Derivation of velocity dispersion from virial theorem?

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?
 

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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