# Potential energy of a sphere

1. Oct 27, 2006

### lark

Something I realized the other day - trying to figure out what the gravitational (or electrostatic) force would be between two spheres -
the force ON a sphere from another sphere, is the same as if the other sphere's mass were concentrated at its center.

So what is this force? It turns out that the force on a sphere FROM a point mass is the same as the force a sphere exerts ON a point mass - that is, the sphere is attracted to another point as if the sphere were a point itself! (from newton's third law or whatever - action = reaction)

So the force between two spheres is the same as if the mass in the two spheres were concentrated at their centers.

In general if potential energy is 0 at infinity, the potential energy of object 1 from the gravitational field of object 2 is the same as the potential energy of object 2 in the grav. field of object 1 ...

laura

2. Oct 27, 2006

### arildno

Congratulations!
You have just shown one of the most important discoveries Sir Isaac Newton made with his theory of gravitation.
this was not meant ironic, it is indeed a pleasing and elegant result.

3. Oct 28, 2006

### Meir Achuz

Poor Newton didn't know Gauss's law (He didn't even know Gauss), so he had to work that out in a very complicated derivation.

4. Oct 28, 2006

### rbj

just want to reiterate to the OP what Meir said, that this can be shown pretty clearly using spherical symmetry and Gauss's Law.

5. Oct 29, 2006

### arildno

Is it Newton's fault he didn't know Gauss, and essentially proved this, if I recall correctly, within the context of Euclidean geometry?