How high above the earth would you have to go before your weight would be one quarter (1/4) of its value on th

Question

How high above the earth would you have to go before your weight would be one quarter (1/4) of its value on the earth's surface?

Answer 1

Force of gravity goes like 1/r^2

So 1/r^2 has to be 1/4 what it is on the earth's surface: (1/(radius earth))^2.

So you can solve for r (in terms of the earth's radius). To get your altitude (height above surface), you will have to subtract the radius of the earth from your answer for r.

altitude = r - radiusearth

Answer 2

g = GM/r^2
if weight is 1/4th, then gravity (g) is also one fourth

g/4 = GM/(2r)^2
g/4 = GM/4r^2

therefore, u have to go up to a height = to the radius of the earth, so that the distance between u and the center of the earth is 2r

Answer 3

You would have to double your distance from the earth's center that means you would have to go out one more radius.

Answer 4

6400 km.

This is equivalent to earth's radius.