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1.
The thermal inertia values of Saturn’s main rings (the A, B, and C rings and the Cassini division) are derived by applying our thermal model to azimuthally scanned spectra taken by the Cassini Composite Infrared Spectrometer (CIRS). Model fits show the thermal inertia of ring particles to be 16, 13, 20, and 11 J m−2 K−1 s−1/2 for the A, B, and C rings, and the Cassini division, respectively. However, there are systematic deviations between modeled and observed temperatures in Saturn’s shadow depending on solar phase angle, and these deviations indicate that the apparent thermal inertia increases with solar phase angle. This dependence is likely to be explained if large slowly spinning particles have lower thermal inertia values than those for small fast spinning particles because the thermal emission of slow rotators is relatively stronger than that of fast rotators at low phase and vise versa. Additional parameter fits, which assume that slow and fast rotators have different thermal inertia values, show the derived thermal inertia values of slow (fast) rotators to be 8 (77), 8 (27), 9 (34), 5 (55) J m−2 K−1 s−1/2 for the A, B, and C rings, and the Cassini division, respectively. The values for fast rotators are still much smaller than those for solid ice with no porosity. Thus, fast rotators are likely to have surface regolith layers, but these may not be as fluffy as those for slow rotators, probably because the capability of holding regolith particles is limited for fast rotators due to the strong centrifugal force on surfaces of fast rotators. Other additional parameter fits, in which radii of fast rotators are varied, indicate that particles less than ∼1 cm should not occupy more than roughly a half of the cross section for the A, B, and C rings. 相似文献
2.
Spectra taken by the Cassini Ultraviolet Imaging Spectrograph (UVIS) of Saturn’s C ring, B ring, Cassini Division, and A ring have been analyzed in order to characterize ring particle surface properties and water ice abundance in the rings. UVIS spectra sense the outer few microns of the ring particles. Spectra of the normalized reflectance (I/F) in all four regions show a characteristic water ice absorption feature near 165 nm. Our analysis shows that the fractional abundance of surface water ice is largest in the outer B ring and decreases by over a factor of 2 across the inner C ring. We calculate the mean path length of UV photons through icy ring particle regolith and the scattering asymmetry parameter using a Hapke reflectance model and a Shkuratov reflectance model to match the location of the water ice absorption edge in the data. Both models give similar retrieved values of the photon mean length, however the retrieved asymmetry (g) values are different. The photon mean path lengths are nearly uniform across the B and A rings. Shortward of 165 nm the rings exhibit a slope that turns up towards shorter wavelengths, while the UV slope of 180/150 nm (reflectance outside the water absorption ratioed to that inside the absorption band) tracks I/F with maxima in the outer B ring and in the central A ring. Retrieved values of the scattering asymmetry parameter show the regolith grains to be highly backscattering in the FUV spectral regime. 相似文献
3.
We both test and offer an alternative to a meteoroid bombardment model (M. R. Showalter 1998, Science282, 1099-1102) and suggest that anomalous localized brightenings in the F ring observed by Voyager result from disruptive collisions involving poorly consolidated moonlets, or “rubble piles.” This model can also explain the transient events observed during ring plane crossing. We have developed an evolutionary model that considers both the competing effects of accretion and disruption at the location of the F ring. Our numerical model is a Markov process where probabilities of mass transfer between the states of the system form a “transition matrix.” Successive multiplications of this matrix by the state vector generate expectation values of the distribution after each time step as the system approaches quasi-equilibrium. Competing effects of accretion and disruption in the F ring are found to lead to a bimodal distribution of ring particle sizes. In fact, our simulation predicts the presence of a belt of kilometer-sized moonlets in the F ring. These moonlets may continually disrupt one another and re-accrete on short time scales. We also agree with J. N. Cuzzi and J. A. Burns (1988, Icarus74, 284-324), who suggest that the classical F ring itself may be the consequence of a relatively recent collision between two of the largest of these yet unseen objects. Cassini observations can confirm the existence of the moonlet belt by directly observing these objects or the waves they create in the rings. 相似文献
4.
