SOLUTION: The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut wei

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Question 1032109: The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 222 pounds on the surface of the Earth, what will this astronaut weigh 200 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
The working equation would be , for some undetermined constant.
To find k, We substitute the initial conditions in to the working equation:
==> lb-mi^2.
==>
==> pounds, or 201 pounds to the nearest pound.
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
From the condition, you have this proportion:

 = ,

where  = 222 pounds is the astronaut weight on the surface of the Earth and  is the astronaut weight 200 miles above the Earth.

Substitute your data into the proportion. You will get

 = .


Hence,

 =  = 201.36 pounds.


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