Yike! Don't go there - the formulae are wrong. The density terms haven't been cube-rooted correctly, the constant of proportionality given is for a fluid body rather than a rigid structure, and that constant isn't quite correct anyway ...
But I should have mentioned the difference between the Roche limit for a "fluid" body and for a rigid object,
since it's relevant to where you can place rings.
A "rock-pile" asteroid like Mathilde seems to be held together by its own self-gravity, and if it were to drift towards a massive planet it would deform in a fluid sort of way as the tidal stress built up, and so would disintegrate farther out than a more solid object would - the constant in the equation I gave above turns into 2.46 rather than 1.44. More importantly, if a rigid object is knocked apart by an impact when it's closer to the parent planet than the "fluid" Roche limit, it can't reaccrete under gravitational interaction - it'll turn into a ring, even though it's outside the "solid" Roche limit. So rings will persist out to the "fluid" Roche limit, but small solid satellites can exist as close to the planet as the "solid" Roche limit.
So
all the giant planets have small moons closer than 2.46 radii, but none have been detected closer than 1.44 radii. Rings will have a reasonably long life span out to 2.46 radii, but will tend to reaccrete into solid bodies beyond that limit. So in many cases close-in moons coexist with rings.
Another important thing to note is that these close-in satellites will be small and irregularly shaped - there won't be anything more than 500km in diameter. Below that diameter, solid bodies of "normal" density are rigid enough to resist the effects of their own gravity, and retain a lumpy shape. They'll also tend to resist tidal forces, and will stick in the same shape until the tidal pull effectively reverses the force of gravity at their surface.
Large objects can't resist their own gravity, and settle into a stable spherical form - and if they are exposed to tidal forces they accommodate the new force by shifting into an egg shape. So they deform fluidly, and will come apart at the "fluid" Roche limit. Nothing bigger than ~500km across will make it any further in.
Grant
