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Eratosthenes Model
written by Todd Timberlake
The Eratosthenes model displays the shadows cast by two gnomons (sticks) at different locations on Earth. For one gnomon, Sun is directly overhead (as would be the case if the gnomon was on the Tropic of Cancer at the summer solstice). The other gnomon is due north of the first gnomon. The sizes of the gnomons are greatly exaggerated for visibility. This simulation can be used to help illustrate how Eratosthenes was able to measure the diameter of Earth using the shadows cast by two gnomons, one situated due north of the other, on a day when the southerly gnomon cast no shadow at all. The distance between the two gnomons (along Earth's surface) can be adjusted. The length of the shadow is given, and this length can be used to determine the angle between the gnomon lines and from that the circumference (and diameter, radius, etc) of Earth. Earth can be hidden to give a better view of the relevant geometry.

Eratosthenes model is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_astronomy_Eratosthenes.jar file will run the program if Java is installed.  You can modify this simulation if you have EJS installed by right-clicking within the plot and selecting "Open EJS Model" from the pop-up menu item.

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
General Physics
- History
- Measurement/Units
- Lower Undergraduate
- High School
- Middle School
- Instructional Material
= Curriculum support
= Interactive Simulation
Intended Users Formats Ratings
- Educators
- Learners
- General Publics
- application/java
  • Currently 5.0/5

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Access Rights:
Free access
This material is released under a Creative Commons Attribution 3.0 license.
Rights Holder:
Todd Timberlake
EJS, Earth, Easy Java Simulations, Eratosthenes, OSP, Open Source Physics, Sun, circumference, gnomon, measure, shadow, similar triangles, triangles, trigonometry
Record Cloner:
Metadata instance created January 2, 2010 by Mario Belloni
Record Updated:
November 6, 2021 by Lyle Barbato
Last Update
when Cataloged:
January 2, 2010
Other Collections:

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Record Link
AIP Format
T. Timberlake, Computer Program ERATOSTHENES MODEL, Version 1.0 (2010), WWW Document, (
T. Timberlake, Computer Program ERATOSTHENES MODEL, Version 1.0 (2010), <>.
APA Format
Timberlake, T. (2010). Eratosthenes Model (Version 1.0) [Computer software]. Retrieved July 21, 2024, from
Chicago Format
Timberlake, Todd. "Eratosthenes Model." Version 1.0. (accessed 21 July 2024).
MLA Format
Timberlake, Todd. Eratosthenes Model. Vers. 1.0. Computer software. 2010. Java (JRE) 1.5. 21 July 2024 <>.
BibTeX Export Format
@misc{ Author = "Todd Timberlake", Title = {Eratosthenes Model}, Month = {January}, Year = {2010} }
Refer Export Format

%A Todd Timberlake %T Eratosthenes Model %D January 2, 2010 %U %O 1.0 %O application/java

EndNote Export Format

%0 Computer Program %A Timberlake, Todd %D January 2, 2010 %T Eratosthenes Model %7 1.0 %8 January 2, 2010 %U

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Eratosthenes Model:

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 Eratosthenes Model.

relation by Mario Belloni

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