# How does physicists calculate the gravitational self collapsing force of a star?

The nuclear fusion taking place inside the stars opposes its gravitational self collapsing force. But, how does physicists calculate it? I just know the classical gravitational theory and not a bit of general relativity. So, I would like to take the situation in a classical way. For example, in terms of Lyttleton-Bondi Model for the Expansion of the Universe the expansion of the universe is explained if matter has a net charge. Imagine a spherical volume containing un-ionized atomic hydrogen gas of uniform density. Assume the proton charge is $ke$ (where $e$ is the charge of an electron (this situation is taken for net charge of matter)). How to calculate the gravitational self collapsing force of this so that I could calculate the value of $k$ for which the electrostatic repulsion opposes it and the volume doesn't collapse on itself? I know how to calculate the gravitational force between masses or simple shapes(found using integration). But,I have no idea on how to calculate this.

(Even though Lyttleton-Bondi Model for the Expansion of the Universe model is discarded I would like to proceed with this as I don't know any high level math or other theories except classical mechanics taught in high school).

The interior pressure is calculated by "simply" integrating the weight of the overlying material.

Doing this is non-trivial because it depends on the density of that material which depends on the pressure and temperature as a function of radial position, so you have a set of self-consistency conditions to meet (including ones for heat transfer, which brings up the possibility of convection).

This is a whole semester course at the advanced upper-division or graduate level. I got to take it from Stan Peale at UCSB and really wish I'd been a slightly more mature physicist at the time as I might have gotten more out of it.

I took it out of Schwarzchild's book, which was dated even then but covers the basics in a form fairly accessible to the advanced college student.

• I have assumed uniform density for simplicity. The only force coming into the picture is the gravitational force tries to collapse the system on itself and the electrostatic force which tries to pull them apart.How should I calculate this total gravitational and electrostatic force? I have only done calculations which govern the gravitational or electrostatic force between two or more bodies. – Rajath Radhakrishnan Oct 28 '13 at 1:21
• If you have an assumed uniform condition tent most of the complexity drops out. You know both the fields from the densities and the symmetry (having a $r^{-2}$ force law means that you can treat spherically symmetric distributions closer to the center as if they were point-like and ignore everything further from the center ...) and you just go. – dmckee --- ex-moderator kitten Oct 28 '13 at 1:53
• Sir, but in this case if I choose this method it would be like finding the gravitational force of a point mass on itself(as there is no other body).Then, it will be the self collapsing force of the point mass(at the center of the spherical distribution).But, while dealing with classical mechanics it is told that the force of a mass on itself is zero.So, how to proceed with this? – Rajath Radhakrishnan Oct 28 '13 at 7:49
• You will be finding the forces on one part of the mass due to another part. You are dealing with an extended object, here, not an idealized point mass. – dmckee --- ex-moderator kitten Oct 28 '13 at 7:58
• But, I have not done such calculations before(force on one part by another part of the same body). How to calculate it sir? – Rajath Radhakrishnan Oct 28 '13 at 8:10