A space capsule weighing 5000 pounds is propelled to an altitude of 200 miles above the surface of the earth. How much work is done against the force of gravity? Assume that the earth is a sphere of radius 4000 miles and that the force of gravity is f(x) = -k/x2, where x is the distance from the center of the earth to the capsule (the inverse-square law). Thus, the lifting force required is k/x2, and this equals 5000 when x = 4000.