G'day! I was looking over my notes about gravitational potential energy and I came across the graphs that I drew in class of the gravitational potential energy of a mass with reference point at infinity compared with the potential energy of a mass with reference point at the surface of the earth. They had totally different potential energies, one was negative, the other was positive. And then I jotted down a little side note saying, "potential difference is important, not potential energy". School isn't until another 6 weeks so could someone please help me justify why its more important to observe a mass' potential difference rather than its potential energy? I sorta have the idea in my head but I just can't express it in words...
The point being made is that only changes in potential energy (from one point to another) have physical significance. The particular value you may assign at some location depends on where you choose your reference point, but the change in PE when going from point A to point B does not. For example: If a mass m is lifted from a desk to a shelf, it doesn't matter if you take the reference point (where PE = 0) to be the floor or the desk or anywhere else. The change in PE will be mgΔh no matter what.
With gravity, the Potential is always Negative. It's just a matter of 'how much negative'. In some places, the potential will be Higher (less negative) than in others.