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1.
2.
We have calculated the radar backscattering characteristics of a variety of compositional and structural models of Saturn's rings and compared them with observations of the absolute value, wavelength dependence, and degree of depolarization of the rings' radar cross section (reflectivity). In the treatment of particles of size comparable to the wavelength of observation, allowance is made for the nonspherical shape of the particles by use of a new semiempirical theory based on laboratory experiments and simple physical principles to describe the particles' single scattering behavior. The doubling method is used to calculate reflectivities for systems that are many particles thick using optical depths derived from observations at visible wavelengths. If the rings are many particles thick, irregular centimeter- to meter-sized particles composed primarily of water ice attain sufficiently high albedos and scattering efficiencies to explain the radar observations. In that case, the wavelength independence of radar reflectivity implies the existence of a broad particle size distribution that is well characterized over the range 1 cm ? r ? m by n(r)dr = n0r?3dr. A narrower size distribution with a ~ 6 cm is also a possibility. Particles of primarily silicate composition are ruled out by the radar observations. Purely metallic particles, either in the above size range and distributed within a many-particle-thick layer or very much larger in size and restricted to a monolayer, may not be ruled out on the basis of existing radar observations. A monolayer of very large ice “particle” that exhibit multiple internal scattering may not yet be ruled out. Observations of the variation of radar reflectivity with the opening angle of the rings will permit further discrimination between ring models that are many particles thick and ring models that are one “particle” thick.  相似文献   

3.
The origin of the multiple concentric rings that characterize lunar impact basins, and the probable depth and diameter of the transient crater have been widely debated. As an alternative to prevailing “megaterrace” hypotheses, we propose that the outer scarps or mountain rings that delineate the topographic rims of basins—the Cordilleran at Orientale, the Apennine at Imbrium, and the Altai at Nectaris—define the transient cavities, enlarged relatively little by slumping, and thus are analogous to the rim crests of craters like Copernicus; inner rings are uplifted rims of craters nested within the transient cavity. The magnitude of slumping that occurs on all scarps is insufficient to produce major inner rings from the outer. These conclusions are based largely on the observed gradational sequence in lunar central uplifts:. from simple peaks through somewhat annular clusters of peaks, peak and ring combinations and double ring basins, culminating in multiring structures that may also include peaks. In contrast, belts of slump terraces are not gradational with inner rings. Terrestrial analogs suggest two possible mechanisms for producing rings. In some cases, peaks may expand into rings as material is ejected from their cores, as apparently occurred at Gosses Bluff, Australia. A second process, differential excavation of lithologically diverse layers, has produced nested experimental craters and is, we suspect, instrumental in the formation of terrestrial ringed impact craters. Peak expansion could produce double-ring structures in homogeneous materials, but differential excavation is probably required to produce multiring and peak-in-ring configurations in large lunar impact structures. Our interpretation of the representative lunar multiring basin Orientale is consistent with formation of three rings in three layers detected seismically in part of the Moon—the Cordillera (basin-bounding) ring in the upper crust, the composite Montes Rook ring in the underlying, more coherent “heald” crust, and an innermost, 320-km ring at the crust-mantle interface. Depth-diameter ratios of 110to115 are consistent with this interpretation and suggest that volumes of transient cavities and hence of basin ejecta may be considerably greater than commonly assumed.  相似文献   

4.
Gravitational perturbations in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 AU) out to 10 Tisserand sphere of influence radii were calculated by two- and three-dimensional numerical integration. These are compared with the results of treating the encounter as a two-body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of (VVe) ? 0.35 (V = relative velocity, Ve = escape velocity of largest body), the two-body body approximation fails to describe the outcome of individual encounters. In this low-velocity region, the two-body “gravitational focusing” cross section is no longer valid; “anomalous gravitational focusing” often leads to bodies on distant unperturbed trajectories becoming close encounters and vice versa. In spite of these differences, average perturbations given by the two-body approximation are valid within a factor of 2 when VVe > 0.07. In this same velocity range the “Arnold extrapolation,” whereby a few very close encounters are used to estimate the effect of many more distant encounters, is found to be a useful approximation.  相似文献   

