help please?

Question

At what height above the earth would a 4000 kg weather satellite have to orbit in order to experience a graviational force half as strong as that on the surface of the earth?

Answer 1

The mass of the satellite is irrelevant.

at the surface of the earth: g = GM/R^2 where R = radius of the earth

At some other distance above the surface: a = GM/r^2

a/g = (GM/r^2)/(GM/R^2) = R^2/r^2 = 1/2

So: r = SQRT(2)R = 1.414R
Radius of Earth = 6378.1 kilometers
r = 2642 km

The satellite would have to be a height of about 2642 kilometers above the surface of the earth