Halliday, Resnick & Walker — Gravitation: Problem 44

44 Moon effect. Some people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percent does (a) the Moon’s gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? Assume that the Earth–Moon (center-to-center) distance is $3.82 \times 10^8 \text{ m}$ and Earth’s radius is $6.37 \times 10^6 \text{ m}$.