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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)/d^{2}

So if Planet = m1 = 4 and the moon = m2 = 1

The force due to the planet is: F1 = M1/d1^{2} and the force due to the moon is: F2 = M2/d2^{2}

At the point where the gravitational forces are equal F1 = F2.

So M1/d1^{2} = M2/d2^{2} and M1/ M2 = 4/1 = d1^{2}/d2^{2}

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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