Ptolemy’s Geometric Devices Deferent, Epicycle, Eccentric, & Equant
Ptolemy’s geocentric astronomical system used four geometric devices, the deferent, epicycle, eccentric, and equant, to explain the observed motions of the planets.
Ptolemy was of Greek ancestry but lived and worked in Alexandria Egypt during the second century. Ptolemy is most famous for his astronomical work, published in the Almagest, which accurately predicts planetary positions using a geocentric model of the cosmos. Ptolemy also did important work in geography.
Ptolemy’s Geometric Devices
The Ptolemaic system used four geometric devices to predict planetary positions. They are the: deferent, epicycle, eccentric, and equant. Hipparchus invented the deferent and epicycle. Ptolemy later added the eccentric and equant for increased accuracy.
All these geometric devices rest on Ptolemy’s basic assumptions that the Earth and heavens are spherical and that all motions of heavenly bodies must be some combination of uniform circular motions. Ptolemy may have considered these geometric devices as computational tools rather than real physical objects.
We know that Earth spins on its axis daily, causing the Sun, Moon, planets, and stars to rise in the east, move westward across the sky, and set in the west. Not thinking that Earth spins, Ptolemy used the deferent to explain these daily westward motions. Each celestial object had its own deferent, which was a circle that moved daily around the Earth.
In addition to the daily motion with respect to the horizon, the planets move slowly when compared to the background stars. Usually this planetary motion compared to the stars is eastward and takes weeks or longer to observe without instruments. Occasionally the planets appear to reverse their direction compared to the background stars for a few weeks. This retrograde motion is an illusion caused by planets moving at different speeds as they orbit the Sun.
Ptolemy explained retrograde motion using the epicycle. Each planet had an epicycle as well as a deferent. The planet moved around the epicycle in uniform circular motion. The center of the epicycle also moved around the deferent in uniform circular motion. When the planet was on the portion of the epicycle inside the deferent, it appeared to be moving in retrograde as seen from Earth. This combination of two circles allowed Ptolemy to explain retrograde motion using only uniform circular motions.
Eccentric and Equant
Ptolemy’s observations showed that at times the planets appeared to move at slightly different rates. The planets speeds do actually vary as they orbit the Sun, but Ptolemy required uniform circular motion. So Ptolemy invented the eccentric and equant.
Aristotle’s physics, now known wrong, required Ptolemy to place Earth at the center of the cosmos, but made no requirement about the deferent. Ptolemy therefore placed the center of each planet’s deferent at a point displaced slightly from Earth. These displacements were the eccentrics. The point directly opposite the Earth from the eccentric was the equant point for each planet.
With their eccentrics the planets were sometimes closer to or farther from Earth appearing to move more rapidly or slowly.
The equant points fudged the uniform circular motion requirement. Normally uniform circular motion would be as seen from the center of the circle. However in Ptolemy’s system the uniform circular motion along the deferent was as seen from the equant point. Hence the motion, as seen from Earth, would appear nonuniform.
Using these four geometric devices the Ptolemaic system predicted the motions and positions of the planets as accurately as any observations available until Tycho Brahe’s time. The equant however was the downfall of Ptolemy’s system. Copernicus objected to the fact that it cheated on the uniform circular motion requirement.