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A planet with a moon of 1/4 its mass are 10,000 km apart. At what distance from the planet will the gravitational pull of the planet and moon be equal?

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Correct Answer: B. 6,667 km
The Universal Law of Gravity is an “Inverse Square Law”: F a (m1.m2)/d2
So if Planet = m1 = 4 and the moon = m2 = 1
The force due to the planet is: F1 = M1/d12 and the force due to the moon is: F2 = M2/d22
At the point where the gravitational forces are equal F1 = F2.
So M1/d12 = M2/d22 and M1/ M2 = 4/1 = d12/d22
Therefore d1 = sqrt4 = 2 and d2 = sqrt1 = 1
The distance from the planet = 2/3 x 10,000 = 6,667 km.
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