5.
Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in 43 resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity ?0.1 km/sec rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ~ 10 km/sec with a projectile-to-target mass ratio of the order of 10?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.  相似文献   

6.
We study the viscosity of a differentially rotating particle disk in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid. The pressure tensor is derived from the equations of hydrodynamics and from a simple kinetic model of collisions described by Haff (1983). We find that density waves and narrow circular rings are unstable if the liquid approximation applies. The resulting development of nonlinear perturbations may give rise to “splashing” of the ring material in the vertical direction. These results may help in understanding the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturnian B ring, and the unexplained residuals in kinematic models of the Saturnian and Uranian rings.  相似文献   

7.
We discuss certain dynamical processes during the final stage of the sinking of the dust layer. We supposed that turbulance gave rise to a state of slow sinking (quasi-equilibrium) and evaluated the critical thickness at the onset of gravitational instability in the radial direction. We gave a precise numerical relation between 3 length-scales: 〈|Z|〉c : h1 : λT = 0.02107 : 0.1592 : 1, the first being the mean height of the dust particles at the onset of radial instability, the second being that value of the half-thickness and of the height at which the self-gravity of the dust layer is equal to the solar z-component, and the last being the longest wavelength at the onset of ring instability. We also calculated the time required for the formation of rings and found it to be far shorter than the sinking time.  相似文献   

8.
A clue towards a retrieval of the zodiacal brightness gathering along a line of sight in the ecliptic plane consists in introducing the other intersection of that line with the terrestrial orbit (Fig. 1). The distribution of the elemental contribution to the brightness, or of the local quantity D [directional scattering coefficient, i.e. cross-section of the unit-volume, which gives very simple expressions (1), (2) for the brightness integral] can then be approached with reduced uncertainty. The assumptions-steady state of the zodiacal cloud; smooth distribution of D—are strongly suggested by the observations, and are much less controversial than the classical assumption of uniform composition and size everywhere.The scattering coefficient may vary along the line of sight as seen in Fig. 3 : an uncertainty bar highly dependent of the abscissa, and considerably reduced in the vicinity of two “nodes”. Both in abscissae and in ordinates, these nodes are conspicuously insensitive to the arbitrary choice of a mathematical model (Table 1).The node exterior to the Earth's orbit (“martian node”) remains at r ? 1.5 a.u. from the Sun (Fig. 4). It gives access to a range of the scattering phase function near Mars' orbit, deconvolved from any radial dependence of that function (Fig. 5). The backscattering effect obtained is a new confirmation of the non-terrestrial origin of the gegenschein.The node interior to the Earth's orbit remains located not far from the middle of each chord (“quasi-radial node”. Fig. 4). It allows to retrieve the radial dependence of D, partly deconvolved from its angular dependence, between 0.5 and 1 a.u. (Fig. 6 and Table 4).The uncertainty bars on D at the two observing locations yield two uncertainty bars of the phase function σ(θ) at 1 a.u. (Fig. 7). At θ = 30°, the forward scattering efficiency (normalized to θ = 90°) cannot exceed 6 and more likely 4. This disagrees with higher values obtained assuming spherical particles, and even obtained in part of the more realistic studies (assuming irregularly shaped particles, or mainly observational) reviewed in Table 5.All of these results are derived, with fair agreement, from three independent observational sources.  相似文献   

