Ptolemy's Spheres

This Demonstration shows the Earth-centric model of the universe that Claudius Ptolemy (90–168 AD) inherited from his predecessors and improved. The mathematical model was used in various derivations to show the movements of the Sun, Moon, and the five planets known at the time (Mercury, Venus, Mars, Jupiter, and Saturn). In the years 1514–1543, Ptolemy's Earth-centric model began to be superseded by Copernicus's heliocentric model of the solar system.

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DETAILS

Ptolemy's system consists basically of two circles, the Earth-centric circle named "deferent" and the circle of the planet called "epicycle," which is centered on the rim of the deferent.  Both circles move counterclockwise (west to east) with a uniform angular velocity. The diameters of these two circles and their rotational speeds are set so as to give the best agreement with observations of the present configuration of the planets, thus allowing predictions of their future positions.
Noting that this design did not produce results exactly matching the observations, Ptolemy added two more parameters to the system. The first was a shift of the center of the deferent. This improved agreement with observed data to a certain extent. His second innovation was definition of a new point (equant) for the epicycle, rather than the center of the deferent, as the center of rotation. Although this system gave a better approximation of the observed data, it never achieved full agreement.
In the Demonstration, a trajectory is first obtained by adjusting the deferent and epicycle radii and speeds. Then, for better agreement with the observed data, the shift of the deferent center (green dot) and the equant (brown spot) are set. With these parameters, it is possible to determine a large number of possible planetary trajectories. 
Reference
[1] T. S. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Cambridge: Harvard University Press, 1992.
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