Some people believe that the Moon controls their activities. The Moon moves from being directly on the opposite side of Earth from you to be being directly overhead. Assume that the Earth-Moon (center-to-center) distance is 3.82 multiplied by 108 m and Earth's radius is 6.37 multiplied by 106.
(a) By what percent does the Moon's gravitational pull on you increase?
(b) By what percent does your weight (as measured on a scale) decrease?
F = (GMm)/r^2
The Attempt at a Solution
First I found the force of the gravitational force between me and the moon, then for me and the Earth. Then I set up a proportion and found the percent that the gravitational force between me and the moon is to the gravitational force between me and the Earth.
F(moon) = (6.67e-11 * 7.36e22 * 70.76)/(9.55e7)^2 = 3.81e-2
F(Earth) = (6.67e-11 * 5.98e24 * 70.76)/(9.55e7)^2 = 8.56
F(moon)/F(Earth) = x/100
x = [100 * F(moon)] / F(Earth) = .44