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In statistical mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path) with that of the total potential energy of the system.
The virial theorem is an important theorem for a system of moving particles both in classical physics and quantum physics. The Virial Theorem is useful when considering a collection of many particles and has a special importance to central-force motion.
In this lecture we will discuss the virial theorem, which relates the kinetic energy (or temperature) of particles to their potential energy. This will give us, in a surprisingly simple
use the virial theorem to estimate the mass of the Coma Cluster. Express your result in solar masses.
The virial theorem relates the time-average kinetic energy of a system to the time-average potential energy. In the common situation that the force is proportional to some power of the distance, \[F \propto r^{n},\]
I. Development of the Virial Theorem. 1. The Basic Equations of Structure. Before turning to the derivation of the virial theorem, it is appropriate to review the origin of the fundamental structural equations of stellar astrophysics.
The virial theorem relates the total kinetic energy of a self-gravitating body due to the motions of its constituent parts, T to the gravitational potential energy, U of the body.