# Newton's Law of Universal Gravitation

Imagine a line drawn from the center of the earth to the center of the moon. At some point on this line the magnitude of the gravitational attraction of the moon on a space vehicle would be equal to the magnitude of the earth's gravitational attraction on the vehicle. If the distance from the earth to the moon is about 4.0 x 10^5 km and the mass of the moon is about 1/80 that of the earth, at what distance from the earth's center will the resultant force acting on the space vehicle be zero?

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Let be the distance from the earth's center, the distance from the moon's center and R is the distance between earth's and moon's center. is the mass of the earth, the mass of the moon and the mass of the spacecraft.

Since the force exerted by the earth must be the same as the force exerted by the moon we have:

(1.1)

Or we can write:

(1.2)

We also know that:

(1.3)

Therefore:

(1.4)

Or:

(1.5)

All that is left is to plug in the numbers:

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