We correct a calibration error in our earlier analysis of Voyager color observations of Saturn's main rings at 14° phase angle (Estrada and Cuzzi, 1996, Icarus 122, 251) and present thoroughly revised and reanalyzed radial profiles of the brightness of the main rings in the Voyager green, violet, and ultraviolet filters and the ratios of these brightnesses. These results are consistent with more recent HST results at 6° phase angle, once allowance is made for plausible phase reddening of the rings (Cuzzi et al., 2002, Icarus 158, 199). Unfortunately, the Voyager camera calibration factors are simply not sufficiently well known for a combination of the Voyager and HST data to be used to constrain the phase reddening quantitatively. However, some interesting radial variations in reddening between 6 and 14° phase angles are hinted at. We update a ring-and-satellite color vs albedo plot from Cuzzi and Estrada (1998, Icarus 132, 1) in several ways. The A and B rings are still found to be in a significantly redder part of color-albedo space than Saturn's icy satellites. 相似文献
5.
We have completed a series of local N-body simulations of Saturn’s B and A rings in order to identify systematic differences in the degree of particle clumping into self-gravity wakes as a function of orbital distance from Saturn and dynamical optical depth (a function of surface density). These simulations revealed that the normal optical depth of the final configuration can be substantially lower than one would infer from a uniform distribution of particles. Adding more particles to the simulation simply piles more particles onto the self-gravity wakes while leaving relatively clear gaps between the wakes. Estimating the mass from the observed optical depth is therefore a non-linear problem. These simulations may explain why the Cassini UVIS instrument has detected starlight at low incidence angles through regions of the B ring that have average normal optical depths substantially greater than unity at some observation geometries [Colwell, J.E., Esposito, L.W., Srem?evi?, M., Stewart, G.R., McClintock, W.E., 2007. Icarus 190, 127-144]. We provide a plausible internal density of the particles in the A and B rings based upon fitting the results of our simulations with Cassini UVIS stellar occultation data. We simulated Cassini-like occultations through our simulation cells, calculated optical depths, and attempted to extrapolate to the values that Cassini observes. We needed to extrapolate because even initial optical depths of >4 (σ > 240 g cm−2) only yielded final optical depths no greater than 2.8, smaller than the largest measured B ring optical depths. This extrapolation introduces a significant amount of uncertainty, and we chose to be conservative in our overall mass estimates. From our simulations, we infer the surface density of the A ring to be , which corresponds to a mass of . We infer a minimum surface density of for Saturn’s B ring, which corresponds to a minimum mass estimate of . The A ring mass estimate agrees well with previous analyses, while the B ring is at least 40% larger. In sum, our lower limit estimate is that the total mass of Saturn’s ring system is 120-200% the mass of the moon Mimas, but significantly larger values would be plausible given the limitations of our simulations. A significantly larger mass for Saturn’s rings favors a primordial origin for the rings because the disruption of a former satellite of the required mass would be unlikely after the decay of the late heavy bombardment of planetary surfaces. 相似文献
6.
Stellar occultations by Saturn’s rings observed with the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty features such as the F ring and the ringlets in the Encke and the Laplace Gaps have distinctive infrared transmission spectra. These spectra show a narrow optical depth minimum at wavelengths around 2.87 μm. This minimum is likely due to the Christiansen Effect, a reduction in the extinction of small particles when their (complex) refractive index is close to that of the surrounding medium. Simple Mie-scattering models demonstrate that the strength of this opacity dip is sensitive to the size distribution of particles between 1 and 100 μm across. Furthermore, the spatial resolution of the occultation data is sufficient to reveal variations in the transmission spectra within and among these rings. In both the Encke Gap ringlets and F ring, the opacity dip weakens with increasing local optical depth, which is consistent with the larger particles being concentrated near the cores of these rings. The Encke Gap ringlets also show systematically weaker opacity dips than the F ring and Laplace Gap ringlet, implying that the former has a smaller fraction of grains less than ∼30 μm across. However, the strength of the opacity dip varies most dramatically within the F ring; certain compact regions of enhanced optical depth lack an opacity dip and therefore appear to have a greatly reduced fraction of grains in the few-micron size range. Such spectrally-identifiable structures probably represent a subset of the compact optically-thick clumps observed by other Cassini instruments. These variations in the ring’s particle size distribution can provide new insights into the processes of grain aggregation, disruption and transport within dusty rings. For example, the unusual spectral properties of the F-ring clumps could perhaps be ascribed to small grains adhering onto the surface of larger particles in regions of anomalously low velocity dispersion. 相似文献
7.
