Gravity Moon and Earth

Classical Mechanics Level 2

An astronaut measures the acceleration due to gravity on the moon and finds it to be 1/6th that on the earth.

He knows that the Earth is about 80 times more massive than the moon. His estimate of the radius of the earth as compared to that of moon is _ _ _ _ _ _ _ ?

DETAILS AND ASSUMPTIONS:

1) Answer in terms of R (of the Earth)/ R (of the moon)

5.367 3.56 4.53 4.99 3.65

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Sravanth C. by Sravanth C. , 21, India

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1 solution

a c c = G M e R e 2 = 6 ∗ G M m R m 2 ∴ R e 2 R m 2 = M e M m ∗ 1 6 ⟹ R e R m = 80 6 = 3.65. acc=\dfrac{GM_e}{R_e^2}=6*\dfrac{GM_m}{R_m^2}\\\therefore~\dfrac{R_e^2}{R_m^2}=\dfrac{M_e}{M_m}*\dfrac{1}{6}\\\implies\dfrac{R_e}{R_m}=\sqrt{\dfrac{80}{6}}=3.65.

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