  We consider the Roche critical density (rho_Roche), the minimum density of an
orbiting object that, at a given distance from its planet, is able to hold
itself together by self-gravity. It is directly related to the more familiar
"Roche limit," the distance from a planet at which a strengthless orbiting
object of given density is pulled apart by tides. The presence of a substantial
ring requires that transient clumps have an internal density less than
rho_Roche. Conversely, in the presence of abundant material for accretion, an
orbiting object with density greater than rho_Roche will grow.
  Comparing the rho_Roche values at which the Saturn and Uranus systems
transition rapidly from disruption-dominated (rings) to accretion-dominated
(moons), we infer that the material composing Uranus' rings is likely more
rocky, as well as less porous, than that composing Saturn's rings.
  From the high values of rho_Roche at the innermost ring-moons of Jupiter and
Neptune, we infer that those moons may be composed of denser material than
expected, or more likely that they are interlopers that formed farther from
their planets and have since migrated inward, now being held together by
internal material strength.
  Finally, the "Portia group" of eight closely-packed Uranian moons has an
overall surface density similar to that of Saturn's A ring. Thus, it can be
seen as an accretion-dominated ring system, of similar character to the
standard ring systems except that its material has a characteristic density
greater than the local rho_Roche.
