Moon effect. 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 3.82 108 m and Earth's radius is 6.37 106 m.

(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? %

When the moon is on the other side, pull of both moon and earth add up. when moon is overhead, pull of earth and moon acts in opposite direction.

distance of moon from earth = 382 x 10⁶ - 6.37 x 10⁶

Rm = 375 x 10⁶ m. this is the distance of moon when it is overhead.

Rm + 2Re = 375 x 10⁶ + 2 x 6.37 x 10⁶ m = 387.74 x 10⁶, this is the distance of moon from man when moon is on the other side of him

Pull of moon = G Mm / Rm²; M₂ is mass of the moon

maximum force

Pull of moon = G Mm / (Rm+2Re) ²; M₂ is mass of the moon minimum force

maximum force / minimum force = (Rm+2Re) ² / Rm²

= (387.74 x 10⁶) ² / (375 x 10⁶) ²

= 150342.3 / 140625

= 1.06

percentage increase = 6 %

b) Naturally there will be decrease of 6 %.