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

a)
The force exerted by the Earth on the Moon is exactly equal ( and opposite ) that the Moon exerts on Earth and is determined by the law of universal gravitation formulated by Newton which states that the force exerted by a given object mass m1 over another mass m2 is directly proportional to the product of the masses and inversely proportional to the square of the distance that separates them :

Where:

F= gravitational force

G=Gravitational constant

m1= mass body one

m2= mass body two

R=distance between centers of the bodies

With the above equation , the data provided in the statement with the aim of having the value of the gravitational force exerted by the Earth-Moon are replaced

b)

The equation for calculating the gravitational pull of the Earth and the Moon are equal and the gravitational force of the moon is cleared. It takes into account the subscripts E and M signify earth and moon respectively.

Where:

m= mass

g= gravity

Se toma en cuenta que:

Replacing all values ​​in the equation :

Therefore , the weight is proportional to the mass by gravity. If we compare the weight for a given mass, it would have to obtain the reason for the severity of land between the gravity of the moon.

Therefore it concludes that the weight on the moon is 0.165 times that of the earth.