How did Erathones calculate the circumference of the Earth? What device did he use?

Question

GEOLOGY geeks, even Physics guys, i know you know this

Answer 1

Eratosthenes had learned from a traveller that at noon on midsummer's day at Aswan, the image of the Sun could be seen in the water at the bottom of a deep well. Therefore he knew that the Sun was exactly overhead at Aswan on that day.

So he measured the angle of the Sun from vertical at noon on midsummer's day in Alexandria (where he lived) and determined that the angle was 1/50th of a complete circle. He probably used a compass to make that measurement.

Since he knew that Aswan was 500 stadii from Alexandria, he determined the circumference of the earth to be 250,000 stadii.

Answer 2

He calculated the earth's circumference circa 240 BC, using trigonometry and knowledge of the angle of elevation of the Sun at noon in Alexandria and Syene (now Aswan, Egypt). The calculation is based on the assumption that the Earth is spherical and that the Sun is so far away that its rays can be taken as parallel.

Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead- though Syene was in fact slightly north of the tropic. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7° south of the zenith at the same time. Assuming that Alexandria was due north of Syene- Alexandria is in fact on a more westerly longitude- he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth. The distance between the cities was known from caravan travellings to be about 5,000 stadia. He established 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 no longer known (the common Attic stadion was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes' method was used by Posidonius about 150 years later.

Answer 3

using basic trig and a dumb weight at the summer soltice in 240bc ish

Answer 4

Just his knowledge of angles and geometry.