Acknowledgement. We thank Science for their permission to use an excerpt from:

Smith, B. A., et al. 1989. Voyager 2 at Neptune: Imaging science results. Science 246 (4936), 1422-1449. (Excerpt from pp. 1431-1437.)

Copyright AAAS, December 15, 1989.

Voyager 2 Encounter with Neptune: Imaging Report

The Neptune Ring System

Prior to the Voyager reconnaissance of Neptune, very little was known of its ring system. By August 1989, about 50 stellar occultations had been observed from ground-based observatories, representing 100 separate scans through the system. Although more than 90% of these observations yielded no detection, at least five occultations observed between 1981 and 1985 demonstrated with high confidence the presence of material in orbit around Neptune (22).

One of these observations was a detection, observed by more than one telescope, of either a small satellite or an optically thick azimuthally incomplete ring of about 80 km radial width. Several other detections, two of which were confirmed, indicated narrower (approximately 15 to 25 km) but also discontinuous rings. Minimum inferred lengths were 100 km. Thus, the existence of relatively narrow "ring arcs" orbiting between 41,000 and 67,000 km from Neptune was commonly accepted.

On the basis of these ground-based observations alone, however, it was impossible to distinguish between a family of permanent or transient arcs around Neptune or continuous rings of highly variable optical depth. Neptune's ring features became members of a sparsely populated class of ring structures including the narrow, azimuthally incomplete rings in Saturn's ring system [in the Encke gap, the Cassini Division, and around the F ring; see, for example, (23)] and possibly in the Uranian ring system as well (24).

The presence of short evolutionary timescales in ring systems is a well known and as yet unsolved puzzle (25). The time required for longitudinally localized material 20 km in radial width to spread 360 degrees as a result of differential rotation is only about 5 years. Stable, non-transient ring arcs would obviously require a longitudinal confinement mechanism (26, 27); transient arcs require the continual creation, dispersal, and replenishment of local concentrations of ring material. We present here the initial results on the nature and dynamics of Neptune's rings from analyses of Voyager imaging observations, discuss the various theories suggested for the existence of arcs in light of our findings, and compare Neptune's system with the other ring systems we see in the outer solar system.

Radial distribution of ring material. The Neptune ring system, as seen in Voyager images, contains two narrow rings, 1989N1R and 1989N2R, at radial distances of 62,900 km and 53,200 km, respectively; a broad ring, 1989N3R, at a radial distance of 41,900 km; a second broad ring, 1989N4R, extending outwards from 1989N2R to a distance of nearly 59,000 km; and an extended sheet of material that may fill the inner Neptunian system. (We will alternatively refer to 1989N1R, 1989N2R, and 1989N3R as the N63, N53, and N42 rings.) The N63 ring is outermost and includes three arcs of substantially greater optical depth than the ring average. The three arcs are clustered together within a total range of 33 degrees in longitude. 1989N1R and 1989N2R lie about 1000 km outside the newly discovered satellites 1989N3 and 1989N4, respectively.

Neptune's rings were most easily visible at the moderately high phase angles obtained after closest approach to the planet, and three images at these phase angles best characterize the overall distribution of material Figure 14, a 111-second exposure, and Fig. 15, a composite of two 591-second exposures taken 1.5 hours apart, were all imaged through the clear filter of the wide angle camera and show the ring system at forward scattering phase angles of about 135 degrees. Figure 14 clearly shows the arcs which are 12 data number units (DN, out of a total range of 255 DN) above background. In comparison, Fig. 16 is also a 111-second exposure taken through the clear filter of the Voyager wide angle camera, but at a phase angle of only 15.5 degrees. It shows the same three arcs within the optically thin N63 ring; the second, even fainter N53 ring is also visible. Though Fig. 16 is one of the best Voyager images taken of Neptune's ring system at low phase, the average brightness in the arcs measured only about 2.5 DN above background.

