Eratosthenes of Cyrene the Astronomer

Eratosthenes of Cyrene (Greek Ἐρατοσθένης; c. 276 BC[1] c. 195 BC) was a Greek mathematician, elegiac poet, athlete, geographer, and astronomer. He made several discoveries and inventions including a system of latitude and longitude. He was the first Greek to calculate the circumference of the earth (with remarkable accuracy), and the tilt of the earth's axis (also with remarkable accuracy); he may also have accurately calculated the distance from the earth to the sun and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. Eratosthenes was also the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.
Eratosthenes measured the circumference of the earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the earth. His estimated distance between the cities was 5000 stadia (about 500 geographical miles or 950 km). He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadium was about 185 m, which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadium" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.

Although Eratosthenes' method was well founded, the accuracy of his calculation was inherently limited. The accuracy of Eratosthenes' measurement would have been reduced by the fact that Syene is slightly north of the Tropic of Cancer, is not directly south of Alexandria, and the sun appears as a disk located at a finite distance from the earth instead of as a point source of light at an infinite distance. There are other sources of experimental error: the greatest limitation to Eratosthenes' method was that, in antiquity, overland distance measurements were not reliable[citation needed], especially for travel along the non-linear Nile which was traveled primarily by boat. Assuming enough difficulties in measurements, the accuracy of Eratosthenes' size of the earth is surprising.
Eratosthenes' experiment was highly regarded at the time, and his estimate of the earths size was accepted for hundreds of years afterwards. His method was used by Posidonius about 150 years later.

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