12.4 Saturn’s Spectacular Ring System

THE VIEW FROM EARTH

The most obvious aspect of Saturn’s appearance is, of course, its planetary ring system. Astronomers now know that all the jovian planets have rings, but Saturn’s are by far the brightest, the most extensive, and the most beautiful. Galileo saw them first in 1610, but he did not recognize what he saw as a planet with a ring. At the resolution of his small telescope, the rings looked like bumps on the planet, or perhaps components of a triple system of some sort. In 1659 the Dutch astronomer Christian Huygens realized what the "bump" was—a thin, flat ring, completely encircling the planet.

In 1675 the French-Italian astronomer Giovanni Domenico Cassini discovered the first ring feature, a dark band about two-thirds of the way out from the inner edge. From Earth, the band looks like a gap in the ring (an observation that is not too far from the truth, although we now know that there is actually some ring material within it). This "gap" is named the Cassini Division, in honor of its discoverer. Careful observations from Earth show that the inner "ring" is in reality also composed of two rings. From the outside in, the three rings are known somewhat prosaically as the A, B, and C rings. The Cassini Division lies between the A and B rings. The much narrower Encke gap, some 300 km wide, is found in the outer part of the A ring. These ring features are marked on Figure 12.10. No finer ring details are visible from our Earthly vantage point. Of the three main rings, the B ring is brightest, followed by the somewhat fainter A ring, and then by the almost translucent C ring. A more complete list of ring properties appears in Table 12.1. (The D, E, F, and G rings listed in the table are discussed later in this section.)

Figure 12.10 Saturn, Up Close Much fine structure, especially in the rings, appears in this image of Saturn taken while the Voyager 2 spacecraft approached the planet in 1981. (One of Saturn’s moons appears at bottom, and a second casts a black shadow on the cloud tops.) The banded structure of Saturn’s atmosphere is also more evident in this photograph. Note the absence of the vivid colors that characterize Jupiter’s atmospheric cloudlayers. (NASA)

WHAT ARE SATURN’S RINGS?

A fairly obvious question—and one that perplexed the best scientists and mathematicians on Earth for almost two centuries—is: What are Saturn’s rings made of? By the middle of the nineteenth century, various dynamical and thermodynamic arguments had conclusively proved that the rings could not be solid, liquid, or gas! What is left? In 1857 Scottish physicist James Clerk Maxwell, after showing that a solid ring would become unstable and break up, suggested that the rings are composed of a great number of small particles, all independently orbiting Saturn, like so many tiny moons. That inspired speculation was verified in 1895, when Lick Observatory astronomers measured the Doppler shift of sunlight reflected from the rings and showed that the velocities thus determined were exactly what would be expected from separate particles moving in circular orbits in accordance with Newton’s law of gravity.

What sort of particles make up the rings? The fact that they reflect most (over 80 percent) of the sunlight striking them had long suggested to astronomers that they were made of ice, and infrared observations in the 1970s confirmed that water ice is indeed a prime ring constituent. Radar observations and later Voyager studies of scattered sunlight showed that the diameters of the particles range from fractions of a millimeter to tens of meters, with most particles being about the size (and composition) of a large snowball on Earth.

We now know that the rings are truly thin—perhaps only a few tens of meters thick in places. Stars can occasionally be seen through them, like automobile headlights penetrating a snowstorm. Why are the rings so thin? The answer seems to be that collisions between ring particles tend to keep them all moving in circular orbits in a single plane. Any particle that tries to stray away from this orderly motion finds itself in an orbit that soon runs into other ring particles. Over long periods of time the ensuing jostling serves to keep all particles moving in circular, planar orbits. The asymmetric gravitational field of Saturn (the result of its flattened shape) sees to it that the rings lie in the planet’s equatorial plane.

