How High Above Earth is Gravity 10% of Sea Level?

[ryryguy]

Homework Statement

At what height above the Earth's surface is the acceleration due to gravity 10% of that at sea level?

Homework Equations

F= Gm1m2/r(squared)

The Attempt at a Solution

I think some how one of the masses is moved over so that F/m=a and I think .10 is multiplied times something like (r squared) or (r + x)squared.

 

[G01]

As you said, F/m=a. When at the surface of the Earth at sea level:

$$\frac{F}{m}=\frac{GMm}{m(r+x)^2}=\frac{GM}{x^2}$$

where x= radius of Earth, and since at the sea level r would be zero.

Now what is 10% of this? After you find this, can you set up an equation and solve for the distance from Earth? If you need more help feel free to ask. Good Luck!