Posted by **Amanda** on Saturday, October 3, 2009 at 11:05am.

At what altitude above the Earth's surface would your weight be three-fourths of what it is at the Earth's surface? Assume re = 6.371 10^3 km.

- Physics -
**MathMate**, Saturday, October 3, 2009 at 11:26am
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.

- Physics -
**Lindsey**, Tuesday, October 2, 2012 at 12:29am
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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