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 ≥ R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: required force = f(x) = R2P x2 pounds 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 work = b f(x) dx a = 2R R2P x2 dx R = RP 2 mile-pounds 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"? work = mile-pounds