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Aristarchus & the Size/Distance of the Sun and Moon:

An earlier Greek astronomer, Aristarchus, had already provided a means by which Eratosthenes' discovery could be used to get the distances to the Moon and Sun, as well as their diameters.  To do this you must use the Moon.

1)  Sun, Moon, and Earth form a right triangle when the Moon is at quarter phase.  Measurement of sun-moon angle lets you derive ratio of sides.

2)  Moon takes 3 times longer to move across the Earth's shadow than to disappear into it, so the Moon is  ~1/3 the Earth's Diameter.

3) Exercise: Using the angular size of the moon in the sky and its diameter, derive its distance


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