The expression we have used for gravitational potential energy, U = mgh, applies only for a uniform field.

The more general equation is:

U

=

- G m M r

You are NOT free to define the zero anywhere you want - it is pre-defined to be zero at r = infinity.

Does it matter that the potential energy is negative everywhere? Not at all - all that matters is how the potential energy changes. If a mass moves from close to an object to further away, the potential energy changes from a larger negative number to a smaller one - this is an increase, as we expect.

This is consistent with the mgh we used for potential energy near the surface of the Earth, which can be proved.