An interplanetary spaceship passes through the point in space where the gravitat

Question

An interplanetary spaceship passes through the point in space where the gravitational forces from the moon and the earth on the ship exactly cancel.

Part a. How far from the center of the earth is it?

moon Orbit Period 27.3 days

Please show work with equations. Not just looking for the answer.

An interplanetary spaceship passes through the point in space where the gravitational forces from the moon and the earth on the ship exactly cancel. Part a. How far from the center of the earth is it? Moon Mass 7.35*1022 kg moon Radius 1.74*10 6 m moon Orbit Radius from earth 3.84*10 8 m moon Orbit Period 27.3 days Earth Mass 5.97*10 24 kg Earth Radius 6.38*106 m G 6.67*10 -11 Please show work with equations. Not just looking for the answer.

Explanation / Answer

F = G m1 m2 / r2

The distance between the moon and the spaceship is 384,403,000 - x

F = GMMms/(384403000 - x)2 = GMEms/(x2)   

Mm/(384403000 - x)2 = ME/x2

sqrt (7.35 X 1022)/(384403000 - x) = sqrt(5.98 X 1024)/x

2.71 * 1011 x = 9.40 * 1020 - 2.45 X 1012 x

x = 3.45 * 108 m

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