Help with the Virial Theorem please

  • Context: Undergrad 
  • Thread starter Thread starter Alfie114
  • Start date Start date
  • Tags Tags
    Theorem Virial theorem
Click For Summary

Discussion Overview

The discussion revolves around the application of the Virial Theorem to a star cluster system composed of stars and gas. Participants are exploring how to calculate the kinetic energy of the system under specific conditions, including assumptions about mass distribution and equilibrium.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant describes a star cluster consisting of stars and gas, with total masses denoted as M sub * and M sub g, respectively, and proposes that M sub g = f*M sub *.
  • The same participant asks how to calculate the kinetic energy in terms of r sub c, f, and M sub * for an unrotating and equilibrium system.
  • Another participant suggests using mathematical notation for clarity, indicating that the current format of equations is difficult to understand.
  • A later post mentions potential energy, introducing the variable omega without further context.

Areas of Agreement / Disagreement

The discussion remains unresolved, with no consensus on the approach to calculating kinetic energy or the specific equations to use.

Contextual Notes

Participants have not fully defined all variables or assumptions, and there may be dependencies on specific definitions of terms like kinetic energy and potential energy.

Alfie114
Messages
3
Reaction score
0
TL;DR
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?
 
Astronomy news on Phys.org
:welcome:

You might need to provide a bit more detail about your question.
 
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.
 
Alfie114 said:
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.
 
Ok I've got these where omega is the potential energy
1575636887584.png
1575636809181.png
 

Similar threads

Undergrad What is the basic definition and application of the virial theorem?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Virial Theorem and the Ergodic hypothesis
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Why does temperature always rise in stars?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Explaining the Virial Theorem in Astrophysics
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad "Moment of Inertia" in Virial Theorem
  • · Replies 2 ·
Replies
2
Views
2K
Virial Theorem for an expanding globular cluster
  • · Replies 3 ·
Replies
3
Views
1K
Decrease of Solar radius per year using Virial Theorem
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Derivation of velocity dispersion from virial theorem?
  • · Replies 1 ·
Replies
1
Views
5K
Undergrad Some reasoning about Alfvén’s frozen-in flux theorem
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad Virial theorem as applied to hydrogen atom
  • · Replies 2 ·
Replies
2
Views
7K