9.
Observations of microwave opacity τ[λ] and near forward scatter from Saturn's rings at wavelengths λ of 3.6 and 13 cm from the Voyager 1 ring occultation experiment contain information regarding ring particle sizes in the range of about a = 0.01 to 15 m radius. The opacity measurements τ[3.6] and τ[13] are sufficient to constrain the scale factor n(a0) and index q of a power law incremental size distribution n(a) = n(a0)[a0/a]q, assuming known minimum and maximum sizes and a many-particle-thick model. The families of such distributions are highly convergent in the centimeter-size range. Forward scatter at 3.6 cm can be used to solve for a general distribution over the radius range 1 ? a ? 15 m by integral inversion and inverse scattering methods, again assuming a many-particle-thick slab-type radiative transfer model. Distributions n(a) valid over 0.01 ? a ? 15 m are obtained by combining the results from the two types of measurements above. Mass distributions may be computed directly from n(a). Such distributions, partly measured and partly synthesized, have been obtained for four features in the ring system centered at 1.35, 1.51, 2.01, and 2.12 Saturn radii (Rs). The size and mass distributions both cut off sharply at a ? 4–5 m; the mass distribution peaks over the narrow size range 3 ? a ? 4 m for all four locations. No single power law distribution is consistent with the data over the entire interval 0.01 ? a ? 5 m, although a power law-type model is consistent with the data over a limited size range of 0.01 ? a ? 1 m, where the indices q = 3.4 and 3.3 are obtained from the slab model for the features located at 1.51 and 2.01 Rs. The fractional contribution of the suprameter particles to the microwave opacity in each feature appears to be about 13, 13, 23, and 1, respectively, with the fraction at 2.12 Rs being the least certain. The cumulative surface mass per unit area obtained for the classical slab model is approximately 11, 16, 41, and 132 g/cm2 for the four features, respectively, if the particles are solid H2O ice. Both the fractional opacity and the mass density estimates represent upper bounds implied by the assumption of a uniformly mixed set of particles in a many-particle-thick vertical profile; lower estimates would result if the rings were assumed to be nearly a monolayer or if the vertical distribution of particles were size dependent.  相似文献   

10.
We present a conceptual model of the formation of the plasma sheet and of its dynamical behavior in association with magnetospheric substorms. We assume that plasma mantle particles E×B drift toward the current sheet in the center of the tail where they are accelerated by magnetic-field annihilation to form the plasma sheet. Because of the velocity-dependent access of mantle particles to the current sheet, we argue that the convection electric field and the corresponding rate of field annihilation decrease with increasing radial distance. As a consequence, there exists no steady-state configuration for the plasma sheet, which must instead shrink continuously in thickness until the near-earth portion of the current sheet is disrupted by the formation of a magnetic neutral line. The current-sheet disruption launches a large-amplitude hydromagnetic wave which is largely reflected from the ionosphere. The reflected wave sets the neutral line in motion away from the earth; the neutral line comes to rest at a distance (which we estimate to be a few hundred earth radii) where the incoming mantle particles enter the current sheet at the local Alfvén velocity. At this “Alfvén point” reconnection ceases and the thinning of the plasma sheet begins again. Within this model, the magnetospheric substorm (which is associated with the current-sheet disruption) is a cyclical phenomenon whose frequency is proportional to the rate of convection in the magnetospheric tail.  相似文献   

11.
C.K. Goertz  G. Morfill 《Icarus》1983,53(2):219-229
We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.  相似文献   

12.
Plasma and magnetic field data from PROGNOZ-7 have revealed that solar wind (magnetosheath) plasma elements may penetrate the dayside magnetopause surface and form high density regions with enhanced cross-field flow in the boundary layer.The injected magnetosheath plasma is observed to have an excess drift velocity as compared to the local boundary layer plasma, comprising both “cold” plasma of terrestrial origin and a hot ring current component. A differential drift between two plasma components can be understood in terms of a momentum transfer process driven by an injected magnetosheath plasma population. The braking action of the injected plasma may be described as a dynamo process where particle kinetic energy is transferred into electromagnetic energy (electric field). The generated electric field will force the local plasma to ε×B-drift, and the dynamo region therefore also constitutes an accelerator region for the local plasma. Whenever energy is dissipated from the energy transfer process (a net current is flowing through a load), there will also be a difference between the induced electric field and the v×B term of the generator plasma. Thus, the local plasma will drift more slowly than the injected generator plasma.We will present observations showing that a relation between the momentum transferred, the injected plasma and the momentum taken up by the local plasma exists. For instance, if the local plasma density is sufficiently high, the differential drift velocity of the injected and local plasma will be small. A large fraction of the excess momentum is then transferred to the local plasma. Conversely, a low local plasma density results in a high velocity difference and a low fraction of local momentum transfer.In our study cases the “cold” plasma component was frequently found to dominate the local magnetospheric plasma density in the boundary layer. Accordingly, this component may have the largest influence on the local momentum transfer process. We will demonstrate that this also seems to be the case. Moreover we show that the accelerated “cold” plasma component may be used as a tracer element reflecting both the momentum and energy transfer and the penetration process in the dayside boundary layer.The high He+ percentage of the accelerated “cold” plasma indicates a plasmaspheric origin. Considering the quite high densities of energetic He+ found in the boundary layer, the overall low abundance of He+ (as compared to e.g. O+) found in the plasma sheet and outer ring current evidently reduces the importance of the dayside boundary layer as a plasma source in the large scale magnetospheric circulation system.  相似文献   

