Quote by bobbles22
Gravitational Potential Energy = E_{g} = (GMm)/r

You omitted a minus sign. In this situation, we consider E
_{g} to be negative.
However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases.

No, the gravitational potential energy decreases as the object approaches the Earth, the same as an object close to the Earth for which we usually use E
_{g} = +mgh. Including a minus sign in your equation for E
_{g} takes care of this.