The Original Experiment
Eratosthenes of Cyrene (275-194 B.C.) was a Greek scholar who lived and worked in Cyrene and Alexandria. Eratosthenes was director of the famous library in Alexandria, and is known for numerous important contributions to mathamatics, geography, and astronomy. In particular, he is remembered for a technique he introduced which enabled him to compute the first reliable determination of the true size of the earth.
This technique is based on the observation by Eratosthenes that the sun is directly overhead at noon in Syene in southern Egypt on the first day of summer. (This is the time of the summer solstice.) While visiting Syene Eratosthenes apparently stopped at a well and noted that the noon sun reflected directly back from the water in the bottom of the well.
Since Eratosthenes knew that the earth was a sphere, he correctly reasoned that if he could determine the altitude of the noon sun at some other location on the first day of summer, AND if he knew the distance between these two locations, he could compute the circumference of the earth as a simple ratio. This principle is illustrated in the following illustration, along with a sketch of a reconstructed map of the world as known by Eratosthenes.
The Eratosthenes Technique for Determining the Size of the Earth
When Eratosthenes returned to Alexandria, being a good astronomer, he knew he could wait until next year on the first day of summer and measure the altitude of the noon sun. Then since he had kept track of how far he had traveled from Syene to Alexandria, he could determine the circumference and the diameter of the earth.
Now, in reality, Eratosthenes, being a good administrator, probably had assistants measuring the altitude of the noon sun on a regular basis from Alexandria, so he could probably simply consult the records of solar observations from Alexandria. However he actually obtained the data, the difference between the noon sun elevations at Syene and Alexandria on the first day of summer was approximately 7 degrees. Furthermore, Eratosthenes probably did not need to measure the distance between the locations since he had the reliable geographic data accumulated by Alexander The Great.
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The Computations
Here is a diagram the shows the details of the computations. Here theta is the difference in the elevation or altitude of the sun, and D is the distance between the two observing locations. Note that this equation correctly describes the situation even if one of the observing locations does not happen to have the sun at the zenith. We just need to have the difference in the altitude of the sun observed at the same time from two different locations.
The World Map
While Eratosthenes certainly prepared numerous maps of the world as it was known by the people of his time, none have survived. He was also the author of several books. Unfortunately, none of his work has survived. We only have descriptions of his work as recorded by others. The following illustration is one of the best available reconstructions of a world map according to Eratosthenes. It is based on descriptions of the Eratosthenes map as provided by Cleomedes and Posidonius, both of whom were able to view the original Eratosthenes map.
Map of the World According to Eratosthenes
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We too, here at Sonoma State University, would like to travel south to a warmer climate to observe the sun. However, travel conditions are uncertain, and there are rumors that the natives to the south (say, near Los Angeles) may be somewhat less civilized ;-). Thus, we look to the north for a location to repeat the experiment. Of course, it is colder to the north!
Fortunately, we have found a university to the north with similiarly minded students who have agreed to collaborate with us to repeat the great Eratosthenes experiment. Students at the University of British Columbia (UBC) who are taking an introductory astronomy course will work with Sonoma State students who are also taking an introductory astronomy course. We will all agree to observe the altitude of the sun on the same date at the same time. If the earth is approximately spherical, and if we can deterrmine the distance between the two universities, we should be able to use our measurements to determine the size of the earth.
Instructions for SSU Team MembersInstructions for UBC Team Members (Acrobat PDF format)
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At present, the time scheduled for the real experiment is Wednesday March 22, 1999 at the time of local noon. Observations will be posted on the class website and on this website. Observations from UBC will also be posted here.
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What will the results be? What will be our result for the size of the earth? Could it be that experiment may indicate that the earth is flat after all? What observational results would suggest that the earth is flat?
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