Pictures of the Hill Sphere
Why does Saturn have rings? Or to rephrase it to a question that is a little easier to answer: why are there moons and rings? Most moons, like our own Moon, are formed from accretion in a disk around a planet similar to how planets formed in a disk around the Sun. Small particles in a disk of material run into each other and stick, gradually forming an object large enough to be called a moon. I’ll get to how large that is in a minute. Since Saturn’s rings is a crowded disk of material, why aren’t the ring particles sticking together to form a moon? The answer has to do with how particles stick. Ultimately, when making a moon, our good friend gravity, the weakest force in the universe, is the chief sticking force. In Saturn’s rings, as in the rings of the other giant planets, the gravitational attraction between ring particles that would otherwise lead them to accrete into a moon, is thwarted by the tidal force from the planet they are orbiting. The tidal force is the differential force of gravity across an object that results from the dependence of the strength of gravity on the distance separating the two gravitating objects. Consider, for example, two particles in orbits around Saturn with the particles coming close enough to each other to touch, but one particle on an orbit slightly closer to Saturn than the other. When those two particles are in contact with each other, the gravitational attraction between them is strongest. But at the same time they are both experiencing slightly different gravitational accelerations from Saturn. The closer one feels a stronger pull from Saturn than the further one. This difference in the gravitational force between the particles and Saturn is strong enough to overcome the attraction between the two particles, so they don’t end up sticking.
So how do we ever get moons? That differential tidal force depends very strongly on how close the particles are to the planet. Far from the planet, the difference in the gravitational force between the two particles becomes negligible just as the separation between the two particles gets smaller in comparison to their distance from Saturn. The distance from a planet where two ring particles can stick together is called the Roche limit.
Originally the term “Roche limit” referred to the distance beyond which a strengthless, fluid object could stably exist near a planet without breaking apart due to the tidal force. However, since large strengthless fluid objects orbiting planets are not a common situation, the term has been colloquially co-opted to refer to the rather fuzzy boundary separating the region where particles can accrete and where they cannot. As it turns out there are a variety of Roche limits depending on the densities of the objects and their relative sizes, so frequently the term “Roche zone” is used. For example, it is easier for a grain of sand to stick to a boulder than for two boulders to stick together, because when you compare the distances of the two objects, the center of the grain of sand is closer to the boulder than the center of another boulder can get. We can say that the grain of sand fits inside the boulder’s own Roche zone. This region of space around a boulder or moonlet orbiting a planet where the boulder’s gravitational pull wins out over the competing pull of the planet is frequently called the Hill sphere (though it is not spherical), while the term Roche zone is usually used to specify the region of space around a planet where accretion is not possible.
Cassini’s cameras have captured pictures of small moons that orbit within Saturn’s rings near the outer edge of Saturn’s Roche zone. These moonlets have gravitationally accreted some nearby ring material, but they cannot grow without bound because of the strong tidal force from Saturn. In fact, particles can only stick to certain locations on these moons where Saturn’s gravitational pull on them is not as strong as that of the moonlets. Ring particles have, in essence, filled the Hill spheres of these moonlets. Two articles published in Science describe how small moons of Saturn graphically show the accretion of material within their limited Roche lobes (or “Hill sphere”). This NASA press release as well as the Cassini ISS web site have pictures and more information.
Image credit: NASA/JPL/SSI
Click the image to go to the Cassini web site for higher resolution versions with more information.
So how large does something need to be in order for it to be called a moon? While the IAU hasn’t weighed in on this yet, a functional definition that is being used in the Cassini era is that it is a moon if it is big enough to create a gap in the rings and basically be alone in its orbit. This is analogous to the IAU definition of a planet. It’s a relevant issue at Saturn because there are images of objects within the rings that create large disturbances, but are not big enough to create a gap. These objects are large ring particles that probably have the same shape as the moons shown above, but are too small to dynamically open a gap in the rings. They go by the nickname “propeller objects” for the shape of the perturbation they create in the rings.
December 10th, 2007 at 11:43 pm
Very nicely explained!
January 4th, 2008 at 7:41 am
Yes, nice piece of work. But I wish you’d mentioned the fact that one major scientific mystery about Saturn that Cassini has apparently solved is the fact that — as Larry Esposito predicted — this ability of different-sized ring particles to stick together even inside Saturn’s Roche limit seems to solve the long-time mystery of how Saturn’s rings could hold together for billions of years, against the tendency of impacts by infalling meteoroids to grind them to dust so fine that magnetospheric currents and sunlight pressure would blow it away. By his “eternal snowball fight” model, all of Saturn’s ring material spends a substantial amount of its life wrapped up in the interior of these large “propeller-generating” moonlets and thus shielded from meteoroids — until a particularly large metoroid splatters the snowball and spreads its material out into a wide zone within the rings, after which the snowball accumulation process continues elsewhere in the rings.
Cassini seems to have proven that one in a whole series of ways simultaneously:
(1) The confirmation of the existence of the propeller moonlets inside the main rings (plus the accumulation of material at the equatorial zones of Pan and Atlas);
(2) The fact that we see solid signs of similar clumping and re-dispersal cycles in the F and G Rings;
(3) The fact that all of Saturn’s little inner moons out to Prometheus are exactly the size and density that one would expect if they had accumulated loose material until their density dropped to the point that they completely filled up their Hill spheres;
(4) The VIMS compositional maps of the rings that show individual narrow zones with much fresher and lighter-colored ice (just as one would expect if a snoball had recently been splattered by a large impact, and its internal ice chunks hadn’t yet had their surface re-darkened by ice-vaporizing micrometeoroid impacts that left a crust of darker material).
Add to this (as Esposito already did) the fact that all the inner moons out to Pandora should actually have been orbiting INSIDE the rings just a few hundred million years ago, given the fact that the rings’ outer edge should be slowly pushed inward by their tidal forces — unless the inner moons are actually snowballs that used to actually BE dispersed ring material, and will probably become such material again when something big enough to splatter them hits them again.
As I say, it seems to me that the longevity of the rings is one of the two long-time, major mysteries about the Saturn system that Cassini has definitely solved. (The other is Iapetus’ light-dark dichotomy. John Spencer’s “thermal segregation” theory — with the segregation being initially triggered by mild darkening of Iapetus’ leading side by infalling debris from the little outermost irregular moons — already meshed very well with Voyager’s and Cassini’s long-distance observations, and its closeups of that Dalmatian-spotted surface during the September flyby seem to nail it down absolutely conclusively.)
Of course, Cassini — like any good space probe — has obligingly set up a swarm of fascinating new mysteries. Most of them, of course, involve Titan and Enceladus; but Saturn’s own weather patterns and internal structure have produced new puzzles as well.