Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the moon). When the payload is x miles from the center of the moon (x 2 R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: . _ _ RZP reqUIred force f(x) 2 pounds x For example, the amount of work done raising the payload from the surface of the moon (i.e., x = R) to an altitude of R miles above the surface of the moon (i.e., x = 2R) is [7 2R 2 work = / f(x) dx = / dx = mile-pounds a R X2 2 How much work would be needed to raise the payload from the surface of the moon (i.e., x = R) to the "end of the universe"