Virial Theorem -- from Eric Weisstein's World of Physics

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Virial Theorem
(1)

(2)

But

(3)

(4)

and

(5)

(6)
Plugging (4) and (6) into (2),
(7)

(8)

Over short time scales, the arrangement of particles will appear constant, so any function of will time average to zero.

(9)

This means that

(10)




References

Binney, J. and Tremaine, S. "The Virial Equations." §4.3 in Galactic Dynamics. Princeton, NJ: Princeton University Press, pp. 211-219, 1987.



© 1996-2007 Eric W. Weisstein

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