If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

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(2) 1/2mgR. With U=-(GMm)/r and GM=gR², the object moves from r=R to r=2R. Δ U=-(GMm)/(2R)+(GMm)/R=(GMm)/(2R). Replacing GM by gR² gives Δ U=(gR²m)/(2R). So the gain is 1/2mgR.

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

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