13.
Sonoyo Mukai  Tadashi Mukai 《Icarus》1981,48(3):482-487
The computed variation of the infrared flux and polarization of Venus as a function of phase angle, based upon multiple-scattering calculations for the cloud model of Kawabata et al. (1980) with an internal heat source, precludes the possibility of sulfuric acid as the composition of the haze particles located above the main cloud. Furthermore, our calculations reveal that the hazticle should have a large absorption coefficient at these wavelengths, i.e, k(imaginary part of the complex refractive index) ? 1.3 at a wavelength λ = 3.4 μm. The optical thickness of the haze layer must be about 0.15 at λ = 3.4 μm.  相似文献   

14.
E. Grün  H.A. Zook  H. Fechtig  R.H. Giese 《Icarus》1985,62(2):244-272
Taking into account meteoroid measurements by in situ experiments, zodiacal light observations, and oblique angle hypervelocity impact studies, it is found that the observed size distributions of lunar microcraters usually do not represent the interplanetary meteoroid flux for particles with masses ?10?10g. From the steepest observed lunar crater size distribution a “lunar flux” is derived which is up to 2 orders of magnitude higher than the interplanetary flux at the smallest particle masses. New models of the “lunar” and “interplanetary” meteoroid fluxes are presented. The spatial mass density of interplanetary meteoritic material at 1 AU is ~10?16g/m3. A large fraction of this mass is in particles of 10?6 to 10?4 g. A detailed analysis of the effects of mutual collisions (i.e., destruction of meteoroids and production of fragment particles) and of radiation pressure has been performed which yielded a new picture of the balance of the meteoritic complex. It has been found that the collisional lifetime at 1 AU is shortest (~104years) for meteoroids of 10?4 to 1 g mass. For particles with masses m > 10?5g, Poynting-Robertson lifetimes are considerably larger than collisional lifetimes. The collisional destruction rate of meteoroids with masses m ? 10?3g is about 10 times larger than the rate of collisional production of fragment particles in the same mass range. About 9 tons/sec of these “meteor-sized” (m > 10?5g) particles are lost inside 1 AU due to collisions and have to be replenished by other sources, e.g., comets. Under steady-state conditions, most of these large particles are “young”; i.e., they have not been fragmented by collisions and their initial orbits are not altered much by radiation pressure drag. Many more micrometeoroids of masses m ? 10?5g are generated by collisions from more massive particles than are destroyed by collisions. The net collisional production rate of intermediate-sized particles 10?10g ? m ? 10?5g is found to be about 16 times larger at 1 AU than the Poynting-Robertson loss rate. The total Poynting-Robertson loss rate inside 1 AU is only about 0.26 tons/sec. The smallest fragment particles (m ? 10?10g) will be largely injected into hyperbolic trajectories under the influence of radiation pressure (β meteoroids). These particles provide the most effecient loss mechanism from the meteoritic complex. When it is assumed that meteoroids fragment similarly to experimental impact studies with basalt, then it is found that interplanetary meteoroids in the mass range 10?10g ? m ? 10?5g cannot be in temporal balance under collisions and Poynting-Robertson drag but their spatial density is presently increasing with time.  相似文献   

