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During a total eclipse, the Sun and the Moon appear to the observer to be almost exactly the same size. The radii of the Sun and Moon are r sun = 6.96 · 10^8m and r moon= 1.74 ·10^6m , respectively. The distance between the Earth and the Moon is dEM = 3.84 · 10^8m a) Determine the distance from the Earth to the Sun at the moment of the eclipse. b) In part (a), the implicit assumption is that the distance from the observer to the Moonâ s center is equal to the distance between the centers of the Earth and the Moon. By how much is this assumption incorrect, if the observer of the eclipse is on the Equator at noon? [Hint: Express this quantitatively, by calculating the relative error as a ratio: (assumed observer-to-Moon distance â actual observer-to-Moon distance)/(actual observer-to-Moon distance).] c) Use the corrected observer-to-Moon distance to determine a corrected distance from Earth to the Sun.
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