Explaining the Virial Theorem in Astrophysics

In summary, the Virial theorem in astrophysics states that there is a relationship between the mass, gravitational potential energy, and radius of a system, given by the equation 3/5 GM/R = 3/2. The derivation of this theorem can be found in sources such as the book "Galaxy Formation" by Malcom S. Longair or "An Introduction to Modern Astrophysics" by Carroll & Ostlie.
  • #1
shounakbhatta
288
1
Hello,

I am reading Virial theorem from Wikipedia.

It states in astrophysics, virial relations are:

3/5 GM/R=3/2...

I want to know how this 3/5 and 3/2 value comes from?

If somebody can explain the step by step deduction of the Virial theorem in Astrophysics...

Thanks,

-- Shounak
 
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  • #2
Why not look it up yourself? The book Galaxy Formation by Malcom S. Longair has a derivation in section 3.5.1 (page 63). Actually, you can even read this section as part of the Google Books preview:

http://books.google.ca/books?id=e-wJHSBOuZAC&printsec=frontcover#v=onepage&q&f=false

I also seem to recall that Caroll & Ostlie (the huge orange textbook that many undergrads majoring in astro use) has a section on this as well.
 

1. What is the Virial Theorem in Astrophysics?

The Virial Theorem is a fundamental law in astrophysics that relates the total kinetic energy of a system to its potential energy. It states that in a stable system, the average kinetic energy is equal to the negative of half the average potential energy.

2. Why is the Virial Theorem important in astrophysics?

The Virial Theorem is important because it allows us to understand the stability and dynamics of systems in astrophysics, such as galaxies and star clusters. It also helps us to make predictions about the behavior of these systems and their evolution over time.

3. How is the Virial Theorem derived?

The Virial Theorem is derived from the equations of motion for a system of particles, using the concept of the virial and the principle of equipartition of energy. It can also be derived from the more general principle of conservation of energy.

4. What are some real-world applications of the Virial Theorem?

The Virial Theorem has many applications in astrophysics, including the study of stellar structure and the properties of galaxies. It is also used in other fields such as thermodynamics and fluid dynamics to understand the behavior of systems in equilibrium.

5. Are there any limitations to the Virial Theorem?

While the Virial Theorem is a powerful tool in astrophysics, it does have some limitations. It assumes that the system is in equilibrium and that the particles are interacting through a central force. It also does not take into account the effects of external forces or non-gravitational interactions.

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