Introductory Astronomy: Eratosthenes's measurement of the size of the earth

The "Alexandrian School" of Greek thought circa 200 B.C. made astonishing progress in the understanding of astronomy. One Eratosthenes measured (we believe quite accurately) the size of the earth. South of Alexandria was a town called Syene. Eratosthenes heard that, in Syene, on the summer solstice, the sun shines straight down a very deep vertical well. (Syene sat on the tropic of Cancer.) On this day in Alexandria, some 5000 "stadia" north of Syene, the sun cast a shadow 7.2 degrees from the vertical. Eratosthenes correctly deduced that this difference was due to the curvature of the spherical earth:

Furthermore, E. could calculate the circumference of the earth by analogy:

7.2 degrees is to 360 degrees as 5000 stadia is to ?
The proportion version of this analogy is:

Our Version

Now we want to repeat E.'s measurement. We will need a collaborator more than 50 miles north or south of us to measure a shadow. We will measure the shadow with a simple stick of known length. I suggest a plumb-bob attachment (illustrated here as a pencil suporting a paper clip on a thread) so that you will know that the stick is vertical.

A collaborator is needed because we do not have a "Syene," and we do not wish to wait for summer solstice! In our method any old day will do, but the measurement MUST be taken at local noon, simultaneously at both sites.

Last modified: Wed Sep 9 15:49:55 CDT 1998