Astronomy/"Roche limit" in astrophysics
Dear Prof. Seligman,
I would like to know why the "Roche limit" ( or "Limit of Roche" ), doesn't work in all situations. For example, why it doesn't work with the satellite of Saturn, Enceladus, who is orbiting inside that limit, between 2 rings of the mother-planet, and doesn't broke in small fragments of rock and ice, as happen to the small satellites who originated the rings ?
In the case of Enceladus, there seems to be some kind of misunderstanding. It is twice as far from Saturn as the planet's Roche limit, and has no problem holding together. Perhaps you have read that the Roche limit is close to the radius of the ring system, and knowing that there is a "ring" beyond Enceladus, presumed that the Roche limit was further out. However, that ring is far beyond the Roche limit, and was not produced by the disruption of a moon by tidal forces. It consists of ice particles released by geysers on Enceladus that have gradually spread out to form the ring over a period of time. This is made obvious by the fact that the ring gradually "thickens" as you move away from Enceladus: close to that moon the ice particles are nearly confined to its orbital plane, but further from Enceladus the particles are spread out over a much greater distance from that plane.
A better example of a moon holding together inside the Roche limit would be Pan, which is well inside the Roche limit for Saturn; in fact all the moons of Saturn from Janus inward are inside the limit. However, that is true only if we ignore non-gravitational forces that could hold the object together. Objects merely sitting on the surfaces of the infra-Roche-limit moons can "lift off" the surface of the moons as a result of Saturn's tidal force. But objects firmly attached to their surfaces can remain attached as long as the moons have some rigidity (that is, are made of more or less solid material). Pan is well inside the "liquid object" Roche limit, but is about 1.4 times as far from Saturn's center as the Roche limit for "typically" rigid objects, and Janus is about twice as far. So as long as they are relatively rigid (e.g., made of ice or rock), those moons can safely orbit inside the "liquid object" Roche limit.
I should note that for such "rigid" moons, there are two factors that determine whether they can hold together. One is how
rigid they are. A loose accumulation of material, such as a snowball, would have low rigidity, and have a harder time resisting Saturn's tidal forces. A good example would be a comet that is composed of a number of loosely bound fragments. Such an object would break up into smaller pieces if it passed too close to a planet, and in fact such breakups have been observed on several occasions (though most often for Jupiter, due to its much larger gravitational and tidal forces). However, something more rigid, like a large "ball" of hail, would have to be much closer to the planet to be pulled apart.
The second factor is how large the object is. For small objects such as hail balls, tidal forces are extremely small, but tidal forces gradually increase as the size of the moon increases. Even moons a few kilometers in size can hold together fairly well inside the Roche limit (less well if more like a snowball, better if more like a solid chunk). But for very large moons tidal forces are much larger, and as you move toward larger and larger moon sizes, the objects would have to be more and more rigid to avoid being pulled apart. At very large sizes, even a moon made of diamond, which is very rigid, might not survive.