Figure 12.11 Roche Limit The increasing tidal field of a planet first distorts, and then destroys, a moon that strays too close. (The distortion is exaggerated in the second and third panels.)
THE ROCHE LIMIT

But why a ring of particles at all? What process produced the rings in the first place? To answer these questions, consider the fate of a small moon orbiting close to a massive planet such as Saturn. The moon is held together by internal forces—its own gravity, for example. As we bring our hypothetical moon closer to the planet, the tidal force on it increases. Recall from Chapter 7 that the effect of such a tidal force is to stretch the moon along the direction to the planet—that is, to create a tidal bulge. Recall also that the tidal force increases rapidly with decreasing distance from the planet. (Sec. 7.6) As the moon is brought closer to the planet it reaches a point where the tidal force tending to stretch it out becomes greater than the internal forces holding it together. At that point the moon is torn apart by the planet’s gravity, as shown in Figure 12.11. The pieces of the satellite then pursue their own individual orbits around that planet, eventually spreading all the way around it in the form of a ring.

For any given planet and any given moon, the critical distance, inside of which the moon is destroyed, is known as the tidal stability limit, or the Roche limit, after the nineteenth-century French mathematician Edouard Roche, who first calculated it. As a handy rule of thumb, if our hypothetical moon is held together by its own gravity and its average density is comparable to that of the parent planet (both reasonably good approximations for Saturn’s larger moons), then the Roche limit is roughly 2.4 times the radius of the planet. Thus, for Saturn, no moon can survive within a distance of 144,000 km of the planet’s center, about 7000 km beyond the outer edge of the A ring. The main (A, B, C, and E) rings of Saturn occupy the region inside Saturn’s Roche limit.

These considerations apply equally well to the other jovian worlds. Figure 12.12 shows the location of the ring system of each jovian planet relative to the planet’s Roche limit. Given the approximations in our assumptions, we can conclude that all the major planetary rings are found within the Roche limit of their parent planet. Notice that strictly speaking the calculation of this limit applies only to low-density moons massive enough for their own gravity to be the dominant force binding them together. Sufficiently small moons can survive even within the Roche limit because they are held together mostly by interatomic (electromagnetic) forces, not by gravity.

Figure 12.12 Jovian Ring Systems The rings of Jupiter, Saturn, Uranus, and Neptune. All distances are expressed in planetary radii. The red line represents the Roche limit. In all cases the rings lie within the Roche limit of the parent planet.

THE VIEW FROM VOYAGER

Thus it was, as Voyagers 1 and 2 approached Saturn, that scientists on Earth were fairly confident that they understood the nature of the rings. However, there were many surprises in store. The Voyager missions changed forever our view of this spectacular region in our cosmic backyard, revealing the rings to be vastly more complex than astronomers had imagined.

Figure 12.13 Saturn’s Rings, Up Close Voyager 2 took this close-up of the ring structure just before plunging through the tenuous outer rings of Saturn. The ringlets in the B ring, spread over several thousand kilometers, are resolved here to about 10 km. As Voyager approached Saturn, more and more of these tiny ringlets became noticeable in the main rings. The (false) color variations probably indicate different sizes and compositions of the particles making up the thousands of rings. Earth is superposed, to proper scale, for a size comparison. (NASA)
As the Voyager probes approached Saturn it became obvious that the main rings are actually composed of tens of thousands of narrow ringlets (shown in Figure 12.13). Although Voyager cameras did find several new gaps in the rings, the ringlets are generally not separated from one another by empty space. Instead, the rings contain concentric regions of alternating high and low concentrations of ring particles—the ringlets are just the high-density peaks. Although the process is not fully understood, it seems that the mutual gravitational attraction of the ring particles (as well as the effects of Saturn’s inner moons) enables waves of matter to form and move in the plane of the rings, rather like ripples on the surface of a pond. The wave crests typically wrap around the rings, forming tightly wound spiral patterns called spiral density waves that resemble grooves in a huge celestial phonograph record.

Although the ringlets are probably the result of spiral waves in the rings, the true gaps are not. The narrower gaps—about 20 of them—are most likely swept clean by the action of small moonlets embedded in them. These moonlets are larger (perhaps 10 or 20 km in diameter) than the largest true ring particles, and they simply "sweep up" ring material through collisions as they go. Despite many careful searches of Voyager images, only one of these moonlets has so far been found—in 1991, after five years of exhaustive study, NASA scientists confirmed the discovery of the eighteenth moon of Saturn (now named Pan) in the Encke gap. Astronomers have found indirect evidence for embedded moonlets, in the form of "wakes" that they leave behind them in the rings, but no other direct sightings have occurred. Despite their elusiveness, however, moonlets are still regarded as the best explanation for the small gaps.

