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

PART (a):

We have:

Mass of the moon, M = 7.34 × 10²² kg

Radius of the moon, R = 1.74 × 10⁶ m​​​​​​​

Therefore, Acceleration due to gravity at moon surface is given by:

PART (b):

Escape velocity is given by:

PART (c):

Escape speed of an object from earth's gravitational field is 11.2 km/s

PART (d):

At some point between the earth and the moon, an object would be pulled with equal strength towards both bodies.

At this point, the net force and net acceleration on the object will be zero.

Let R be the distance from earth to this point.

Distance between earth and moon is = 384400 km = 384400000 m

So the distance from moon to the object will be (384400000 - R)

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