Universal quality of virial theorem

In summary, distances among galaxies in clusters are not significantly greater than their diameter. The theorem of virial still holds true regardless of scale, and clusters are in equilibrium regardless of rotation curves. This is because individual galaxies are treated as particles in virial equilibrium and the relation 2T+U=0 applies to orbiting masses.
  • #1
giann_tee
133
1
"Distances among galaxies in clusters on average are no greater than their diameter".

Luminosity, color, and other qualities are used to obtain distances - and these values are connected to masses that are observed by motions. If a system is in equilibrium then the theorem is:
2T+U=0
Mv^2/2 - GM^2/2R = 0
M=2Rv^2/G
If rotation curve represents a known function in form of a third Kepler's law for a concentration of mass near the core, then one set of motions is given by that function of mass and distance. Further away from galactic center, the function behind curve is not known, then mass and speed and not connected with known law.
However the theorem of virial still works no matter the scales? ...and the clusters are in equilibrium regardless of rotation curves?
The mass/luminosity ration M/L grows steadily per factor of scale, 20-30 per 50kpc and 200 per 1Mpc.
Luminosity can't be diminishing at large distances? I'm presuming that it is not diminishing at those rates, so the galaxies and clusters are rotating faster at large scales?
 
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  • #2
giann_tee said:
"Distances among galaxies in clusters on average are no greater than their diameter".

If a system is in equilibrium then the theorem is:
2T+U=0
Mv^2/2 - GM^2/2R = 0
M=2Rv^2/G...

... the theorem of virial still works no matter the scales? ...and the clusters are in equilibrium regardless of rotation curves?

Yes, this is so. The individual galaxies in a cluster are treated as if they were particles in virial equilibrium. As for rotation curves --- the relation 2T +U = 0 applies to orbiting masses as well, for example to the Earth in orbit around the sun. So it also applies to individual objects in orbit around the centre of any spherically symmetric mass distribution.
 

1. What is the Universal quality of virial theorem?

The Universal quality of virial theorem is a fundamental concept in physics that relates the average kinetic and potential energy of a system in equilibrium. It states that the average kinetic energy of a system is equal to half of the average potential energy, regardless of the specific details of the system.

2. How is the Universal quality of virial theorem derived?

The Universal quality of virial theorem is derived from the general virial theorem, which relates the average kinetic and potential energy of a system to the forces acting on the particles in the system. By assuming a system in equilibrium and using statistical mechanics, the universal form of the virial theorem can be derived.

3. What is the significance of the Universal quality of virial theorem?

The Universal quality of virial theorem has many applications in physics, including in astrophysics, plasma physics, and molecular dynamics. It is also used in the study of thermodynamics and the behavior of gases. Additionally, it provides insight into the stability and equilibrium of systems.

4. Can the Universal quality of virial theorem be applied to all systems?

Yes, the Universal quality of virial theorem can be applied to any system in equilibrium, regardless of its specific details or physical properties. This is because it is derived from fundamental principles and is not limited by any particular assumptions or simplifications.

5. How is the Universal quality of virial theorem used in practical applications?

The Universal quality of virial theorem is used in various practical applications, such as in the study of star systems, the behavior of gases, and the stability of molecular structures. It is also used in the development of theoretical models and simulations in various fields of physics.

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