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..

 

[pmacias]

I would suggest that before applying any formula, we must first gather all the necessary information and understand the context of the problem. In this case, we are trying to estimate the mass of a globular cluster, which is a tightly packed group of stars.

To solve this problem, we need to use the concept of gravitational dynamics. The mass of a cluster is directly related to the gravitational force it exerts on its stars, which in turn affects their velocities. The root mean square velocity of stars in a cluster is related to the total mass of the cluster and the distance of the stars from the center of the cluster.

To find the mass of the cluster, we can use the formula: M = (Vrms)^2 * R/G, where G is the universal gravitational constant. However, this formula assumes that all stars in the cluster have the same velocity and are evenly distributed. This may not be the case for a globular cluster, where the stars may have varied velocities and are not evenly distributed.

Therefore, to get a more accurate estimate, we can use the virial theorem, which takes into account the kinetic and potential energies of the stars in the cluster. The formula for this is M = 3RVrms^2/G. This formula also requires the assumption that the cluster is in a state of dynamic equilibrium, meaning that the gravitational force is balanced by the kinetic energy of the stars.

In conclusion, to accurately estimate the mass of a globular cluster, we need more information about the distribution and velocities of the stars within the cluster. Without this information, it would be difficult to derive an accurate answer. As a scientist, it is important to consider all the factors and limitations before applying formulas to solve problems.