In 1870 he introduced virial theorem which applied to heat.

It continues to increase in temperature as determined by the virial theorem.

Its statistical properties are superior to those of the virial theorem.

The virial theorem can be extended to include electric and magnetic fields.

Using the virial theorem, the dispersion velocity can be used in a similar way.

A simple application of the virial theorem concerns galaxy clusters.

A variational form of the virial theorem was developed in 1945 by Ledoux.

According to the virial theorem, the gravitational binding energy of a star is about two times its internal heat.

The virial theorem has been generalized in various ways, most notably to a tensor form.

Lord Rayleigh published a generalization of the virial theorem in 1903.

With the virial theorem it is easy to see that any such configuration will expand if not contained by external forces.

The virial theorem, and related concepts, provide an often convenient means by which to quantify these properties.

Thus the virial theorem applies even without taking a time-average:

The underlying assumption is that the system of N objects (stars) satisfies the virial theorem.

However, it requires that two components of the velocity be known for every star, rather than just one for the virial theorem.

According to the virial theorem the mean kinetic and potential energies in harmonic oscillator are equal.

Using the virial theorem we find:

The total energy is half the potential energy, which is true for noncircular orbits too by the virial theorem.

However, the virial theorem does not depend on the notion of temperature and holds even for systems that are not in thermal equilibrium.

Henri Poincaré applied a form of the virial theorem in 1911 to the problem of determining cosmological stability.

Rudolph Clausius proves the scalar virial theorem.

This cancellation is not accidental, it is a consequence of the relativistic virial theorem (Carlip 1999).

Fritz Zwicky was the first to use the virial theorem to deduce the existence of unseen matter, which is now called dark matter.

As another example of its many applications, the virial theorem has been used to derive the Chandrasekhar limit for the stability of white dwarf stars.

To remain gravitationally bound to such a group, each member galaxy must have a sufficiently low velocity to prevent it from escaping (see Virial theorem).