The equation (increase in) Gravitational Potential Energy=
is only an approximation when is is small compared to the radius of the Earth. The graph of gravitational potential
against
the distance from the Earth's centre is shown below.
To move from a distance
say, near to the Earth's surface to a distance
we need to put in an amount of energy per unit mass for the object being moved of
since
the acceleration due due gravity is given by the force of gravity on a 1 Kg mass at the Earth's surface.
The increase in Gravitational Potential is then
and the increase in gravitational potential energy for a mass
is