# at what distance from the earth's surface will a mass of 10.0 kg be just 89.0 N in weight

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formulas:

w=fg

w = GMv1MvE / r^2

Mv1g = GMv1MvE / r^2

G = 6.67 x 10^6

g = 9.8

asked Jan 28, 2015

## 1 Answer

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The gravitational forces between the mass $m=10 kg$ and the earth $M=very big$ is $$w=G\frac{Mm}{r^2}$$

At the earth surface $w_s=10\times 9.8=98N=G\frac{Mm}{R^2}$

At some y above earth surface the weight is 89 N. Thus we can use proportions to figure out the distance.

Solve the following two equations to find y.

$$98=G\frac{Mm}{R^2}$$
$$89=G\frac{Mm}{(R+y)^2}$$
answered Jan 29, 2015 by (21,750 points)