# Max’s Post: How Eratosthenes calculated the radius of Earth.

When travelling to Alexandria (I am sure those of you who have read our novel The Secret of the Cosmographer will remember), we were at the great Ancient Library of Alexandria. I must say here, that the Ancient Library of Alexandria was nothing like modern libraries where people stay quiet and just read. It was a loud place where people gathered to discuss, attend lectures, disagree heavily or even fight. Most scholars of the era studied the works of Ancient Mathematicians and astronomers, one of them being the Great Eratosthenes. He is great to me because he was one of the first to go beyond theory and beliefs, to experimentation and proofs via measurement, paving the way for next scientists to come, centuries after him.

Eratosthenes was born in Cyrene of today’s Libya in 276 BC, and died in Alexandria in 194 BC. He was a mathematician, a geographer, an astronomer. One of his greatest accomplishments was the calculation of the size of Earth, that he constructed a system of co-ordinates of parallels and meridians as well as a world map (as he thought the world was at that time).

He was a really clever guy, I won’t bore you with many details of his life which is certainly exciting (some say he decided he wanted to die in 194 BC and he did it via voluntary starvation).

What I want to talk about is how he measured the radius of Earth around 240 BC:

His experiment was based on measuring Suns height on the same day at two different places. He was certain that the Sun is so far away from Earth, that the light beams arrive on Earth almost in parallel.

Eratosthenes had heard that on June 21st, the day of the Summer solstice the Sun was mirrored on the surface of the wells in the town of Syini, today’s Aswan (Egypt). This meant that this town was on the tropic of Cancer and at noon of June 21st the Sun beams were perpendicular to the water, thus reflected back without changing direction.

Eratosthenes then measured the shadow an obelisk (one of Ancient astronomers oldest instrument) would cast in Alexandria where he lived. By doing some simple calculations between the obelisk’s height and the shadow he measured a 7,2 degrees. This meant that Alexandria was not on tropic of Cancer. He had people walk and calculate the distance of Alexandria to Syini (Aswan). He then knew that this distance meant 7,2 degrees and hence easily calculated what distance the 360 degrees, and calculated that the Earth’s radius was 6316 km, only 1% larger than its actual one!

What a guy, ha?

I’ll tell you more about Zosimos, though, the guy we met in Ancient Alexandria, next time.

Talk to you soon. Max.