This Demonstration shows the trajectory of a planet (orange disk) around an observer (blue circle) according to the epicycle-deferent model. The large gray circle is the deferent and the smaller gray circles are the epicycles. The deferent rotates at a constant speed, and each epicycle revolves at a uniform velocity around a point on the deferent or another epicycle. By adjusting the orbital radius, rate of revolution, and initial position of each epicycle, countless orbits can be obtained that are not observed in reality.

Both Claudius Ptolemy and Nicolaus Copernicus were convinced that the orbits of planets and stars could be described by the epicycle-deferent model used since antiquity. Besides being able to accurately predict the movement of planets and stars, this model also allows for a multitude of orbits that are not observed in the universe, such as square and triangular trajectories.