Physics

A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the earth and the moon. The distance between the earth and the moon is 3.85 × 108 m, and the mass of the earth is 81.4 times as great as that of the moon.

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1. gravityEarth=gravitymoon
let x be distance from center Earth.

GMe*ms/x^2=GMm*ms/(3.85e8-x)^2
81.4/x^2=1/(3.85e8-x)^2

solve for x. Notice it is a quadratic, so I suggest the quadratic equation

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bobpursley

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