Spheres of Eudoxus Documents

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Main Document

Spheres of Eudoxus 

written by Todd Timberlake

This Spheres of Eudoxus model simulates the system devised by the Ancient Greek astronomer Eudoxus to model the motion of the planets. The model consists of four nested concentric spheres. The axis of each sphere is attached to the surface of the next sphere out. The planet itself is located on the surface of the innermost sphere. The outermost sphere rotates with the daily (apparent) rotation of the stars.

The Spheres Frame shows the four spheres of the model. The axis of the inner (red) sphere can be tilted relative to that of the middle (blue) sphere using a slider to adjust the angle. The red sphere automatically rotates with angular velocity +1.0 (in arbitrary units). The angular velocities of the blue and green spheres can be adjusted using sliders. Note that the axis of the blue sphere is attached to the equator of the green sphere. This is a crucial part of Eudoxus' model. The equator of the green sphere is in the plane of the ecliptic. The outermost (white) sphere is essentially the Celestial Sphere containing the fixed stars (or at least it rotates about the same axis and at the same rate as the Celestial Sphere).

The Sky View Frame shows the motion of the planet (relative to the stars) as seen from the earth, which sits at the center of the concentric spheres in the model.

By tilting the red sphere relative to the blue sphere, setting the angular velocity of the blue sphere opposite that of the red sphere, and giving the green sphere a sufficiently small angular speed, Eudoxus was able to qualitatively reproduce the observed retrograde motion of the planets using this model.

Last Modified June 12, 2014

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Source Code Documents

Spheres of Eudoxus Source Code 

The source code zip archive contains an XML representation of the EJS Spheres of Eudoxus Model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.

This material is released under the GNU General Public License Version 3.

Published May 12, 2011
Last Modified June 12, 2014

This file has previous versions.