THE EQUINOX SCIENCE AND MATH EXPERIMENT

ERATOSTHENE’S EXPERIMENT

Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made a surprisingly accurate estimate of the earth's circumference. In the great library in Alexandria he read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth (sorry Columbus) by making two assumptions - that the earth is round and that the sun's rays are essentially parallel. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria. Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. His result, 250,000 stadia (about 46,250 km) is quite close to modern measurements. Investigating the Earth, AGI, l970, Chapter 3, p. 66.

The formula Eratosthenes used is:

D A d=distance between Syene and Alexandria
_____ = _____ A=360 degrees assumption of round earth
a=shadow angle of vertical stick
d a D=to be determined (circumference)
All you need to do is place a vertical stick (shaft) into the ground at your school and when the sun reaches it's highest vertical assent for the day (solar noon therefore the shadow length will be the shortest), measure the angle of the shadow of the stick (a).
-\
- \
stick -> - \
- a \ a=shadow angle
- \
- \
ground___________________-______\shadow_______________________

By doing this experiment on the equinox we all know that the vertical rays of the sun are directly over the equator, like the well at Syene. Using a globe or an atlas the distance between your location and the equator ( d in equation) can be determined and the circumference can be calculated.


How about sharing shadow angle measurement with others around the real globe. Contact others that would be willing to do collect the same data and exchange it possibly using the following format.

Your measurement of the shadow angle____________degrees
Your location city ____________________________________
Your location country _________________________________
Your latitude _________________________________________
Your longitude ________________________________________

When you have different sets of data compile them and compare the various locations and angles.

Original idea by Jim Meinke (September 1994)- Lakewood High School in Cleveland

Dr. Robert Sweetland's Notes ©