Ptolemy (87-150 AD) believed that the Earth is fixed, and only the other (then known) planets circle the sun. But peculiar trackings puzzled him. As the planet Mars is tracked, it arcs across the sky; but at one partial tracking, it seems to go backward, then loops around and goes forward. Ptolemy allowed for these partial trackings by calling them "epicycles" on the CYCLE of Mars around the sun. But, over centuries, the record accrued more and more epicycles. And it didn't seem possible to predict a new epicycle.

Later, Copernicus (1473-1543) promulgated the notion -- first set forth by Pythagoras (c.580-496), and apparently independently by Hipparchus (190-120 BC) -- that Earth is also a planet circling the sun. With this notion, it's easy to explain the EPICYCLE and to predict its next occurrence.

As Earth circles along, it appears to "catch up" with Mars on the "sky-racetrck". As Earth seems to pass Mars, Mars appears to go backward. Then, when Earth is "more ahead", Mars loops forward.

You can observe the same tracking here on Earth on the highway. If some one else is driving and you are a passenger, and the driver catches up with and passes another car, in the rear view mirror the passed car will appear to go backwards, then start to go forward again: an apparent "epicycle".

With present electronic technology, it should be possible to rig up a graphing system to record this and display it to others.

CHALLENGE!