SOLUTION: The weight of a body above the surface of the Earth varies inversely as the square of the distance of the body from the center of gravity of the Earth. Is an astronaut weighs 180

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Question 181844: The weight of a body above the surface of the Earth varies inversely as the square of the distance of the body from the center of gravity of the Earth. Is an astronaut weighs 180 lb on the surface of the Earth, how much would she weigh 500 miles above the surface of the Earth? Assume the radius of the Earth to be 4000 miles.
the answer is 142 lb.....but I have no clue to the steps to take to solve this problem...Please explain your steps..
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
You are told that a person's weight varies with the square of their distance to the center of the Earth. Let C be some constant.
At 4000 miles from the center of the earth (on the surface) you weigh
You are told


Now solve for the weight at 4500 miles (500 miles above the earth)
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