The arcs were not captured in Fig. 15 because of the 50 degrees of orbital motion between the two frames. However, one can easily see the N63 and N53 rings as well as N42 (1989N3R). This latter ring, which is seen at low phase angles only with great difficulty, is clearly resolved and has a full width at half maximum of about 1700 km. Also faintly visible in Fig. 15 is a sheet of material beginning midway between the two outer rings at approximately 59,000 km and possibly extending down to the planet. (We discuss this further below.) There are identifiable features within this sheet. The most prominent among them is the plateau, 1989N4R. A distinct feature or ring at 57,500 km, 1989N5R, on the outer edge of the plateau, can be seen above and below the ansa in Fig. 15. In addition, there are hints of other radial structure in the plateau.

Although one gets the impression from Fig. 15 that material extends continuously inward from 59,000 km, this is difficult to confirm because of the uncertain in the distribution of scattered light. Figure 17 is a radial profile of the intensity seen in the left hand frame of Fig. 15. In this scan, a smooth function has been subtracted to remove the scattered light from the planet; this has the effect of tapering off the brightness distribution to zero at small radii. Though this removal of scattered light is uncertain, the N42 ring does appear to be embedded in material which extends out to the N53 ring, with brightness only slightly less than that of the plateau region but having a local minimum at 52,000 km, approximately the orbit of 1989N3. A similar configuration was observed in the Uranian system between Cordelia and the lambda ring (1986U1R) (1).

In other high-phase frames, a narrow, clumpy ring (as yet unnamed) is also visible just interior to 1989N1R. This feature is not seen in any low phase angle images, and appears to lie at about the same radius as satellite 1989N4. Imaging observations of the arcs and the satellites within the ring region indicate beyond doubt that the direction of orbital motion is prograde. Because of remaining uncertainties in the Laplacian plane pole orientation, we cannot at the present time completely rule out very small ring eccentricities and inclinations relative to this plane, which presumably is identical to that of the inner, regular satellites.

Voyager observations have put strong constraints on the existence of a potential polar ring system (28); several high and low phase angle images of Neptune's north and south polar regions, covering a radial range out to several hundred thousand kilometers from the planet, reveal nothing. Although the upper limiting optical depth for broad sheets of material is roughly 1e-5, it is still impossible to rule out the existence of narrow clumps in polar orbits with somewhat higher optical depths.

High-resolution imaging coverage of the rings, excluding the arc retargeting that is discussed below, was made mostly at sky plane resolutions of 15 and 40 km per line pair. Due to the smear resulting from the long exposures, we have been unable to resolve in the radial direction either the N53 ring or the non-arc part of the N63 ring. Our highest resolution images, obtained within 13 hours of closest approach, were of the arcs and were retargeted approximately 4 days before closest approach, based on earlier imaging observations of arc locations and orbital motion.

The single highest resolution frame, FDS 11386.17, has a sky plane resolution of only 3.0 km per line pair. At the geometry of this observation, radial foreshortening results in a ring-plane resolution of 15 km per line pair. The trailing arc has a full radial width at half maximum that is close to the resolution of the camera. However, in our narrow angle outbound retargetable image (Fig. 18), measurements of variations in the ring width indicate that the ring may be just barely resolved, implying a radial width of about 15 km. This value is in good agreement with the groundbased and Voyager photopolarimetry stellar occultation measurements (22, 29).

Longitudinal Distribution of Material. On longitudinal scales of a radian, all three rings and the plateau region are continuous around the planet. This is very clearly seen in forward-scattering geometry (Fig. 15), but it is also evident, though with greater difficulty, in backscattered light for the N53 and N63 rings. On intermediate scales, the only prominent structures are the three bright arcs seen in the N63 ring (Figs. 14 and 16). The azimuthal lengths of these arcs, measured to be the distance between the half intensity points in azimuthal brightness scans in Fig. 14, are approximately 4 degrees, 4 degrees, and 10 degrees for the leading, middle, and trailing arcs, respectively. The distances between the midpoints of these features are about 14 degrees (leading-middle) and 12 degrees (middle-trailing). To within the measurement uncertainties, the same values are obtained from low phase images. Given the signal-to-noise ratio of the data, we find no convincing evidence at this time for longitudinal structure on scales greater than about 5 degrees in either of the two remaining rings or in the remainder of the outer ring in either forward or backscattering geometry.

