a) the gravitational potential energy at the distance r is
E=−rGMm=−r34πR3ρGm If r = R + h,
E=−R+h34πR3ρGm
b) At the surface of the Moon the potential energy is
E=−R+034πR3ρGm The total energy is
K+E=0.5mv2−34πR2ρGm=−R+h34πR3ρGm
G=8πρR23v2(1−R+hR)−1
c)
G=8π(3340)(1.74⋅106)23(3.630)2(1−1.74⋅106+21.51.74⋅106)−1=6.64⋅10−11kg2Nm2
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