SOLUTION: The weight of an object varies inversely as the square of its distance from the center of the earth. The radius of the earth is 6400 km, if a man is 80 kg on the earth‘s surface,

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Question 1162178: The weight of an object varies inversely as the square of its distance from the center of the earth. The radius of the earth is 6400 km, if a man is 80 kg on the earth‘s surface, what will he weigh 2000 km above the earth? 4000 km above the earth?
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.

Based on the problem condition, you can write the inverse proportion


     =  =  = 0.58.


From this proportion,  the weight of the 80 kg person at the height of 2000 km above the Earth surface is


    x = 0.58*80 = 46.4 kg.

Solved.

Using this solution as your TEMPLATE, you can solve the second problem ON YOUR OWN.

Happy calculations (!)


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The post-solution note. 

    Starting from 60-ies of the last century, kilograms are not used as a unit for weight (and for force).


    It was replaced by N (newtons).  1 kg (force) = 9.81 N (newtons).


So, your source is at least 60 years old . . .



Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
w=k/d^2
80=k/6400^2
k=3,276,800,000
at 2000 km above, r=8400^2
so weight is 3276800000/8400^2=46.44 kg
at 4000 km above r=10400 km, so weight=30.296 or 30.30 kg.
Simpler is that the ratio of the weight on Earth to 2000 km above earth is (6400/8400)^2=0.5805, and that *80 is 46.44 kg.
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