![]() The rest of the error is likely mostly due to imprecision in measuring distances and angles. The distance needs to be adjusted to remove the east-west offset, and if you do this you get an answer even closer to the modern measurement. The main mistake Eratosthenes made was assuming Alexandria was due north of Syene. Not too bad for a measurement made with nothing but a stick! So depending which figure we use for the stadion, Eratosthenes got the answer right to within 9% or 15%, respectively. Modern measurements of the Earth’s circumference around the poles set the figure at 40,008 km. Others think they used a stadion of 184.8 m, giving a result of 46,000 km. Some scholars suggest that Egyptian surveyors used a stadion of 174.6 metres, giving a circumference of 43,650 km. How long is a classical Greek/Egyptian stadion? There is some debate over this. Shadows in Syene and Alexandria, if the Earth were flat, or spherical. ![]() So the circumference of the Earth, Eratosthenes concluded, must be 250,000 stadia. So this meant that the distance from Syene to Alexandria must be one fiftieth of the circumference of the Earth. Eratosthenes also figured that Alexandria was pretty much due north of Syene. The angle of 7☁2′ is exactly one fiftieth of a circle. He realised not only that the Earth’s surface must be curved, but that he could use the length of the shadow to calculate how big the Earth was.īy measuring the length of a vertical stick and its shadow in Alexandria at noon on the solstice, Eratosthenes calculated that the sun was at an elevation of 7☁2′ to the vertical. At noon on the summer solstice, a vertical stick in Alexandria cast a definite shadow. Eusebius’s figures are ambiguous, but can be interpreted as giving a figure of 149 million km, almost exactly correct.) If the Earth were flat, the sun would be directly overhead everywhere at the same time. (According to the writings of Eusebius of Caesarea, Eratosthenes in fact calculated the distance from the Earth to the sun, possibly using a method developed by Aristarchus. He figured that the sun was a very long way away, at least much further away than, say, the distance between Syene and Alexandria on the northern coast of Egypt – measured by surveyors to be 5000 stadia. This property was well known amongst geographers as a curiosity, because it didn’t happen at any cities further north.Įratosthenes took it a step further by thinking about why this was the case. Equivalently, at noon on the solstice, a stick placed vertically in the ground would cast no shadow, because the sun was directly overhead. He had heard that at noon on the day of the summer solstice, the sun shone directly down a vertical well in the Egyptian city of Syene, where the modern city of Aswan now stands. Painting by Bernardo Strozzi (1581-1644)Įratosthenes was the head librarian at the great Library of Alexandria.
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