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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.

Please note that this resource requires at least version 1.5 of Java (JRE).
1 source code document is available
Subjects Levels Resource Types
- Astronomy Education
= Curricula
- Historical Astronomy
= History of Astronomy
- Lower Undergraduate
- High School
- Instructional Material
= Simulation
Intended Users Formats Ratings
- Learners
- Educators
- General Publics
- application/java
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Access Rights:
Free access
This material is released under a GNU General Public License Version 3 license.
Ancient Greek, EJS, Easy Java Simulations, Eudoxus, OSP, Open Source Physics, planet, retrograde
Record Creator:
Metadata instance created May 12, 2011 by Todd Timberlake
Record Updated:
June 12, 2014 by Andreu Glasmann
Last Update
when Cataloged:
May 12, 2011
Other Collections:

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Record Link
AIP Format
T. Timberlake, Computer Program SPHERES OF EUDOXUS, Version 1.0 (2011), WWW Document, (
T. Timberlake, Computer Program SPHERES OF EUDOXUS, Version 1.0 (2011), <>.
APA Format
Timberlake, T. (2011). Spheres of Eudoxus (Version 1.0) [Computer software]. Retrieved August 20, 2017, from
Chicago Format
Timberlake, Todd. "Spheres of Eudoxus." Version 1.0. (accessed 20 August 2017).
MLA Format
Timberlake, Todd. Spheres of Eudoxus. Vers. 1.0. Computer software. 2011. Java (JRE) 1.5. 20 Aug. 2017 <>.
BibTeX Export Format
@misc{ Author = "Todd Timberlake", Title = {Spheres of Eudoxus}, Month = {May}, Year = {2011} }
Refer Export Format

%A Todd Timberlake
%T Spheres of Eudoxus
%D May 12, 2011
%O 1.0
%O application/java

EndNote Export Format

%0 Computer Program
%A Timberlake, Todd
%D May 12, 2011
%T Spheres of Eudoxus
%7 1.0
%8 May 12, 2011

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Spheres of Eudoxus:

Is Based On Easy Java Simulations Modeling and Authoring Tool

The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Spheres of Eudoxus.

relation by Wolfgang Christian

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