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Derivation of velocity dispersion from virial theorem?

  1. Dec 11, 2009 #1
    Derivation of velocity dispersion from virial theorem??

    Hey,

    Im probably being a bit dim here but could anyone help me derive the velocity dispersion from the virial theorem. Ive got 2K+U=0, K/m~sigma^2 and U/m~GM/R.

    From rearranging I get a negative velocity^2? Or maybe its the gravitational force thats negative. Oh and a factor of 2. Is that just ignored??

    My notes say the answer is sigma^2~GM/R

    Just a bit confused, anyone got any clues?
     
  2. jcsd
  3. Dec 11, 2009 #2

    cepheid

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    Re: Derivation of velocity dispersion from virial theorem??

    The virial theorem says that 2T - |U| = 0, where U = -GM/R (the negative sign being important, since gravity is an attractive force).

    2T = |U|
     
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