derive an expression for the potential energy of a particle of mass m above the surface of the earth, and show that it can be written as:

U(r) = -g0 RE/r

where r is the distance from the centre of the earth, RE is the radius of the earth, and g0 is the value of the

gravitational field at the surface of the earth.

To cut to the chase I am at this point.

U(r) - U(RE) = -GMm(1/r - 1/RE) + C

and rewrote it as U(r) - U(RE) = -GMm(RE-R/REr) + C

But I can't seem to figure out how to get it in the form g0 RE/r.