Planet is Greek for wanderer. Against the stars, a planet drifts one way, stops, runs backwards for weeks or months, then turns forwards again. Ptolemy explained it with a small circle, the epicycle, riding on a large one. Later, Copernicus explained why it works: the small circle is the Earth’s own orbit, and seen from a moving Earth, every planet is two turning circles added together.

Each loop is a retrograde, the moment the Earth overtakes the planet or the planet overtakes the Earth. The thin rings are the two circles that draw the pattern, and the colored stroke is the planet itself.

Earth and Mars. Red Mars seen from blue-green Earth loops fifteen times in thirty-two years. Turn the question around, the Earth seen from Mars, and you get the same figure turned half a circle, looping at the same moments.