Here we derive and explore the true Gravitational Potential Energy of an object within a gravitational field. Gravitational Potential Energy (Ug , GPE or PEG , depending on who you ask) is only approximated as mgh when it in fact is not. So here we use Newton's Law of Universal Gravitation to along with the definition of Work to integrate to get the potential energy of an object.

It is important to point out that when using this potential energy function the potential is zero only at an infinite radius. All other radii have negative potentials.

Additionally it is important to point out, that for any object at a nonzero radius from another object, the potential energy of the object is finite. So even if you lift something infinitely high, you will only ever do so much work on that object. This leads to escape velocity, which we will explore in another video.