From http://www.astro.cornell.edu/academics/courses/astro201/vt.htm :(adsbygoogle = window.adsbygoogle || []).push({});

Conditions:

Stable

Self-gravitating

Spherical distributions

Equal mass objects

[itex]KE=\frac{1}{2}M_{tot}v^2[/itex]

[itex]PE\simeq-\frac{1}{2}G\frac{M_{tot}^2}{R_{tot}}[/itex]

[itex]KE\simeq-\frac{1}{2}PE[/itex]

[itex]M_{tot}\simeq 2\frac{R_{tot}v^2}{G}[/itex]

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:

[itex]KE\simeq-\frac{1}{2}PE[/itex]

Given the quote just above:

[itex]Gravitational\ binding\ energy\simeq-PE[/itex]

[itex]Gravitational\ binding\ energy\simeq\frac{1}{2}G\frac{M_{tot}^2}{R_{tot}}[/itex]

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

[itex]Gravitational\ binding\ energy=G\frac{M_{tot}^2}{R_{tot}}[/itex]

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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# Something is not jibing

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