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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 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 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.
Ptolemy's planetary model showing the deferent and epicycle as dashed lines and the Earth and equant equidistant to the center of the deferent. Claudius Ptolemy's planetary model consisted of a stationary earth surrounded by fixed circles, called deferents, which carried smaller, rotating circles called epicycles. Planets rotated on the ...
A given planet then moves around the epicycle at the same time the epicycle moves along the path marked by the deferent. These combined movements cause the given planet to move closer to and further away from the Earth at different points in its orbit, and explained the observation that planets slowed down, stopped, and moved backward in ...
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 ...
Ragep, F. J. "The Two Versions of the Tusi Couple," in From Deferent to Equant: A Volume of Studies in the History of Science in Ancient and Medieval Near East in Honor of E. S. Kennedy, ed. David King and George Saliba, Annals of the New York Academy of Sciences, 500. New York Academy of Sciences, 1987.
and for the epicycle model, the ratio between the radius of the deferent and the epicycle: 3122 + 1 ⁄ 2 : 247 + 1 ⁄ 2. These figures are due to the cumbersome unit he used in his chord table and may partly be due to some sloppy rounding and calculation errors by Hipparchus, for which Ptolemy criticised him while also making rounding errors.