•For
the specific case of a sphere of total mass M, size R,
and constant density, the potential energy U = -3/5 (GM2/R). Thus the virial theorem says T =
½ U, so
–(3/2)
M <vr2> = (3/5) GM2/R
–Mvirial = 5σr2R/G, where σr is the
radial velocity dispersion
•
•
•Works
for elliptical galaxies and yields mass to light ratios
of 10-20 in solar units.
•
•