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Question

Compare the gravitational forces exerted by the sun and the moon on earth. Which exerts a greater force on earth ?
(Given : mass of sun, Ms = 41031 kg; mass of moon, Mm = 6.31022 kg; distance between sun and earth, Rse=1.31012 m and the distance between moon and earth, Rme= 4.5108m)

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Solution

. If mass of sun is Ms and mass of earth is Me and distance between the sun and earth is rse, then force exerted by the sun on earth is

Fs=GMsMer2se -(1)

Similarly, if mass of moon is Mm, mass of earth is Me, the distance between moon and earth is rme, then force exerted by moon on the earth is

Fm=GMmMer2me...(2)

Dividing equation (1) by equation (2), we get

FsFm =GMsMer2se r2meGMmMe = MsMm rme2rse2

= 410316.31022 x (4.51081.31012)2 = 76.07

The force exerted by the sun on earth is about 76 times the force exerted by the moon on earth.


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