Illustrate Ptolemy's orbit with Superior Ptolemaic Model. This simulation illustrates Ptolemy's orbit for a superior planet. The model consists of a deferent circle, centered on a point some distance from Earth (at the eccentric point). Attached to this deferent is the center of another circle, the epicycle. The center of the epicycle moves around the deferent with constant angular speed as seen from the equant point, which is exactly opposite the center of the deferent from Earth (so the center of the epicycle does not move at constant speed along the defernet). The planet moves along the epicycle at constant speed. This model is capable of reproducing retrograde motion and variations in the planet's brightness. It can also reproduce variations in the apparent size and spacing of the retrograde arcs. In this simulation the planet is assumed to move in the plane of the ecliptic, so its latitude is always zero.
This model also shows the orbit of Sun around Earth. This illustrates the fact that the line from the center of the epicycle to the planet is always parallel to the line from Earth to Sun.
The parameters are initially set to model the orbit of Mars. The user can select orbits for Mars, Jupiter, Saturn, or a user-defined orbit. Parameters for the Mars, Jupiter, and Saturn orbits are taken from Ptolemy's Almagest. The simulation can also display simplified orbits that do not use the eccentric and equant.
The top window shows the elements of the model. The bottom window shows the view from Earth.

Requirements:
* Java

The license of this software is Freeware, you can free download and free use this graphing software.