# Something is not jibing

1. Jan 11, 2007

### kmarinas86

Conditions:
Stable
Self-gravitating
Spherical distributions
Equal mass objects

$KE=\frac{1}{2}M_{tot}v^2$
$PE\simeq-\frac{1}{2}G\frac{M_{tot}^2}{R_{tot}}$
$KE\simeq-\frac{1}{2}PE$
$M_{tot}\simeq 2\frac{R_{tot}v^2}{G}$

http://www.physics.uq.edu.au/people/ross/phys2080/nuc/virial.htm [Broken]

"When an ideal self gravitating system contract, half of the gravitational binding energy goes into thermal motion (heat) and the other half goes into radiation which is lost into space."

From above:

$KE\simeq-\frac{1}{2}PE$

Given the quote just above:

$Gravitational\ binding\ energy\simeq-PE$

$Gravitational\ binding\ energy\simeq\frac{1}{2}G\frac{M_{tot}^2}{R_{tot}}$

But, this is not right for a star. For a star, it is:

$Gravitational\ binding\ energy=G\frac{M_{tot}^2}{R_{tot}}$

This would mean that one fourth of the gravitational binding energy goes in to thermal energy, or one half of of the gravitational potential energy.

Something is not jibing, but what is it?

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Last edited by a moderator: May 2, 2017
2. Jan 11, 2007

### Gokul43201

Staff Emeritus
Well, at least one of those two expressions must be wrong (I think they both are). Where did you get them from? Shouldn't there be a 3/5 factor for the GPE of a uniform, spherical object?

3. Jan 12, 2007

### kmarinas86

Yes. But for a star its different $GM^2/r$.

http://en.wikipedia.org/wiki/Gravitational_binding_energy

For a galaxy, I'm not sure.

The fact that there are different fractions used makes me wary. Anyone have the full list?