Derivation:

We have already learnt that the gravitational potential energy of a body near the surface of the earth is Gravitational PE = mgh

This expression is an approximation based on the assumption that g is constant, an assumption that is approximately valid near the surface of earth

Now let us consider gravitational potential energy of an object that is far removed from the earth's surface. This is the work done in bringing the object from infinity to the desired point.

Suppose that the object is situated outside the earth at point A which is at a distance r from the center of the earth.

The gravitational force exerted by the earth on the object at point P is

Total work done by the gravitational force to move the object from infinity to point P which is at a distance r from the centre of the earth is

Therefore the gravitational potential energy of an object at a distance r from the earth, which is defined as the work done in bringing it from infinity to that point is

This is negative because work is done by gravitational field and not against it in bringing from infinity to the point under consideration. The gravitational potential energy increases as the object is raised from the surface of the earth and decreases as it is brought closer to the earth.