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Question

The masses and the radii of the earth and the moon are M1,R1 and M2,R2 respectively. Their centres are at a distance d apart. Find the minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape it to infinity.

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Solution

The P.E. of the mass at d/2 due to the earth and the moon is
U=GM1md×2GM2md×2
or U=2Gmd(M1+M2)(numerically)=12mV2e=U
Ve=2[Gd(M1+M2)].

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