Question

The mass of the moon is 7.34 × 1022 kg, and its radius is about 1.74 × 106 m (a) What is the value of “gmoon”, that is, the acceleration of gravity for a falling object near the surface of the moon? (b) What is the escape speed (from the moon) for an object on the surface of the moon? (c) What is the escape speed from the earth for an object that is as far from the earth as the orbit of the moon? (d) At some point between the earth and the moon, an object would be pulled with equal strength towards both bodies. How far from the earth is that point?

Answer 1

A)

G_moon​​​ = GM/R^2 = (6.67 x 10^-11)(7.34 x 10^22)/(1.74 x 10^6)^2 = 1.617 m/s^2

B)

Escape velocity, v = sqrt(2 gR) = sqrt(2 x 1.617 x 1.74 x 10^6) = 2.37 x 10^3 m/s

C)

Velocity, v = sqrt(2 GMe/R) = sqrt(2 x 6.67 x 10^-11 x 5.97 x 10^24/3.84 x 10^8) = 1.44 x 10^3 m/s

D)

Sqrt(Me/Mm) = x/(3.84 x 10^7)

X = (384400 x 9.018)/10.018 = 3.46 x 10^5 km

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