m= your mass measure in kilograms n=the mass of the other object (star, moon, pl

Question

m= your mass measure in kilograms

n=the mass of the other object (star, moon, planet in kilograms)

r= the distance in kilograms between you and the center of the object

the moon's mass is 1.23% of the mass of the earth. also the moon's distance from the earth is not constant (it ranges from 362,600 km at perigee and 405,400 km at apogee). assume that the moon is currently (d) kilometers from earth.

the missing value is d=387100

1. let x represent the number of kilometers that you are from the earth. for what value of x will the moons force of gravity be equal to the earths? (its called the gravitational neutral point). make sure to round the answer to the nearest kilometer.

Explanation / Answer

d = 3.871 x 108 m

x = distance from earth

Given that

Mm = 0.00123 Me

using equilibrium of force

GMe/x2 = GMm/(d - x)2

Me/x2 = 0.00123 Me /((3.871 x 108) - x)2

x = 3.74 x 108 m = 3.74 x 105 km

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