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Locate the position of a spaceship on the Earth-Moon center line such that the tug of each celestial body exerts on it would cancel and the craft would literally be weightless.

I found two equations:

A.

(Distance between the aircraft and the Earth) + (Distance between the aircraft and Moon) = (Distance between the Earth and Moon)

B.

(The gravitational force between the aircraft and Moon) = ( The gravitational force between the aircraft and the Earth)

After doing the Algebra:

The distance between the aircraft and the Earth = 350 * 10^6 meters

Distance between the aircraft and Moon = 34 * 10^6 meters

As I expected, the air craft is nearer to Moon. So the less distance will cancel by the more mass of the Earth. But there is a question. If my answer is right, I'll ask it.

Thanks