The size of the Earh

Erastosthenes was the director of the great library of Alexandria where one day he read in a papyrus book that in the southern frontier outpost of Syene, near the first cataract of the Nile, at noon on June 21 vertical sticks cast no shadows. On the summer solstice, the longest day of the year, as the hours crept toward midday, the shadows of temple columns grew shorter. At noon, they were gone. A reflection of the Sun could then be seen in the water at the bottom of a deep well. The Sun was directly overhead.
Erastosthenes did an experiment to observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And he discovered that sticks do.
He asked himself how, at the same moment, a stick in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a pronounced shadow. Consider a map of ancient Egypt with 2 vertical sticks of equal length, one stuck in Alexandria, the other in Syene. Suppose that at a certain moment the two sticks cast shadows of equal length, that would make sense under the consideration of the Earth being flat. But, how could it be that at the same instant there was no shadow in Syene and a big one in Alexandria?
The only possible answer, was that the surface of the Earth is curved. Not only that, the greater the curvature, the greater the difference in the shadow lengths.
For the difference in the shadow lengths, the distance between Alexandria and Syene had to be about 7 degrees along the surface of the Earth. 1/50 of the 360 degrees of the full circumference of the Earth. He knew that the distance between the 2 cities was approx. 800 km, because he hired a man to pace it out. 800 km times 50 is 40.000 km: so he thought that must be the circumference of the Earth. (25.000 miles).
With just sticks he deduced the circumference of the Earth with an error of only a few percent, 2200 years ago.
(From Carl Sagan's "Cosmos")

Posted by Eider at June 21, 2004 02:56 PM