Epicycles

In the astronomical theories of Ptolemy, epicycles were a geometric model used to explain the variations in speed and direction of the apparent motion of the Sun, Moon, and planets. The theory was proposed by Apollonius at the end of the 3rd century B.C. It was later formalized by Ptolemy in his 2nd century A.D. astronomical treatise the Algemest. The theory was used to explained the retrograde motion of the five planets known at the time. It also explained changes in the apparent distances of the planets from Earth.

According to Ptolemy, the planets moved in a small circle called an epicycle, which in turn moves along a larger circle called a deferent. Both circles rotate eastward and are roughly parallel to the plane of the Sun’s orbit(the ecliptic). The orbits of planets are called epitrochoids in this system. This view is considered to be geocentric, but the planets’ motion was not actually centered on the Earth. Instead, the deferent was centered around a point halfway between the Earth and another point called the equant. The epicycle, meanwhile, rotated and revolved along the deferent with uniform motion. The rate at which the planet moved on the epicycle was fixed so that the angle between the center of the epicycle and the planet was the same as the angle between the Earth and the Sun.

The apparent motion of the heavenly bodies with respect to time was cyclical in nature. Apollonius discovered that the cyclical variation could be represented mathematically by circles, or epicycles, running on a larger circle, or deferent. Deferents and epicycles in the ancient models didn’t represent orbits in the modern sense. The ancient astronomers did not know about orbits or any kind of connections between the heavenly bodies. They simply saw lights moving about the sky until the times of Galileo. Ptolemy refined the concept and introduced the equant to account for velocity variations in the motions of the planets. The empirical methods that he developed proved to be extraordinarily accurate for its day and was still in use at the time of Copernicus and Kepler.

Try this article about epicycles and deferents. Here on Universe Today we have a great article about Nicolaus Copernicus and his use of Ptolemy’s theory. Astronomy Cast offers a good episode about solar system movements.

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