# Potential energy of gravity

1. Jun 27, 2010

### Antiphon

Frankly, I think gravity should be repulsive force on the basis of a simple energy argument which I will now make. I request anyone with insight to find the flaw in my argument. (there has to be one since I think we'd all agree that gravity is an attractive force.)

One way to compute forces is to take a differential of a field energy along some spatial displacement. The force will point in the direction that decreases the energy of the field. Simple example: two electrons near one another. If you integrate the energy of the electrostatic fields through space 1/2*epsilon*E^2 in MKS units, you'll find that there is less energy in the field if the electrons are further apart. Therefore the force they experience is repulsive.

Why is this not the case for gravity? By this reasoning, masses should repel one another.

What am I missing?

2. Jun 27, 2010

### Staff: Mentor

What is the energy density of the gravitational field?

3. Jun 27, 2010

### Antiphon

Good question. But there has to be one otherwise lifting weights at the gym wouldn't build muscles, right?

4. Jun 27, 2010

### johng23

Using a field argument to claim that a force should be opposite to what is observed seems backwards. Isn't a field essentially a mathematical construct for describing the force that a body would feel at every point in a space?

5. Jun 27, 2010

### Antiphon

Yes.

I found a thread with a good review of the question at https://www.physicsforums.com/showthread.php?t=316784&page=3

I'm comfortable with a negative energy density in the gravitational field as the origin of it.

6. Jun 27, 2010

### Staff: Mentor

Building muscles requires a force, not necessarily a conservative force that would be associated with an energy density and a conserved energy.