Determining the mass of globular cluster?

[trina1990]

: Estimate the mass of a globular cluster with the radius of R=20pc and root
mean square velocity of stars equal to Vrms=3km/s

i can apply the formula like
Vrms=(root over) 3RT/M ( where R=gas constant, T= absolute temperature, M=mass of the cluster)

but here the variable of the "T" is missing...
how can i derive the answer?

another formula applies like
V rms= (root over) 3p/k (here, p=pressure of the gasses within the cluster, k=density of the cluster)

here, Pressure is missing..

should i guess these amounts or there are some hidden clues here to solve it out?

please help

 

[nicksauce]

Use the virial theorem instead of trying to use thermodynamics. It doesn't really make sense to talk about the temperature of a globular cluster.

 

[cepheid]

Use the virial theorem instead of trying to use thermodynamics.

Sure, but...

It doesn't really make sense to talk about the temperature of a globular cluster.

Longair talks about modelling the velocity distribution of galaxies in a galaxy cluster (or stars in a globular cluster) as an "isothermal gas sphere" http://books.google.ca/books?id=e-w...tion by Longair&pg=PA103#v=onepage&q&f=false"

In this situation, it looks like the "temperature" is defined by setting $(3/2)kT = (1/2)\mu \langle v^2 \rangle$.

 

[trina1990]

thank you ...
i didn't even heard of this theory earlier as i am not a physics student...
any way i got the equation for the mass to be

M=2v^2R/G
now i can easily solve this out...

but can you please help me a bit more to completely understand the equation..?
as it says
the kinetic energy=-1/2 potential energy
then i derived kinetic energy to be 1/2Mv^2...
but how do they derive the potential energy to be
1/4 GM^2/R
please make me it understand with simple mechanics..no calculus please..