Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990mnras.247..702k&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 247, Dec. 15, 1990, p. 702-704.
Astronomy and Astrophysics
Astronomy
9
Gravitation Theory, Gravitational Fields, Virial Theorem, Moments Of Inertia, Radial Velocity, Stellar Systems, Velocity Distribution
Scientific paper
Merrifield and Kent (1990) have noted that, at fourth order, there are actually two virial theorems involving the projected fourth moments; they proceeded to speculate as to the existence of virial theorems for all the higher moments. It is presently shown that analogs of the classical virial theorem for the projected second velocity moments in a spherically symmetric system indeed exist for all higher moments; at order 2n, there are n such virial theorems, and these relate the projected velocity moments to the spatial velocity moments of order 2n-2 and the potential. Measurements of the sixth and higher moments requires such a large number of velocities as to be of essentially academic interest only.
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