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In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) ' upon the circle ', meaning "circle moving on another circle") [1] was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets.
The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Equant (or punctum aequans ) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets.
The notion of an epicycle was to say that there was a circle of rotation around the earth, but to reject the idea that the rotating body itself would be placed on that circle. Instead, a smaller rotating circle would be placed on the larger circle rotating around the earth, and this smaller circle is called a deferent.
English: Qualitative epicycle-and-deferent model as it was used by Apollonius, Hipparcus, Ptolemy and others in order to explain the apparent retrograde motion of planets in a geocentric model. The small circle in the center represents the Earth; the larger circle centered on the Earth is the deferent; the smaller circle centerd on a point of ...
The rate at which the planet moved on the epicycle was fixed such 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 claim can be seen to be nonsense, since a heliocentric system requires less complication in the math than a deferent-centric system of the kind described.
It shows a planet rotating on an epicycle which is itself rotating around a deferent inside a crystalline sphere. The center of the system is marked with an X, and the earth is slightly off of the center.
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