- #1
kmarinas86
- 979
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From http://www.astro.cornell.edu/academics/courses/astro201/vt.htm :
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
"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 into thermal energy, or one half of of the gravitational potential energy.
Something is not jibing, but what is it?
_________
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
"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 into thermal energy, or one half of of the gravitational potential energy.
Something is not jibing, but what is it?
_________
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