The Ptolemaic model is built on concentric, circular shells moving about the earth as the center of the system. This fits the observational data well — the constellations, fixed in their arrangement, circle us each night in an orderly, predictable rotation about the Pole Star. The implication is a spherical shell of stars.

The planets — sun, moon, Mercury, Venus, Mars, Saturn, Jupiter — change position in the stellar field but on their own predictable paths, along the ecliptic and with regular periodicity. The implication here is of a spherical shell for each planet, moving within the stellar sphere. Thus the positions of the planets were modeled, in two dimensions, as a series of concentric circles about the earth.

Although the stars and planets can be seen to rotate around the earth, the difficulties arise because their positions don’t quite match with a perfect circle. When a simple circle failed to predict the exact location observed, the astronomer adjusted the model, adding geometric techniques to match the observed motion of the planet. The epicycle, for instance, would easily provide a more complex motion by simply adding another circular rotation.

The epicycle was a powerful tool for fitting such motions, and indeed quite elaborate observed motions can be matched with the proper combinations of epicyles, radii, periodicities, and eccentrics. By adjusting the geometical parameters, the motion can be made to loop, fitting model to observation.