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?