dChan - Q Origins Project Archive

Measuring the Earth

By the age of forty, Eratosthenes' varied knowledge was so highly regarded that Ptolemy III offered him the role of director of the Alexandrian Library, one of the most important positions which included the obligation of tutoring the crown prince. It was probably here where he read that in Syene (modern Aswan, Egypt), a city located due south of Alexandria, during the summer solstice (June 21st) something curious took place: the shadows of all objects would grow shorter as noon approached and finally, during noon, temple columns would cast no shadow and the sun would shine directly overhead. Deep wells, which at any other time of the year would remain in shadow, would have the sun shining directly down into them. He noticed that in Alexandria, during that same moment, objects would clearly cast a shadow. This account was surely read by many others, but nobody seemed to think it had any particular importance. Eratosthenes, as impossible as it may sound, saw in this report an opportunity to calculate the circumference of the Earth. It occurred to him he could do so by measuring the length of the shadow of the sun in Alexandria at the time when there was no shadow in Syene. On June 21st at noon, he measured the shadow of an obelisk in Alexandria and by simple geometry he calculated that the sun was 7° 14' from overhead.

It is because the surface of the Earth is curved that at the same time there would be no shadow in Syene and a clear shadow in Alexandria. Moreover, the greater the curvature, the bigger the difference in the length of the shadows. The sun is so far away from us that its rays are parallel when they reach the Earth: objects at different angles to the sun's rays would cast shadows of different lengths. Eratosthenes, based on the observed differences in the shadows' lengths, came to the conclusion that the distance between Alexandria and Syene had to be 7° 14' along the surface of the Earth. In other words, if we imagined one obelisk in Alexandria and another obelisk in Syene extending all the way down to the centre of the Earth, they would there intersect at an angle of 7° 14'. Since a full circle has 360°, 7° 14' is roughly one-fiftieth of the total circumference. Thus, the total circumference of the Earth was fifty times the distance from Alexandria to Syene.

https://www.worldhistory.org/Eratosthenes/