Astronomy
Measuring the Diameter of the Earth
Eratosthenes' Method
Eratosthenes made a calculation of the Earth's diameter, based on one assumption and two measurements. The assumption was that the Earth was a sphere. This assumption is required since the method relies on accepting that the Earth's diameter is a total of 360o. The two measurements made are the degree of the Earth's shadow at noon at two points and the distance between those points.
Eratosthanes used the city of Syene in Egypt as the first point. This point was selected because it was known that on noon on the first day of summer the sun was directly overhead. This was known because people observed that at this time, the buildings cast no shadows (York University). Therefore, the degree of the shadow at Syene was 0o.
Eratosthanes then needed to know the degree of the shadow at another point either directly north or directly south, at the same time of day. Eratosthanes selected Alexandria as the second city. The degree of the sun's shadow was measured and found to be 7.2o (HEASARC).
Eratosthanes then knew that the degree of difference between Syene and Alexandria was 7.2o. The final item Eratosthanes needed to know was the distance between the two cities. This was done by sending a runner to pace out the distance (York University). Eratosthanes found that the distance between the two cities was 5000 stadia. A stadium was an ancient measurement, thought to equal around...
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