The Dynamics of Globular Clusters and Elliptical Galaxies
  Equations of motion are generated for an idealised model spherical galaxy or
globular cluster evolving from the epoch of galactic separation until it
attains a semi-equilibrium state through gravitational collapse. The
theoretical radial surface density is computed and compared with two globular
clusters, M15 and M80, and shows a good fit to observational data. The model is
contrasted with King's model, and mean cycle time and velocity are computed.
The velocity-radius curve is developed, and Gaussian RMS values derived from
which half-light radius vs. mass are plotted for 735 spherical objects,
including 544 normal ellipticals and compact, massive, and intermediate mass
objects. These latter show a linear mean log-log $R-M_{vir}$ slope of
${0.604\pm0.003}$, equivalent to a Faber-Jackson slope of
$\gamma=3.66{\pm}0.009$ over a mass range of 7 decades. and a slope of
$0.0045\pm0.0001$ on a semi-log plot of $R_{1/2}-\sigma$. Globular clusters,
dwarf elliptical and dwarf spherical galaxies show a distinct anomaly on these
plots, consistent with the ellipticals containing a supermassive black hole
(SMBH) whose mass increases as the velocity dispersion increases, compared with
the remaining types of spherical or irregular galaxies without a massive core.
