# Zero Potential Energy

1. Jan 4, 2015

### Inpyo

I was thinking about the concept of the ground being the arbitrary zero potential point for gravitational potential energy and considered that since gravity is the attractive force between two objects that there would be no potential energy if an object's center of mass were somehow situated exactly at the earth's center of mass. So would it be correct to say that a point of absolute zero potential exist within a system of say the earth and something else?

-Ted

2. Jan 5, 2015

### Nathanael

I wouldn't say it's arbitrary, it's chosen because it's often useful. If there is a more useful spot (for a specific problem) then I would take that to be the 'zero potential point.'

I am unsure if you're treating all of the Earth's mass as being located at the center, but just in case, I will remind you of the obvious: not all of Earth's mass is located at the center. As you move below the surface and approach the center, there is less mass pulling you down and the force of gravity gets weaker. Once you get to the center, if you could, then there would be no gravitational force on you and, as you said, no potential energy.

Can you think of anywhere else where there's zero gravitational potential energy?

3. Jan 5, 2015

### Staff: Mentor

That won't work with the forces between two idealized point particles, because the gravitational force becomes arbitrarily large as $r$ in $Gm_1m_2/r^2$ approaches zero. This means that dropping a particle from any height to zero will release an unbounded amount of energy and therefore the potential at $r=0$ is negative infinity. (This is the reason for the common convention of choosing the zero point of potential to be an infinite distance away).

With a real earth instead of an idealized point particle, the potential energy at $r=0$ remains finite and lower than anywhere else, so we can say that the potential energy is at a minimum there. However, just because it's a minimum doesn't mean that it has to be zero.

4. Jan 5, 2015

### Nathanael

What does it mean for the potential energy to be minimum but nonzero? What is the meaning of "potential" energy if there's no means of realizing it?

5. Jan 5, 2015

### Staff: Mentor

I didn't say it's "non-zero", I said that it doesn't have to be zero - and that's exactly what you said a few posts back, that we can put the zero point wherever we please.

6. Jan 5, 2015

### Nathanael

Sorry, I misunderstood.