Determining the mass of globular cluster?

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Discussion Overview

The discussion revolves around estimating the mass of a globular cluster using various physical principles and equations. Participants explore different approaches, including thermodynamic formulas and the virial theorem, while addressing the challenges posed by missing variables.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant suggests using the formula Vrms = (root over) 3RT/M, noting the absence of the temperature variable T as a challenge in deriving the mass.
  • Another participant recommends using the virial theorem instead of thermodynamic approaches, arguing that temperature is not a relevant concept for globular clusters.
  • A third participant references Longair's work on modeling velocity distributions in clusters, indicating that temperature can be defined in terms of kinetic energy and velocity distribution.
  • A later reply provides a derived equation for mass, M = 2v^2R/G, and seeks clarification on the derivation of potential energy as 1/4 GM^2/R, expressing a desire for a simpler explanation without calculus.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to estimate the mass of the globular cluster, with differing opinions on the relevance of thermodynamics versus the virial theorem.

Contextual Notes

The discussion highlights limitations related to missing variables in the initial formulas and the assumptions underlying the use of the virial theorem in this context.

trina1990
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: 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
 
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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.
 
nicksauce said:
Use the virial theorem instead of trying to use thermodynamics.
Sure, but...

nicksauce said:
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 [itex](3/2)kT = (1/2)\mu \langle v^2 \rangle[/itex].
 
Last edited by a moderator:
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..
 

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