Moving closer to the gravitating object is what turns the potential energy into all its other forms. Where do you think all the energy comes from to ignite fusion within stars? A shit ton of tiny gravitating objects all move closer to a shit ton of other tiny gravitating objects. Bam, suddenly every single one of these little particles has accumulated enough momentum to shear right through an atom's electric field and smash it straight in the nucleons. Ouch!

Take another look at Newton's law of universal gravitation my friend. Do you see that distance squared on the divisor side? Do you know what happens when the bottom part of a fraction when it goes to zero? Many calculators will just say Err, but they are just trying to hide the truth. It blows up to infinity. (Technically negative infinity is also possible depending on the equation and depending on how you approch zero, but that's not applicable here.)

That's right, a singularity has existed in the equation for gravity since the very moment that Newton invented it and things started falling to Earth. Theoretical physicistspiss their pants and faff about the infinite curvature that was Einstein's contribution to gravity, but a similar singularity in the form of infinite gravitational potential energy has always existed right there in the equation.

If pay attention in physics class then you might see that gravitational potential energy is always represented as negative. That's because just by existing in a world with gravity, we stand at the edge of a cliff with infinite gravitational potential energy, and it's a lot easier to play funny tricks like saying that potential energy can just go below zero than it is to work with the reality that any amount of potential energy we could ever save up would only ever amount to going from infinity to infinity plus one.

All gravitating objects have this singularity. The only reason the universe doesn't explode every time I reach for my stapler is pesky little details like atomic forces, the centrifugal pseudoforce, and fact that objects have a size. Rats, there goes my plan to generate infinite energy for society by repeatedly dropping them closer and closer to a point-mass.

Does that answer your questions?