I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by integrating Newton's law of gravitational force)...
$$PE_1 = -\frac{GMm}{r}$$
..has me thrown for a loop, especially after this answer.
- If potential energy really meant what I thought it did, then it would always have to be non-negative... but this equation is always negative. So what does "negative potential energy" mean!?
- If $KE + PE$ is always a constant, but PE is not only negative but becomes more negative as the particles attract, doesn't that mean the kinetic energy will become arbitrarily large? Shouldn't this mean all particles increase to infinite KE before a collision?
- If we are near the surface of the earth, we can estimate PE as $$PE_2 = mgh$$ by treating Earth as a flat gravitational plane. However, $h$ in this equation plays exactly the same role as $r$ in the first equation, doesn't it?
- So why is $PE_1$ negative while $PE_2$ is positive? Why does one increase with $h$ while the other increases inversely with $r$?
- Do they both represent the same "form" of energy? Since $PE_2$ is just an approximation of $PE_1$, we should get nearly the same answer using either equation, if we were near Earth's surface and knew our distance to its center-of-mass. However, the two equations give completely different answers! What gives!?
Can anyone help clear up my confusion?