Posted by Amanda on Saturday, October 3, 2009 at 11:05am.
Based on Newton's law of universal gravitation,
F=GMm/r²
which means that the weight would be inversely proportional to the square of the distance from the centre of the Earth.
If H is the altitude when the weight becomes 3/4 of what's on the surface, then
(re/(re+H))^2=3/4
Solve for H.
Solved out for H:
(6371/sqrt(3/4)) - 6371 = H
for other fractions just plug in where 3/4's is.
Hope this helps!
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