Small-scale azimuthal structure is most easily seen in the retargeted image of the trailing arc taken at high phase (Fig. 18). Several long linear features are apparent, which we believe are formed by discrete clumps in the ring, trailed out by a combination of orbital motion along the ring and the motion of the spacecraft across the ring. These features are unresolved and appear to be associated with microscopic particles because of their enhanced brightness in forward scattered light (phase angle of 135 degrees). One of the retargeted images taken of the trailing arc at low phase shows structure similar to that seen in Fig. 18 when the image contrast is strongly enhanced. Though it is not yet certain if these are the same clumps seen in Fig. 18 it is noteworthy that the typical separation between these clumps, approximately 0.1 degrees to 0.2 degrees is the same in both frames. A similar object within the leading arc is seen in another low phase image not reproduced here. These features may be large embedded ring particles or associated clumps of debris similar in morphology to the discrete features found in the F-Ring or Encke gap ringlet of Saturn (23).

Moonlet Search. A search for additional small satellites orbiting near the rings of Neptune is still being conducted (30), but the lack of confirmed sightings implies that few or no additional satellites larger than 12 km in diameter with assumed geometric albedo of 0.05 are orbiting in the ring region. To discriminate actual sightings from noise we required each candidate object to be in a circular equatorial orbit. Because of this requirement our limiting radii are roughly twice as large for satellites with orbits inclined by more than 10 degrees or eccentric by more than 0.1.

Ring Photometry and Particle Properties. The ability of spacecraft to observe a system over a range of viewing angles is of great importance to our understanding of planetary ring systems since the scattering behavior of particles of microscopic and macroscopic sizes differs dramatically with phase angle. Observations at high phase angles (>150 degrees) have been important in establishing that the microscopic "dust" particle fractional area in the main rings of Saturn and Uranus is quite small - between 0.01 and 0.001 by area (3l). In other rings the dust fraction can be considerably larger; for example, Saturn's F ring, a narrow clumpy ring, and Saturn's E ring, a broad, diffuse ring, are both visible primarily because of microscopic particles - dust fractions greater than 80% (32). In the case of Neptune the spacecraft trajectory did not allow any extremely high phase angle observations; however, the rings themselves compensated for this lack of observational sensitivity by being extremely "dusty ."

Our preliminary photometric analysis relies on only two phase angles (approximately 14 degrees and 135 degrees) for the following regions: the middle arc of 1989N1R, wide azimuthal averages in the N42, N53, and N63 rings (excluding the arc material) and the constant brightness region ranging between 54,500 and 57,500 km from Neptune. In order to suppress the effects of possibly variable smear in the long exposures that were used, the radial integral of the brightness profile, or "equivalent width," was employed (33).

Figure 19 shows the observations for the different regions, converted to the quantity omega_0 P integral[taudr], as functions of phase angle (33). The fact that all regions are more reflective at high phase angles is direct evidence for a substantial dust population, since the brightness of macroscopic objects depends primarily on the fraction of the visible illuminated area and decreases by an order of magnitude as phase angle increases over this range. We have modeled the particle properties in these regions to obtain the optical depth of macroscopic and microscopic material, using assumptions as to the individual particle properties based on prior experience. We have assumed that the large macroscopic particles in the Neptune ring system have the Uranus ring particle phase function and a Bond albedo between 0.01 and 0.02, which brackets the Uranus ring particles, Phobos, Diemos, and Amalthea. This combination results in a geometric albedo of about p=0.05, similar to that seen for the newly discovered Neptune satellites.

