SOLUTION: If you fly towards the moon, the Earth's gravitational grip becomes weaker, and the moon's gravitational grip becomes stronger. If you continue, the moons gravity will eventually b

Question 957006: If you fly towards the moon, the Earth's gravitational grip becomes weaker, and the moon's gravitational grip becomes stronger. If you continue, the moons gravity will eventually becomes stronger than the Earth's and the moon will win the tug of war.
The force of gravity F (measured in newtons) between you and an object is measured by Newton's Law of Universal Gravitation: F= G(m*N/ sqrt r)
G= the gravitational constant
m= your mass (in kilograms)
N= the mass of the other object (planet, moon, stars..... in kilograms)
r= the distance (in kilometers) between you and the center of the object
The mass of the moon is only 1.23% of the mass of the Earth. Also, the moon's distance from the Earth is not constant. It ranges between 362,600 km at perigee and 405,400 km at apogee. Let's assume that the moon is currently 398,300 km from the Earth.
Let's x represent the number of kilometers you are from the Earth. For what value of x will the moon's force of gravity be equal to the Earth's? (this is called the gravitational Neutral Point)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Your equation is incorrect.
It's not the square root of the distance but rather the square of the distance.

Where,

In this case,

and

Substituting,

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