  The masses of star clusters range over seven decades, from ten up to one
hundred million solar masses. Remarkably, clusters with masses in the range
10^4 to 10^6 solar mases show no systematic variation of radius with mass.
However, recent observations have shown that clusters with masses greater than
3x10^6 solar masses do show an increase in size with increasing mass. We point
out that clusters with m>10^6 solar masses were optically thick to far infrared
radiation when they formed, and explore the hypothesis that the size of
clusters with m> 3x10^6 solar masses is set by a balance between accretion
powered radiation pressure and gravity when the clusters formed, yielding a
mass-radius relation r~0.3(m/10^6M_\odot)^{3/5} pc. We show that the Jeans mass
in optically thick objects increases systematically with cluster mass. We
argue, by assuming that the break in the stellar initial mass function is set
by the Jeans mass, that optically thick clusters are born with top heavy
initial mass functions; it follows that they are over-luminous compared to
optically thin clusters when young, and have a higher mass to light ratio
Upsilon_V=m/L_V when older than ~1 Gyr. Old, optically thick clusters have
Upsilon_V~ mcl^{0.1-0.3}. It follows that L_V~\sigma^{\beta}, where \sigma is
the cluster velocity dispersion, and \beta~4. It appears that Upsilon_V is an
increasing function of cluster mass for compact clusters and ultra-compact
dwarf galaxies. We show that this is unlikely to be due to the presence of
non-baryonic dark matter, by comparing clusters to Milky Way satellite
galaxies, which are dark matter dominated. The satellite galaxies appear to
have a fixed mass inside a fiducial radius, M(r=r_0)=const.
