Epicycles were mathematical modifications added to the geocentric theory to ensure that the model was consistent with astronomical observations. Geocentrism proposed that Earth was a stationary object at the center of the universe and that the planets, the Moon, the Sun, and the sphere of the fixed stars revolved about earth in a series of concentric orbits. This model implies that the planets always traverse the night sky in the same direction, from west to east with respect to the stars. Three planets visible to the naked eye (Mars, Jupiter, and Saturn) do not behave in this manner. Rather, their orbits exhibit the property of retrograde motion in which the planet appears to slow down in its eastward motion, stop, and briefly change its direction, traveling west with respect to the stars. It again stops and resumes its eastward journey. To explain this phenomenon, the astronomer Ptolemy proposed the notion of epicycles.
Epicycles are smaller circles pinned to a circle around Earth. The planet revolves around the center of the epicycle, which is called its deferent. The deferent is what revolves around Earth. Suppose that the deferent is rotating clockwise around Earth and that the planet is also rotating clockwise around the deferent. When the planet is closest to Earth, it travels in the direction opposite that of the deferent. Projecting its motion against the distant stars, it appears to have changed direction. In this way retrograde motion is explained.
A further emendation is required in order that the planets move with uniform angular velocity. Earth is not positioned at the center of the deferent's orbit, but it is instead displaced to one side by a distance called the eccentricity. A planet travels with uniform angular velocity with respect to another point, which is also displaced from the center by the eccentricity in the opposite direction as Earth. Such a circle, where Earth is not at the center, is called an equant.
Combining epicycles, deferents, and equants, and sometimes invoking epicycles nested upon epicycles, it becomes possible to fit the observed data regarding a planet's orbit to the geocentric model. Ptolemy's theory is therefore not a predictive one. Newer and more accurate measurements invariably necessitate further fine-tuning, and with a sufficient amount of tinkering, the model can reproduce the observations. The model does not tell us how or why the planet moves as it does. Also, the refinements introduced by Ptolemy are inconsistent with the philosophical ideas of Aristotle, who believed that planets traveled on crystalline spheres. With epicycles, the planets would crash into those spheres. In a heliocentric model with planets orbiting the Sun in ellipses, the ad hoc complications of geocentrism disappear.
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