that we are not the center of the universe. If we, along with the planets, are rotating around the sun, we can go right back to the simplicity of one perfect sphere, and retrograde motion could then simply be understood as a function of the change in our position along our orbit relative to the change of the position of other planets along their own orbits. Problem solved!
Or if that seems needlessly difficult to grasp (and remember we haven't gotten into the math Copernicus used!), Brian Cox has a nice little demonstration of this revolutionary new vision that seems blindingly obvious in retrospect, but which took the genius of someone like Copernicus to think it for the first time: