(7) is equal to zero due to the classical virial theorem. Thus, we conclude that in classical physics averaged over time passive gravitational mass of a composite body is equivalent to its energy, taken in the absence of gravitational field [7, 8].
(10) is zero in accordance with the quantum virial theorem [13].
Assuming that the virial theorem holds for galaxies, the velocity v is derived from Eq.
For simplicity, we assume that the cluster system is in the n = 1 state, that the virial theorem applies, that [a.sub.0] = 1.2x[10.sup.-10] m/[s.sup.2], and that the cluster is approximately a flattened ellipsoid similar to the Local Group [6] that includes our Galaxy and M31.
While the
virial theorem derives its name from the work of Clausius [1], credit for its initial formulation has also been ascribed to Lagrange [2], as the theorem can be derived from the Lagrange identity [3, 4].
Weidmann, "The
virial theorem and its application to the spectral theory of Schrodinger operators," Bulletin of the American Mathematical Society, vol.
Virial theorem is useful to handle all the difficulties facing the spectrum changings, where these changings subject to change of pressure, temperature, and density of O2 real gas.
What would seem like an obvious candidate for dealing with complex systems, the
virial theorem, receives only passing mention.
From the
virial theorem, which applies to stable systems composed of many bodies, we get: