InferiorPtolemaic


General Description

This simulation illustrates Ptolemy's orbit for a inferior 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 equant point to the center of the epicycle is always parallel to the line from Earth to Sun.

The parameters are initially set to model the orbit of Venus. The user can select orbits for Venus, Mercury, or a user-defined orbit. Parameters for Venus and Mercury orbits are taken from Ptolemy's Almagest, but Ptolemy uses a moving deferent for Mercury which is not used in this simulation. The simulation can also display simplified orbits that do not use the eccentric and equant.

In addition, users can choose to display simplified Tychonic orbits of all five visible planets. Tycho Brahe used the same basic structure for all the planets that Ptolemy used for the inferior planets, with the main difference being that in the Tychonic system the deferent of each planet is just the orbit of Sun.

The top window shows the elements of the model. The bottom window shows the view from Earth.


Orbit Frame


Sky View Window


Orbit Parameters (for User Defined orbit)


Todd K. Timberlake (ttimberlake@berry.edu)