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
%0 Computer Program %A Timberlake, Todd %D January 2, 2010 %T Eratosthenes Model %7 1.0 %8 January 2, 2010 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=9756&DocID=1449
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