Which of the following has the greatest mass?

If M is the mass of the earth, m is the mass of the moon, and d is the distance between their centers, which of the following gives the in?

If M is the mass of the earth, m is the mass of the moon, and d is the distance between their centers, which of the following gives the instantaneous velocity of the moon as it orbits ...show more
Answer:

The gravitational force (F) between two masses M and m is given by: F = GMm/d² In this case this force is providing the centripetal force to keep the moon in a circular orbit about earth. Centripetal force = mv²/r {Here, r = d of course} So we can write: GMm/d² = mv²/d { m appears on both sides and cancels out} GM/d² = v²/d {multiply both sides by d} GM/d = v² v = √(GM/d) (a)

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