Two objects each of mass m are in circular o bird around the earth. Let Me be th

Question

Two objects each of mass m are in circular o bird around the earth. Let Me be the earths mass and Re be earths radius. Object one is at a distance Re from the earth surface and object 2 is at a distance 2Re from the earths surface. A) what is the ratio of the object ones kinetic energy to object 2s kinetic energy? B) what is the radio of object ones angular momentum to object twos? Two objects each of mass m are in circular o bird around the earth. Let Me be the earths mass and Re be earths radius. Object one is at a distance Re from the earth surface and object 2 is at a distance 2Re from the earths surface. A) what is the ratio of the object ones kinetic energy to object 2s kinetic energy? B) what is the radio of object ones angular momentum to object twos?

Explanation / Answer

As, GMm/r2 = mv2/r

=> v = sqrt(GM/r)

=>   v2 = GM/r

A) the ratio of the object ones kinetic energy to object 2s kinetic energy = 3/2

B) the ratio of object ones angular momentum to object twos = [2r/sqrt(2r)] * [sqrt(3r)/3r]

                                                                                                 =   sqrt(2)/sqrt(3)

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