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Claudius Ptolemy refined the deferent-and-epicycle concept and introduced the equant as a mechanism that accounts for velocity variations in the motions of the planets. The empirical methodology he developed proved to be extraordinarily accurate for its day and was still in use at the time of Copernicus and Kepler.
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.
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 path-line is the combined motion of the planet's orbit (deferent) around Earth and within the orbit itself (epicycle). Around 210 BCE, Apollonius of Perga shows the equivalence of two descriptions of the apparent retrograde planet motions (assuming the geocentric model), one using eccentrics and another deferent and epicycles. [42]
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.
Ptolemaic model of the spheres for Venus, Mars, Jupiter, and Saturn with epicycle, eccentric deferent and equant point. Georg von Peuerbach, Theoricae novae planetarum, 1474. In the second century AD, astronomer and astrologer Vettius Valens wrote: There are many wheels, most moving from west to east, but some move from east to west.
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