Where does the gravity of the moon become stronger than that of the earth so that an object in space between the two is drawn towards the moon instead of earth?

Answer 1

First, this isn't a simple "statics" problem. For example, the Moon is orbiting Earth. Also the Earth-Moon distance varies (elliptical orbit).

(The distances mentioned below are, strictly speaking, distances from the centres of the Earth and Moon.)

However, a simple answer is: at about a tenth of the Earth-Moon distance from the Moon. Here's why:

The Moon's mass is about 1/81 of the Earth's mass.

Gravitational force is directly proportional to the mass of an object.

Gravitational force is inversely proportion to the square of the distance between objects.

When the ratio of the distance to Moon to the distance to the Earth is 1/9

gives the "neutral gravity point". That's because 1/9 x 1/9 = 1/81.

So, the place where the Moon's gravity takes over is one tenth of the Earth-Moon distance from Moon.

The Moon's average distance from Earth is about 238,000 miles. That means the answer is: at about 23,800 miles from the Moon.

(Remember there are other ways of looking at this problem. There is more than one "correct" answer, depending on your approach.)