Question

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 percentage 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 × 108 m, Earth's radius is 6.37 × 106 m, Moon's mass is 7.36 × 1022 kg, and Earth's mass is 5.98 × 1024 kg.

Answer 1

GIVEN:

The distance between the center of the earth and the center of the moon=

The radius of the earth is

Mass of the earth is

Mass of the moon is

SOLUTION

a) Percentage increase in the moon's gravitational pull when the moon moves from the opposite side to directly overhead:

The gravitational pull between two masses is given by:

Where G is the universal gravitation constant

M and m are the masses involved

r is the distance between the masses.

Let be the gravitational force on an object when the moon is opposite and be the gravitational force on an object when the moon is directly overhead. The percentage increase is given by

Now,

b) Percentage decrease in weight:

The change of gravitational pull is given by

It can be approximated as follows,

On the other hand, your weight as measured on earth is given by,

Since the moon pulls you up, the percentage decrease in the weight is