15.
The particles making up the Jovian ring may be debris which has been excavated by micrometeoroids from the surfaces of many unseen (R ? 1 km) parent bodies (or “mooms” as we will occasionally call them) residing in the ring. A distribution of particle sizes exists: large objects are sources for the small visible ring particles and also account for the absorption of charged particles noted by Pioneer; the small grains are generated by micrometeoroid impacts, by jostling collisions among different-sized particles, and by self-fracturing due to electrostatic stresses. The latter are most effective in removing surface asperities to thereby produce smooth and crudely equidimensional grains. The presence of intermediate-sized (radius of several to several hundred microns) objects is also expected; these particles will have a total area comparable to the area of the visible ring particles. The nominal size (?2 μm) of the visible particles derived from their forward-scattering characteristics is caused, at least in part, by a selection effect but may also reflect a fundamental grain size or the preferential generation of certain sizes along with the destruction of others. The tiny ring particles have short lifetimes (?102?103 years) limited by erosion due to sputtering and meteoroid impacts. Plasma drag significantly modifies orbits in ~102 years but Poynting-Robertson drag is not effective (TPR ~ 105 years) in removing debris. The ring width is influenced by the distribution of source satellites, by the initial ejection velocity off them, by electromagnetic scattering, and by solar radiation forces. In the absence of electromagnetic forces, debris will reimpact a mother satellite or collide with another particle in about 10 years. A relative drift between different-sized particles, caused by a lessened effective gravity due to the Lorentz force, will substantially shorten these times to less than a month. The ring thickness is determined by a balance between initial conditions (abetted perhaps by electromagnetic scattering) and collisional damping; existence of the “halo” over the diffuse disk compared to its relative absence over the bright ring indicates the presence of mooms in the bright ring but not in the faint disk. Small satellites (R ? 1 km) will not reaccumulate colliding dust grains whereas satellites having the size of J14 or J16 may be able to do so, depending upon their precise shape, size, density, and location. Visible ring structure could indicate separate source satellites. The particles in the faint inner disk are delivered from the bright ring by orbital evolution principally under plasma drag. The halo is comprised of small particles (~0.1 μm) partially drawn out of the faint disk by interactions with the tilted Jovian magnetic field.  相似文献   

16.
Stable rings can exist at inclinations of 0–15°, 165°–180°, or ~90° to Neptune's equator, but perturbations due to the massive satellite Triton would produce a severe “warping” of the ring plane. If Neptune possesses rings, they may not lie in the plane of its equator.  相似文献   

17.
Whistlers recorded at Eights (L ? 4) and Byrd (f ? 7), Antarctica have been used to study large-scale structure in equatorial plasma density at geocentric distances ?3–6 RE. The observations were made during conditions of magnetic quieting following moderate disturbance. The structures were detected by a “scanning” process involving relative motion, at about one tenth of the Earth's angular velocity or greater, between the observed density features and the observing whistler station or stations. Three case studies are described, from 26 March 1965, 11 May 1965 and 29 August 1966. The cases support satellite results by showing outlying high density regions at ?4–6 RE that are separated from the main plasmasphere by trough-like depressions ranging in width from ?0.2 to 1 RE. The structures evidently endured for periods of 12 hr or more. In the cases of deepest quieting their slow east-west motions with respect to the Earth are probably of dynamo origin. The cases observed during deep quieting (11 May 1965 and 29 August 1966) suggest the approximate rotation with the Earth of structure formed during previous moderate disturbance activity in the dusk sector. The third case, from 26 March 1965, may represent a structure formed near local midnight. The reported structures appear to be closely related to the bulge phenomenon. The present work supports other experimental and theoretical evidence that the dusk sector is one of major importance in the generation of outlying density structure. It is inferred that irregularities of the type reported here regularly develop near 4–5 RE during moderate substorm activity. This research suggests that at least a major class of the density structures that develop near 4 RE are tail-like in nature, joined to the main body of the plasmasphere. The apparent disagreement with Chappell's results from OGO 5, which are interpreted as showing regions of “detached” plasma beyond 5 RE, may be related to the pronounced spatial structure of electric fields observed in high-latitude ionospheric regions that are conjugate to the magnetospheric regions in which the OGO-5 observations were made.  相似文献   

