Eratosthenes' Calculation of Earth's Circumference

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Eratosthenes was a Greek astronomer in ancient times. Around 240 B.C. he made the first good measurement of the size of the Earth. How did he do that?

Eratosthenes used the lengths of shadows to figure out how high in the sky the Sun was in a certain place on a certain day. He knew of another place where there was no shadow at all on the same day. That meant the Sun was straight overhead. He found out the distance between the two places, then used some geometry to figure out the rest. Let's take a closer look!

Eratosthenes lived in the city of Alexandria. Alexandria is in northern Egypt. It is by the Nile River and the Mediterranean Sea. There was a tall tower in Alexandria. Eratosthenes measured the length of the tower's shadow on the Summer Solstice. He used that information plus some geometry to figure out the angle between the Sun and straight up.

There was a town in southern Egypt called Syene. There was a well in Syene. On the Summer Solstice, the Sun shone straight down the well to the very bottom. That meant the Sun must be straight overhead.

Eratosthenes had someone measure the distance between Alexandria and Syene. He used that distance, what he knew about the Sun's angles, and a bit of geometry to figure out the size of the Earth.

We aren't quite sure what answer Eratosthenes came up with, though. The distance between Alexandria and Syene was measured in stadia. The stadion was a distance unit that was often used in ancient times. However, not everybody used a stadion of the same length. If Eratosthenes used one length for the stadion, his answer was really, really good. The Earth is about 40 thousand kilometers (about 24,860 miles) around. The measurement that Eratosthenes made might have been within about 1% of this. That would be amazing! However, he might have used a different length stadion. If that is true, his answer was off by about 16%. That is still pretty good!

Eratosthenes may have also done some measurements of the distance from Earth to the Moon and from Earth to the Sun. Unfortunately, the records of that are not very clear. So we aren't quite sure whether he ever did make those measurements, or what his answers really were if he did.

Last modified July 31, 2007 by Randy Russell.

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