To bound the properties of the microscopic dust component, we chose coal dust (which is used to model the Uranus rings) and a typical silicate (which is used to model the Jupiter ring). Mie scattering, as modified by a simple irregular particle algorithm, was used to obtain the range of dust particle albedo and phase functions for material with this range of composition. We assumed a power law size distribution with index of 2.5, such as has been observed to characterize the dust in the Uranus and Jupiter rings; microscopic dust in ring systems tends to have a somewhat flatter size distribution than typical comminution products due to the size dependence of removal processes. The results of this preliminary photometric modeling are shown in Fig. 20.

The N42 ring and the plateau are clearly low optical depth structures, although two orders of magnitude more substantial than the Jupiter ring or the E and G rings of Saturn and about one order of magnitude more substantial than the Uranus dust bands. The optical depth of the middle arc, about 0.04 to 0.09, is in excellent agreement with ground-based values when appropriate diffraction corrections are made. Within the uncertainties, the N42, N53, and arc regions have the same dust fraction (0.5 to 0.7), which is about twice as large as the fraction found in the N63 ring and the plateau regions, and significantly larger than found in the main rings of Saturn or Uranus (1e-3 to 1e-2).

Comparison of Ground-based and Voyager Observations. Re-analysis of the geometries for the most reliable ground-based stellar occultation tracks by means of the improved Voyager Neptune pole position has indicated that the observations of 22 July 1984, 7 June 1985, and 20 August 1985 are all consistent with occultation by material near the radius of 1989N1R (34). These are also the only three observations which yield equivalent widths of up to 2.0 km consistent with the abundance of material that we find in the three Voyager arcs (Figs. 19, 20) when diffraction effects are appropriately accounted for. Although this suggests that the Voyager arcs are the same as those observed from Earth in 1984 and 1985, a much more stringent test of this hypothesis and one that could rule out the notion of transient and evolving arcs, would be the successful prediction of longitudinal location at the time of the Voyager encounter by use of the observed arc locations in both ground-based and Voyager observations and the mean motion derived from Voyager images.

A precise determination of the arcs' mean motions must necessarily await careful arc position measurements in images spanning as large a temporal range as possible, and the fitting of such measurements with a general model describing an eccentric and inclined orbit as well as an evaluation of the pole of Neptune's Laplacian plane, which is independent of the assumed ring arc model. A preliminary value was obtained, however, by assuming the arcs' orbits to be identical circular, and equatorial [Neptune rotational pole orientation (alpha, delta)1950= (298.904, +42.841)], and by measuring the beginning and ending longitudes of each arc in smoothed, radially averaged azimuthal scans taken from at most five images spanning a total of about 6.5 days. For each of the three arcs, a weighted least-squares fit to the measured locations versus time was used to determine the mean motions; the final value and its uncertainty, 820.12 +/- 0.06, are the mean and the standard error of the mean, respectively, of these three numbers. Using this value, we projected forward from the longitudes of arc detection in the three reliable ground-based stellar occultations in the N63 region mentioned above (35), correcting for light travel time, to the epoch of our best single image (FDS 11412.51, Fig. 14): for 22 July 1984, the processed longitude is 227 degrees; for 7 June 1985, 238 degrees; and for 20 August 1985, 224 degrees. The large uncertainty in the rate, 0.06 degrees per day, maps into a longitude uncertainty at the time of Fig. 14 of approximately +/-100 degrees. Nonetheless, the agreement found with the use of the nominal rate is astonishingly good: the ground-based observations fall within about 15 degrees of each other and comfortably intercept the longitude range, 206 degrees to 240 degrees, subtended by the three arcs in Fig. 14. (Although the ground-based longitudes are measured in the Neptune-Triton invariable plane, and the Voyager longitudes in the Neptune equator plane, the difference amounts to at most a few degrees.)

