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Using this result, |
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A postulate of spherical astronomy is that the Earth is a small point in relation to the heavenly bodies. From this Eratosthenes reasoned the Sun's rays strike the Earth parallel over its entire surface. Working in Syene and Alexandria, which Eratosthenes assumed were on the same meridian, he estimated the distance between the cities to be about 5,000 stades (a stade is believed to be about 559 feet - approximately one-tenth of a mile). At summer solstice, at noon, the Sun cast no shadow in Syene, but in Alexandria a shadow was visible. Using a gnomon (a vertical stick), Eratosthenes measured the shadow's angle to be about one-fiftieth of a circle.
In the diagram, m<a = m<B (alternate interior angles), and since angle "a" is one-fiftieth of a circle so is angle B. Since angle B is one-fiftieth of a circle and AS = 5000 stades, the entire circumference is 50(5000) = 250,000 stades.
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Using this result, |
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r = 39,788.7 stades = 22,241,883.3 feet = 4,212.5 miles
(The actual radius of the Earth is 3,963.21 miles) Using the work of
Aristarchus with that of Eratosthenes we find:
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The radius of the Moon is, |
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Since |
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the radius of the Sun is, |
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miles |
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