Question

At what altitude above the earths surface is the acceleration due to gravity equal to g/2?

Answer 1

You can use Gauss' law here to simplify the problem. Once you are outside of a sphere of matter, it is OK to treat it as a point mass located at its centre of mass. This means that once you are above the Earth's surface (disregarding mountains and stuff) the gravitational field you experience is exactly the same as that of a point mass at the Earths core with the same mass as the Earth.

This is a really useful theorem and you probably use it in a lot of other cases without thinking about it.

So, now that we have this, remember that gravity is an inverse square law. If the field has fallen by a factor of 2, then the distance must have increased by a factor sqrt(2). Thus, the 'height' you are looking for is sqrt(2)*R, where R is the radius of the Earth. This is measured from the centre of the Earth however - height above the surface will by sqrt(2)*R - R.

Hope that all makes sense

Answer 2

i thought that was called as the shell theorem.. didn't know it was gauss theorem :P