I Help with the Virial Theorem please

[Alfie114]

TL;DR Summary

I have a question about the virial theorem as applied to a cluster of stars.

Anyone able to help if I provide you with more details?

 

[PeroK]

You might need to provide a bit more detail about your question.

 

[Alfie114]

OK we have a star cluster (the system) which is made up from stars (total mass M sub *) and gas (total mass M sub g). The stars and gas are all distributed as spheres of constant density and a finite radius r sub c.

The total mass of the stars and the gas is different but we can assume that M sub g = f*M sub *

If the system is unrotating and in equilibrium how do we calculate the kinetic energy in terms of r sub c, f and M sub *?

We can take 2KE + PE = 0 where KE = (-3/5) (GM^2/R) and PE = (3kT/2)*n where n is the total number of particles = (M/mu*m sub H) where mu=1 and m sub H is the mass of a hydrogen atom.

 

[Arman777]

OK we have a star cluster (the system) which is made up from stars (total mass M sub *) and gas (total mass M sub g). The stars and gas are all distributed as spheres of constant density and a finite radius r sub c.

The total mass of the stars and the gas is different but we can assume that M sub g = f*M sub *

If the system is unrotating and in equilibrium how do we calculate the kinetic energy in terms of r sub c, f and M sub *?

We can take 2KE + PE = 0 where KE = (-3/5) (GM^2/R) and PE = (3kT/2)*n where n is the total number of particles = (M/mu*m sub H) where mu=1 and m sub H is the mass of a hydrogen atom.

You need to use math latex notation. Its hard to understand your equations like this.

 

[Alfie114]

Ok I've got these where omega is the potential energy