The Problem of Retrograde Motion 

Before the glare of streetlights swallowed the night sky, humanity was much more keenly aware of the cycle of changes exhibited there. The monthly path and phases of the moon, along with the yearly cycle of the Sun's risings and settings were noted, tracked and followed for their religious and economic (i.e. agricultural) significance. People also tracked the motion of the planets - the bright points of light that wandered in less obvious cycles across the background of fixed, twinkling stars. 

One particularly baffling aspect of planetary wanderings were the periods of retrograde motion. A planet such as Mars would spend much of the year moving slowly eastward against the background of fixed stars. Then, to everyone's surprise, it would change direction and slide westward for a couple of months or so before stopping again and returning to its easterly path. This is retrograde motion (retro meaning backward). The image below traces the positions of the planet Mars as it executed a retrograde loop in 1995.

As you might imagine, these cosmic loop-de-loop's seemed pretty weird to ancient astronomers. The retrograde motion of the planets was particularly bothersome to the ancient Greek philosophers/scientists. They had established the tradition of demanding a physical model for whatever they were studying. They wanted something they could picture in their heads that was logical and self-consistent. As for the planets, the Greeks wanted a model for the solar system that could replicate all the motions seen in the sky, including the wacky retrograde loops. Most Greeks believed the Earth - and not the Sun - lay at the center of the solar system. While the Greeks did manage to develop an Earth-centered model for the solar system, it was not simple, but had little orbits laid on top of bigger ones. That bothered some aesthetically minded astronomers who believed that Nature in both appearance and plan should be beautiful and therefore simple. Developing a simple picture for the real paths of planets, that put the Sun at the solar system's center, was a job that waited almost two millennia.