We consider these results convincing evidence that the Voyager arcs themselves were the occulting material for all ground-based occultations at this radius and, therefore, that the arcs are stable over intervals of at least 5 years. Future work in this area, taking into account the geometrical considerations mentioned above, may in fact allow us to determine with high probability which of the three arcs was observed in each of these three ground-based occultations and to predict the locations of these features at the times of upcoming Neptune stellar occultations observable from the ground or from the Hubble Space Telescope. It is not surprising that ground-based observations, in general, do not detect material in the non arc regions to the N53 and N63 rings - the estimated optical depth of 0.01 to 0.02 in these regions is below the ground-based threshold. However, it is worth noting that (unconfirmed) ground-based stellar occultation observations, revised by using Voyager improvements to the Neptune pole orientation (35), indicate events at around 42,000 kilometers and 55,000 kilometers - opening the possibility that dumpy material may now or did then, exist in regions where we now observe broad, diffuse belts of material (see Fig. 21).

One other important result concerns the identity of the object that was responsible for the first occultation observation of material orbiting Neptune (22). Using the mean motions for the small satellites determined from imaging observations, we obtained their positions at the time of the 1981 event. Since this event did not occult the planet, some astrometric uncertainty remains in addition to the uncertainty in the mean motion of the candidate satellites. However, we find that 1989N2 falls within the total uncertainty (about 8 degrees of orbital longitude or less than 1 arc second) of the location of the event, and that the only other possible candidate (1989N4) is on the other side of the planet. This excellent positional agreement, combined with the fact that the 1981N1 occultation was completely opaque and 180 km across and 1989N2 has a diameter of about 200 km, makes us confident that 1981N1 and 1989N2 are one and the same object (Fig. 21).

Discussion of Ring Observations. Despite the singular nature of Neptune's system of relatively large satellites (in particular, retrograde Triton and highly eccentric Nereid), and despite the dramatically different visual impression that Neptune's rings give in comparison with those of Jupiter, Saturn, and Uranus, the combined system of rings and inner satellites has surprised us by sharing many characteristics with the other giant planet ring-satellite systems. To wit, Neptune's rings comprise an extensive prograde system, essentially confined to the planets equatorial plane and filling the planets Roche zone, a region lying between the classical stability limit for a liquid satellite [r/R_p = 2.44(rho_s/pho_p)^0.33, where rho_s and rho_p are the densities of the satellite and the planet, respectively, R_p is the planet's radius and r is the distance from the planet's center] and the "accretion limit" at which equal-sized particles are destabilized by differential Keplerian motion [1.44(rho_s/rho_p)^0.33] (36).

It is a system containing narrow dusty rings like the Uranus lambda ring (1986U1R) and the Saturn F ring; diffuse dusty rings, perhaps similar to the Jupiter ring and Saturn G ring; azimuthally confined arcs embedded with a ring reminiscent of Saturn's F and Encke rings; and possibly a broad sheet of dust like that which is seen around Uranus at high phase angles.

An examination of Neptune's system of satellites and its distribution with orbital radius (Table 1) supports the generality that as the distance from a giant planet decreases, there is a gradual transition from large, isolated satellites to families of more numerous, smaller satellites and ring material. The presence of relatively massive objects (for instance, satellites at Neptune, rings at Saturn) well within the outer planets' Roche limits, where structural stability depends on internal strength but where accretion to radii of tens of kilometers is difficult or impossible, supports the idea that the parent objects of these outer planet ring-satellite systems migrated into their respective Roche zones from elsewhere long ago (37).

In comparing only Uranus with Neptune, we find that the reflectivities of the surfaces of their inner satellites are similar and very low. Also, the agreement between our derived Neptune ring arc optical depths and those obtained from ground-based stellar occultation measurements supports equivalently low albedos for the ring particles, comparable to those found for Uranus. Compositionally, therefore, the Neptune and Uranus ring-satellite systems appear to be quite similar, suggesting chemical origins and/or evolutionary histories that proceeded in tandem, histories that may well characterize the outer solar system beyond Saturn.

