How did the Ptolemaic system explain retrograde motion of the planets?

The Ptolemaic system explained the retrograde motion of planets—the apparent brief reversal of a planet's path as viewed from Earth—by utilizing an epicyclic model.1

In this geocentric framework, each planet was modeled as revolving uniformly along a smaller circular path called an epicycle. The center of this epicycle simultaneously revolved around Earth along a larger circular path known as a deferent. Because one half of the epicycle’s rotation moved in the opposite direction to the general motion of the deferent, the combined path caused the planet to appear to slow down or reverse its direction when it reached the point in its orbit closest to Earth, known as perigee. By carefully coordinating these two circular motions, Ptolemy was able to create an accurate predictive model for these observed planetary movements.21