Meridian Arc - The Earth As A Sphere

The Earth As A Sphere

Early estimations of Earth's radius are recorded from Egypt in 240 BC, and from Baghdad caliphs in the 9th century, but it was the Alexandrian scientist Eratosthenes who first calculated the circumference a reasonably good approximate value for the radius. He knew that on the summer solstice at local noon the sun goes through the zenith in the ancient Egyptian city of Syene (Assuan). He also knew from his own measurements that, at the same moment in his hometown of Alexandria, the zenith distance was 1/50 of a full circle (7.2°).

Assuming that Alexandria was due north of Syene, Eratosthenes concluded that the distance between Alexandria and Syene must be 1/50 of Earth's circumference. Using data from caravan travels, he estimated the distance to be 5000 stadia (about 500 nautical miles)—which implies a circumference of 252,000 stadia. Assuming the Attic stadion (185 m) this corresponds to 46,620 km, or 16% too great. However, if Eratosthenes used the Egyptian stadion (157.5 m) his measurement turns out to be 39,690 km, an error of only 1%. Syene is not precisely on the Tropic of Cancer and not directly south of Alexandria. The sun appears as a disk of 0.5°, and an estimate of the overland distance traveling along the Nile or through the desert couldn't be more accurate than about 10%.

Eratosthenes' estimation of Earth’s size was accepted for nearly two thousand years. A similar method was used by Posidonius about 150 years later, and slightly better results were calculated in AD 827 by the Gradmessung of the Caliph al-Ma'mun.