However, the dramatic differences also call for our attention. The amount of mass in Neptune's rings is approximately 10,000 times less than that at Uranus and many orders of magnitude less than that at Saturn, yet the inner Neptune satellites are significantly larger, and presumably more massive, than the bodies in similar locations in the ring-satellite systems of the other giant planets. At Neptune, the five satellites 1989N2 through 1989N6, with diameters ranging from approximately 55 to 190 km, all fall within the Roche "liquid" limit at roughly 77,000 km; at Uranus, the nine satellites falling within its Roche limit, 1986U1 through 1986U9, range from about 25 to 110 km in diameter (38). If we assume the overall satellite-size distributions to be similar among the outer planets, the relatively large number of big bodies close to Neptune might lead one to expect a proportionately large abundance of smaller moonlets in the ring region. Yet, our search for satellites to date does not support the existence of more than two objects (1989N5 and 1989N6) with diameters less than 100 km.

Evidently, the distribution of mass among the inner satellites of each planet, and between each planets satellites and rings, is very different. The absolute amount of mass within these zones is also notably different: All the mass in Saturn's rings, which fill Saturn's Roche zone, can be contained within an icy body approximately the size of Mimas, 195 km in radius; in Neptune's Roche zone, the rings' and satellites' masses can be contained within an icy body 130 km in radius; and for Uranus, within an icy body 75 km in radius. It is interesting to compare these differences with the variation in present-day cratering rates on the inner satellites of these three planets: The ratio for Saturn/Neptune/Uranus is roughly 3/50/100 (39). It would appear that where bombardment is greatest, there is less overall mass. However, the present-day differences in the distribution of mass around the giant planets may reflect, in part, the varying degrees to which bombardment and collisional processes have combined to shape their ring satellite systems.

The presence and distribution of dust in those systems may provide a direct indication of the relative importance of these processes today. The relatively large number of microscopic particles spread throughout the Neptune rings (Fig. 20) is not unique; the Jupiter ring and the Saturn E ring contain a fractional optical depth of 50% to 80% in dust. However, the absolute abundance of dust in the Neptune system, which is about two orders of magnitude larger than the Jupiter and Saturn counterparts, presents a serious problem. Because microscopic particles are very short-lived (40), they must be continually replenished. When material is in a state of dynamic balance, equilibrium abundances are maintained by equal rates of creation and destruction.

Different removal processes dominate in different environments: In the Uranus rings, microscopic material is removed primarily by gas drag (41) and, in the Jupiter rings, by plasma drag (40). In the Neptune rings, in which dust has a relatively large optical depth (approximately 1e-4) and which are relatively free of plasma or neutral gas, simple sweep-up on the surfaces of macroscopic particles dominates dust removal.

If the source of the dust is meteoroid bombardment, as believed for the Jupiter ring, the creation and removal processes are both proportional to parent body optical depth. Consequently, the dust optical depth resulting from meteoroid bombardment is independent of the large particle optical depth and depends instead on the meteoroid flux and impact field parameters (40). For heliocentric distances less than 15 to 20 AU observed by the Pioneer 10 and 11 dust detectors, a value of interplanetary meteoroid flux of about 1e-16 g cm^(-2) s^(-1) is generally accepted. Given this value and ejecta yields of about 104 [see, for example (42)], "Jupiter ring" dust optical depths on the order of 10 to the minus 6 are easily obtained. However, dust optical depths in N42 and the plateau (and the Uranus dust bands) are around 1e-4 (Fig 20), requiring a bombarding flux roughly two orders of magnitude larger than found at Jupiter and Saturn. This larger dust abundance is qualitatively consistent with the previously mentioned larger estimated projectile population at Uranus and Neptune. Although the estimate falls short by a factor of 3 to 10, this may be within the uncertainty in the Neptune dust optical depths and in the estimated projectile populations.

