Question

The moon is 3.9 x 105 km from Earth’s center and 1.5 x 108 km from the sun’s center. If the masses of the moon, Earth, and sun are 7.3 x 1022 kg, 6.0 x 1024kg, and 2.0 x 1030kg, respectively, find the ratio of the gravitational forces exerted by Earth and the sun on the moon.

Answer 1

Gravitational force is given as

F = GMm / r²

where M and m are two masses and r is the center to center distance

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force between sun and moon

F = 6.67e-11 * 2e30 * 7.3e22 / 1.5e11²  

F = 4.328e20 N

and

force between earth and moon

F = 6.67e-11 * 6e24 * 7.3e22 / 3.9e8²  

F = 1.92e20 N

Therefore,

ratio of the gravitational forces exerted by Earth and the sun on the moon

F (earth on moon) / F ( sun on moon) = 1.92e20 / 4.328e20

F (earth on moon) / F ( sun on moon) = 0.4436

OR

F ( sun on moon) / F (earth on moon) = 2.254