On Epicycles and Ellipses

The ancient Greek astronomers invented models of the Solar system based on epicycles. The most famous of these astronomers was Ptolemy who lived in the second century AD, and it is his model that we will consider. By the fifteenth century the planets were not in the positions in the sky predicted by his model, and due to the observations of Tycho Brahe and the work of Copernicus, Kepler and Newton, a new model of the solar system was constructed based on ellipses. In this short note we will consider the differences between the two types of models and show that the differences in their prediction is not due to the reasons often stated.