Measuring the Earth with camels and sticks

Classical Mechanics Level 3

One of the first intellectual achievements of the human race was Eratosthenes' measurement of the Earth's circumference around 240 BC. Not only did he measure the circumference using only sticks and observations, but he also assumed that the Earth was round and not flat.

Eratosthenes used the following method: he observed that the Sun creates a \(16~\mbox{m}\) shadow off the Lighthouse of Alexandria at the same time when it is straight above Syene (no shadow). He hired a caravan of camels that went back and fourth couple of times between Alexandria and Syene to establish the distance between them. The measured distance was around \(928~ \mbox{km}\). What was the circumference of the Earth in km that Eratosthenes calculated?

Details and assumptions

  • It is thought that the Lighthouse of Alexandria was around \(130~\mbox{m}\) tall.
  • Eratosthenes assumed the Earth was perfectly spherical.
  • Since the Sun is very far away, Eratosthenes assumed that its rays are parallel.

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