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From parallax measurement, the sun is fo...

From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.

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From parallax measurement given that sun is at a distance of about 100 times the earth- moon distance, hence `=(d_(sun))/(d_("moon"))=400`
(Suppose, here r stands for distance and D for diameter) sun and moon both appear to be of the same angular diameter as seen from the earth.
`:. (D_("sun"))/(d_(sun))=(D_("moon"))/(d_("moon"))`
`:.(D_(sun))/(D_("moon"))=(d_(sun))/(d_("moon"))=400 " "..(1)`
But `(D_("earth"))/(D_("moon"))=4 " "....(2)`
By taking ratio of (1) to (2),
`:.(D_(sun))/(D_("eart"))=100`
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