At a point between the earth and the moon, the magnitude of the force exerted on

Question

At a point between the earth and the moon, the magnitude of the force exerted on a object by the earth's gravity equals the magnitude of the force exerted on the object by the moon's gravity. What is the distance from the center of the earth to that point to three significant digits? The distance from the center of the earth to the center of the moon is 383000 km, and the radius of the earth is 6370 km. The radius of the moon is 1738 km, and the acceleration due to gravity at its surface is 1.62 m/s^2

Explanation / Answer

the acceleration due to gravity on earth is 9.81 m/s^2 the acceleration due to gravity at moon's surface is 1.62 m/s^2 the distance from the center of the earth to the center of the moonis 383000 km let Xis the distance between from the center of earth to therequired point then X +1.62X/9.81 = 383000 X(1+0.16514) =383000 X*1.16514 =383000 X = 328715.862 km

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