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Something is not jibing

  1. Jan 11, 2007 #1
    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 in to thermal energy, or one half of of the gravitational potential energy.

    Something is not jibing, but what is it?

    _________
     
  2. jcsd
  3. Jan 11, 2007 #2

    Gokul43201

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    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?
     
  4. Jan 12, 2007 #3
    Yes. But for a star its different [itex]GM^2/r[/itex].

    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?
     
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