Figure 12.14 Spokes in the Rings Saturn’s B ring showed a series of dark temporary "spokes" as Voyager 2 flew by at a distance of about 4 million km. The spokes were caused by small particles suspended just above the ring plane. (NASA)
Voyager 2 found a series of faint rings, now known collectively as the D ring, inside the inner edge of the C ring, stretching down almost to Saturn’s cloud tops. The D ring contains relatively few particles and is so dark that it is completely invisible from Earth. Another faint ring, also a Voyager 2 discovery, lies well outside the main ring structure. Known as the E ring, it appears to be associated with volcanism on the moon Enceladus.

The Voyager 2 cameras revealed one other completely unexpected feature. A series of dark radial "spokes" formed on the B ring, moved around the planet for about one ring orbit period, and then disappeared (Figure 12.14). Careful scrutiny of these peculiar drifters showed that they were composed of very fine (micron-sized) dust hovering a few tens of meters above the plane of the rings. Scientists believe that this dust was held in place by electrostatic forces generated in the ring plane, perhaps resulting from particle collisions there. The electrical fields slowly dispersed, and the spokes faded as the ring revolved. We expect that the creation and dissolution of such spokes is a regular occurrence in the Saturn ring system.

ORBITAL RESONANCES AND SHEPHERD SATELLITES

Figure 12.15 Cassini Division Close inspection by Voyager 2 revealed that the Cassini Division (shown here as the darker color) is not completely empty. It contains a series of faint ringlets and gaps, assumed to be caused by unseen embedded satellites. The density of material in the division is very low, accounting for its dark appearance from Earth. (NASA)
Voyager
images show that the largest gap in the rings, the Cassini Division, is not completely empty of matter. In fact, as shown in Figure 12.15, the Division contains a series of faint ringlets and gaps (and, presumably, embedded moonlets too). The overall concentration of ring particles in the division as a whole is, however, much lower than in the A and B rings. Although its small internal gaps probably result from embedded satellites, the Division itself does not. It owes its existence to another solar system resonance, this time involving particles orbiting in the Division and Saturn’s innermost major moon, Mimas.
(Sec. 8.4) A ring particle moving in an orbit within the Cassini Division has an orbital period exactly half that of Mimas. Particles in the Division thus complete exactly two orbits around Saturn in the time taken for Mimas to orbit once—a configuration known as a 2:1 resonance. Applying Kepler’s third law (recast to refer not to the planets but to Saturn’s moons), we can show that this 2:1 resonance with Mimas corresponds to a radius of 117,000 km, the inner edge of the Division. (More Precisely 2-3) The effect of this resonance is that particles in the Division feel a gravitational tug from Mimas at exactly the same location in their orbit every other time around. Successive tugs reinforce one another, and the initially circular trajectories of the ring particles soon get stretched out into ellipses. In their new orbits these particles collide with other particles and eventually find their way into new circular orbits at other radii. The net effect is that the number of ring particles in the Cassini Division is greatly reduced.

Particles in "nonresonant" orbits (that is, at radii where the orbital period is not simply related to the period of Mimas) also experience Mimas’s gravitational pull. But the times when the force is greatest are spread uniformly around the orbit, and the tugs cancel out. It’s a little like pushing a child on a swing—pushing at the same point in the swing’s motion each time produces much better results than do random shoves. Thus, Mimas (or any other moon) has a large effect on the ring at those radii where a resonance exists and little or no effect elsewhere.

We now know that resonances between ring particles and moons play a very important role in shaping the fine structure of Saturn’s rings. For example, the sharp outer edge of the A ring is thought to be governed by a 3:2 resonance with Mimas (three ring orbits in two Mimas orbital periods). Most theories of planetary rings predict that the ring system should spread out with time, basically because of collisions among ring particles. Instead, the A ring’s outer edge is "patrolled" by a small satellite named Atlas, held in place by the gravity of Mimas, which prevents ring particles from diffusing away. Compare Tables 12.1 and 12.2 and see if you can identify other resonant connections between Saturn’s moons, or between the moons and the rings. (You should be able to find quite a few—Saturn is a very complex place!)