However, the dust within the N53 and N63 rings is orders of magnitude larger than than can be explained by the meteoroid bombardment mechanism. Therefore, we suspect that it is most likely generated locally through vigorous collisions between larger, unseen particles. In this mode, the equilibrium dust optical depth depends in a more complicated and model-dependent way on the optical depth of the parent bodies that create it. The dust optical depth does tend to increase with that of the colliding parents as long as the latter is much less than unity and the mass injected per collision is a constant. This creation of dust through interparticle collisions, assuming relative velocities consistent with radial excursions as large as the observed ring widths, may explain the generally large dust abundance in the Neptune rings, given reasonable assumptions about the yield per impact (43). The brightening at 57,500 km (1989N5R) near the outer edge of the plateau is one Neptune ring feature which, by analogy with Uranus, may be the manifestation of a moonlet belt (1). The lack of other noticeable fine structure, in contrast to the nearly 100 belts revealed in the Uranus rings or the internal structure of the Saturn D ring, may be due to long exposure times of the images and the corresponding smear rather than to actual absence. Of course, greatly increased optical depth will diminish the dust population because the attendant large collision rate tends to damp the relative velocities. For instance in the large optical depth rings of both Saturn and Uranus, the dust fraction is extremely small. For this reason, it is not clear whether the amount of dust in the Neptune arcs is consistent with a relatively simple moonlet-belt model or whether additional stirring of the ring arc material by unseen perturbing bodies is implied. Nonetheless, it appears overall that the moonlet-belt hypothesis that has been proposed for the Uranus rings (1) and recently modeled in more detail (44) may go a long way toward explaining some of the global characteristics seen in the Neptune ring system.

While it seems clear that the 1989N1R arcs are stable over an interval of at least 5 years, a search for dynamical relationships between the Neptune rings, ring arcs, and the new satellites found within the ring region has demonstrated that none of the current hypotheses based on the combined action of satellite coronation and Lindblad resonances can explain the persistence of the arcs. Confinement of the ring arcs through a combination of corotational and Lindblad resonances with a single satellite (27) can be easily discounted on several grounds: (i) 1989N4 has zero inclination and eccentricity to within measurement uncertainties, thereby rendering it incapable of corotationally shepherding 1989N1R; (ii) the 3:2 corotation resonances of 1989N6 fall some 250 km outside 1989N1R, and the expected scale for this resonance (about 60 degrees) is too large; (iii) the 5 degree inclination of this satellite is insufficient to allow it to confine a ring arc 15 km wide, given its radius of 27 km and a reasonable assumed density. The Lagrange point satellite shepherding model (26) can be discounted because no Lagrange point satellite of sufficient mass has been found. The only relationships that hold some promise for being significant are the standard outer Lindblad-type resonances of 1989N4 on the N63 ring and 1989N3 on the N53 ring, which might account for the locations of the inner edges of these rings in much the same way as Cordelia shepherds the inner edge of the Uranus epsilon and probably lambda (1986U1R) rings (45). Though both inertial and acoustic waves in Neptune were proposed as a possible mechanism for the azimuthal confinement of arc material, these mechanisms can now be discounted because the required planetary wave amplitudes would have to be impossibly large to produce arcs with the observed longitudinal scale of 12 degrees (46). Moreover, acoustic mode corotation resonances at Neptune do not fall outside 28,000 km (47). At the present time, therefore, there are no theories explaining ring arcs that are verified in Voyager imaging data.

The effort to date that has focused on the details of a longitudinal confinement mechanism for the arcs, while now clearly justified, does not address the larger question of the origin of rings and ring arcs themselves. This question will require studies of catastrophic disruptions and the subsequent dispersal and distribution of collisional fragments, as well as the study of the coupled behavior of ensembles of moonlets and ring material, both under the influence of a variety of ongoing processes, like tidal evolution and meteoroid bombardment, which continually sap orbital energy and angular momentum from the system. However, knowing as we do now the basic properties of the four ring-satellite systems of the outer solar system, we can begin to explore comprehensive models of their undoubtedly

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