18.
Reexamination of a photograph of Saturn taken on 15 November 1966, when the earth was nearly in the ring plane, indicates that ring material may exist outside the visible rings, extending to more than 6 Saturnian radii. Although the suspected feature on the photograph appears to be real, the possibility of its being a developed pressure mark or a chance alignment of grains cannot be ruled out. The observed brightness in blue light was estimated to be mB = 19.5 ± 0.5 per linear arcsecond, implying a normal optical thickness, τ ? 10?7, for ice-covered particles. For spacecraft passing through this region, the hazards are found to be minimal.  相似文献   

19.
Radio occultation observations of Saturn's rings with Voyager 1 provided independent measurements of complex (amplitude and phase) microwave extinction and near-forward scattering cross section of the rings at wavelengths (λ) of 3.6 and 13 cm. The ring opening was 5.9°. The normal microwave opacities, τ[3.6] and τ[13], provide a measure of the total cross-sectional area of particles larger than about 1 and 4 cm radius, respectively. Ring C exhibits gently undulating (~ 1000 km) structure of normal opacity τ[3.6] ? 0.25 except for several narrow imbedded ringlets of less than about 100 km width and τ[3.6] ~ 0.5 to 1.0. The normalized differential opacity Δτ/τ[3.6], where Δτ = τ[3.6] ? τ[13], is about 0.3 over most of ring C, indicating a substantial fraction of centimeter-size particles. Some narrow imbedded ringlets show marked increases in Δτ/τ[3.6] near their edges, implying an enhancement in the relative population of centimeter-size and smaller particles at those locations. In the Cassini division, several sharply defined gaps separate regions of opacity τ ~ 0.08 and τ ~ 0.25; the opacity in the Cassini Division appears to be nearly independent of λ. The boundary features at the outer edges of ring C and the Cassini Division are remarkably similar in width and opacity profile, suggesting a similar dynamical control. Ring A appears to be nearly homogeneous over much of its width with 0.6 < τ[3.6] < 0.8 but with considerable thickening, to τ[3.6] ~ 1.0, near its inner boundary with the Cassini division. Normalized differential opacity decreases from ~0.3 at the inner and outer edges of ring A to Δτ/τ[3.6] ~ 0 at a point about one-third of the distance from the inner edge to the outer. The inner one-fourth of ring B has τ[3.6] ~ 1.0, except very near the boundary with ring C, where it is greater. The outer three-fourths of ring B has τ[3.6] ? 1.2. The differential opacity for the inner one-fourth of ring B is Δτ/τ[3.6] ~ 0.15. There are no gaps in ring B exceeding about 2 km in width. Ring F was observed at 3.6 cm as a single ringlet of radial width ? 2 km, but was not detected in 13 cm data.  相似文献   

20.
We study the short-term effects of “shepherding” satellites on narrow rings, in the general case where all bodies move along eccentric orbits. We do this by following numerically a ring of test particles as their orbits evolve under the gravitational perturbations of the shepherds. Planar motion is assumed. Our numerical scheme vastly improves (by a factor of ~104) the computation speed over conventional orbital integration methods by constructing a table of the perturbation integrals and then utilizing it over and over. The approach is applicable to any narrow ring with a nearby satellite, such as a ring confined by the shepherding mechanism of P. Goldreich and S. Tremaine [Nature277, 97–99 (1979)]. We arrive at results for a variety of orbital configurations, and then apply these to the F-ring of Saturn. Several features of the numerical integration are reminiscent of the kinks and clumps observed by Voyager. If the ring-to-satellite distance changes significantly due to eccentricities, then the ring can break up into periodic clumps in an azimuthal domain which trails the satellite. This region may lag somewhat in longitude. The perturbations may also cause the ring to vary significantly in width, being narrowest near the point of closest approach of the shepherd and widest at the opposite side. It is as yet unclear whether this effect is, or could be, observed in the Voyager images. And finally, the perturbations of the shepherds can impact a significant, but probably time variable, eccentricity to the ring. The short-term tendency is not toward alignment of ring and satellite apsides; longer time effects have not been explored.  相似文献   

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