Gravitational potential energy

We have already found the equation DPE = -FDy for the gravitational potential energy when the change in height is not enough to cause a significant change in the gravitational force F. What if the change in height is enough so that this assumption is no longer valid? Use the equation W = GMm(1/r₂ - 1/r₁) derived in section 3.4 to find the potential energy, using r = ∞ as a reference point.

The potential energy equals minus the work that would have to be done to bring the object from r₁ = 1 to r = r₂, which is

This is simpler than the equation for the work, which is an example of why it is advantageous to record an equation for potential energy relative to some reference point, rather than an equation for work.