Ptolemy's model of the solar system explained the apparent changes in speed and direction of the planets primarily through the use of epicycles. In this model, planets were thought to move in small circles (epicycles) along the larger circular paths (deferents) around the Earth. This allowed for a more accurate prediction of the observed movements, including retrograde motion, as the planets appeared to move backward at certain points in their orbits relative to the stars. Therefore, the correct response is:
The planets spun on epicycles.