In the Ptolemaic system of astronomy, the epicycle (literally: on the circle in Greek) was a geometric model to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. It was designed by Apollonius of Perga at the end of the 3rd century BC. In particular it explained retrograde motion. Secondarily, it also explained changes in the distance of the planet from Earth.

In the Ptolemaic system, the planets are assumed to move in a small circle, called an epicycle, which in turn moves along a larger circle called a deferent. Both circles rotate counterclockwise and are roughly parallel to the Earth's plane of orbit (ecliptic). The orbits of planets in this system are epitrochoids.

The deferent was a circle centered around a point halfway between the equant and the earth. The epicycle rotated on the deferent with uniform motion, not with respect to the center, but with respect to the off-center point called the equant. The rate at which the planet moved on the epicycle was fixed such that the angle between the center of the of epicycle and the planet was the same as the angle between the earth and the sun.

Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent. This is not to say that he believed the planets were all equidistant. He did guess at an ordering of the planets. Later he calculated their distances in the Planetary Hypotheses.

For superior planets the planet would typically rotate in the night sky slower than the stars. Each night the planet would "lag" a little behind the star. This is prograde motion. Occasionally, near opposition, the planet would appear to rotate in the night sky faster than the stars. This is retrograde motion. Ptolemy's model, in part, sought to explain this behavior.

The inferior planets were always observed to be near the sun, appearing only shortly before sunrise or shortly after sunset. To accommodate this, Ptolemy's model fixed the motion of Mercury and Venus so that the line from the equant point to the center of the epicycle was always parallel to the earth-sun line.