# Gravitational acceleration above the Earth's surface

1. Nov 8, 2006

### bearhug

At what altitude above the Earth's surface would the gravitational acceleration be 4.9 m/s^2?

I thought this what very simple but apparently it is not since I got the wrong answer and can't figure out what I did wrong.
I used g= GM/r^2= GM/(R+h)^2 R being radius of earth and h being the altitude.

g= 4.9m/s^2

4.9= (6.73e-11)(5.98e24)/(6.37e6+ h)^2
4.9= 3.99e14-(6.37e6+h)^2
solved for h and got 2.00e7m

Can someone tell me where I went wrong? Thanks

2. Nov 8, 2006

### OlderDan

The approach is OK, but the computation has an error. You really only need the radius of the earth and g at the surface to do this, but your approach is OK too.

9.8m/s^2 = GM/R^2
4.9m/s^2 = GM/(R+h)^2
2 = (R+h)^2/R^2 <== dividing 1st eq by 2nd eq
etc