Check out how Erastosthenes did it 2000 years age
http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/eros2.html
All you need is a little geometry, and, by the way, ancient scientists DID know that the earth was round. There are several simple ways to demonstrate this. One way is to think of a ship sailing away from shore. What part of the ship vanishes first?
What did Erastosthenes know, what assumptions did he have to make, and what did he have to find out to do this amazing work?
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