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.

So what answer did he get? We know now that Earth is about 40 thousand kilometers (about 24,860 miles) around. We don't know for sure what answer Eratosthenes got. His measurement between Alexandria and Syene was in stadia. The stadion was used to measure distance in ancient times. It was used like a kilometer or a mile is used today. We don't know for sure how long the stadion that Eratosthenes used was. It might have been one length, or it might have been another. So maybe his answer was really, really good. It might have been within 1% of the right answer! Or it might not have been quite so good. It may have been off by about 16%. Either way, his answer was at least pretty good.

Last modified July 31, 2007 by Randy Russell.

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