Outside the A ring lies the strangest ring of all. The faint, narrow F ring (shown in Figure 12.16) was discovered by Pioneer 11 in 1979, but its full complexity became evident only when Voyager 1 took a closer look. Unlike the inner major rings, the F ring is narrow, less than a hundred kilometers wide. It lies just inside Saturn’s Roche limit, separated from the A ring by about 3500 km. Its narrowness by itself is unusual, as is its slightly eccentric shape, but its oddest feature is that it looks as though it is made up of several separate strands braided together! This remarkable discovery sent dynamicists scrambling in search of an explanation. It now seems as though the ring’s intricate structure, as well as its thinness, arise from the influence of two small moons, known as shepherd satellites, that orbit on either side of it (Figure 12.17).

Figure 12.16 F Ring Saturn’s narrow F ring appears to contain kinks and braids, making it unlike any of Saturn’s other rings. (NASA) Figure 12.17 Shepherd Moon The F ring’s thinness, and possibly its other peculiarities too, can be explained by the effects of two shepherd satellites that orbit a few hundred kilometers inside and outside the ring. This photo shows one of the shepherding satellites, roughly 100 km in length, at right.

Figure 12.18 Moon–Ring Interaction (a) Strange as it may seem, the net effect of the interactions between a moon and ring particles is that the moon tends to push those particles away from it. (b) The F ring shepherd satellites operate by forcing errant F ring particles back into the main ring. Each moon operates as in part (a) so that the ring is confined between the two moons. As a consequence of Newton’s third law of motion, the satellites themselves slowly drift away from the ring (unless they in turn are held in place by interactions with other, larger moons).
These two small, dark satellites, each about 50 km in diameter, are called Prometheus and Pandora. They orbit about 1000 km on either side of the F ring, and their gravitational influence on the F-ring particles keeps the ring tightly confined in its narrow orbit. As shown in Figure 12.18, any particle straying too far out of the F ring is gently guided back into the fold by one or the other of the moons. (The moon Atlas confines the A ring in a somewhat similar way.) However, the details of how Prometheus and Pandora produce the braids in the F ring and why the two moons are there at all, in such similar orbits, remain unclear. There is some evidence that other eccentric rings found in the gaps in the A, B, and C rings may also result from the effects of shepherding moonlets.

Outside the F ring lie another faint, narrow ring—the G ring. Discovered by Pioneer 11 and imaged in more detail by Voyager 2, it apparently lacks ringlets or the peculiar internal structure found in the F ring. Its narrowness and sharp edges suggest the presence of shepherd satellites, but so far none has been found.

THE ORIGIN OF THE RINGS

Two possible origins have been suggested for Saturn’s rings. Astronomers estimate that the total mass of ring material is no more than 1015 tons—enough to make a satellite about 250 km in diameter. If such a satellite strayed inside Saturn’s Roche limit or was destroyed (perhaps by a collision) near that radius, a ring could have resulted. An alternative view is that the rings represent material left over from Saturn’s formation stage 4.6 billion years ago. In this scenario, Saturn’s tidal field prevented any moon from forming inside the Roche limit, and so the material has remained a ring ever since. Which view is correct?

All the dynamic activity observed in Saturn’s rings suggests to many researchers that the rings must be quite young—perhaps no more than 50 million years old, or 100 times younger than the solar system. There is just too much going on for the ring to have remained stable for billions of years, so they probably aren’t left over from the planet’s formative stages. If this is so, then either the rings are continuously replenished, perhaps by fragments of Saturn’s moons chipped off by meteorites, or they are the result of a relatively recent, possibly catastrophic, event in the planet’s system—perhaps a small moon that was hit by a large comet, or even by another moon.

Astronomers prefer not to invoke catastrophic events to explain specific phenomena, but the more we learn of the universe, the more we realize that catastrophe probably plays an important role. For now, the details of the formation of Saturn’s ring system simply aren’t known.


Concept Check

What do the Roche limit and orbital resonances have to do with planetary rings?