《Icarus》1987,70(1):124-137
The sharp, about 100-km-wide, transition between Saturn's C and B rings is at the inner stability limit of small (micrometer or less) highly charged debris from micrometeorite bombardment of the main ring bodies. The latter vary from about 1 cm to 5 m in radius. In the C ring this charged debris escapes from the ring plane to Saturn along magnetic field lines because of gravitational pull, thus producing a net mass loss. But in the B ring the debris oscillates stably back and forth through the ring plane until reabsorbed by a large ring body. In this model we assume that what is now the B and C rings was initially formed as one ring with the optical thickness of the present B ring. We estimate the C ring net erosion rate and determine the ring age, assuming that the mass influx is small compared with the erosion flux. The erosion rate has been calculated with the use of presently observed micrometeorite fluxes. We also use the best present estimates of the size distribution and total mass eroded by a micrometeorite of a given size and energy. We find that the ring age is between 4.4 and 67 myr. In either case the age is much younger than the 4.5 byr of the solar system. The sharpness of the transition between the B and C rings indicates that the principal mass loss is carried by particles moving at a few meters per second with respect to the parent bodies from which they were eroded. 相似文献
8.
We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch.The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L4 (leading, near Telesto) or L5 (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10 years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period).Still faster debris with azimuthal velocity components ?10 m/s enter horseshoe orbits which enclose both L4 and L5 as well as L3, but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ?40 m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years. 相似文献
9.
High-velocity impacts of interplanetary meteoroids on Saturn's rings are discussed. It is shown that the neutral gas emitted by impact vaporization may be responsible, to a large part, for the observed neutral ring atmosphere. Both the predicted neutral gas injection rate and the gas temperature (or kinetic energy) are compatible with the measurements (see Broadfoot, A. L., B. R. Sandel, D. E. Shemansky, J. B. Holberg, G. R. Smith, D. F. Strobel, J. C. McConnell, S. Kumar, D. M. Hunten, S. K. Atreya, T. M. Dohnahne, H. W. Moos, J. L. Bertaux, J. E. Blamont, R. B. Pomphrey, and S. Linik, Science212, 206–211, 1981). Heavy ejecta particles produce a particulate ring “halo”. The physical properties of this halo are calculated, and it appears to be identical with the tenous particle population discussed by Baum and Kreidl (1982). Erosion of Saturn's ring particles, the resulting mass balance, and regolith formation are estimated. This provides some constraints on surface properties and optical albedo. 相似文献
10.
Sanaz Vahidinia Jeffrey N. Cuzzi Matt Hedman Bruce Draine Roger N. Clark Ted Roush Gianrico Filacchione Philip D. Nicholson Robert H. Brown Bonnie Buratti Christophe Sotin 《Icarus》2011,215(2):682-694
We present models of the near-infrared (1-5 μm) spectra of Saturn’s F ring obtained by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) at ultra-high phase angles (177.4-178.5°). Modeling this spectrum constrains the size distribution, composition, and structure of F ring particles in the 0.1-100 μm size range. These spectra are very different from those obtained at lower phase angles; they lack the familiar 1.5 and 2 μm absorption bands, and the expected 3 μm water ice primary absorption appears as an unusually narrow dip at 2.87 μm. We have modeled these data using multiple approaches. First, we use a simple Mie scattering model to constrain the size distribution and composition of the particles. The Mie model allows us to understand the overall shapes of the spectra in terms of dominance by diffraction at these ultra-high phase angles, and also to demonstrate that the 2.87 μm dip is associated with the Christiansen frequency of water ice (where the real refractive index passes unity). Second, we use a combination of Mie scattering with Effective Medium Theory to probe the effect of porous (but structureless) particles on the overall shape of the spectrum and depth of the 2.87 μm band. Such simple models are not able to capture the shape of this absorption feature well. Finally, we model each particle as an aggregate of discrete monomers, using the Discrete Dipole Approximation (DDA) model, and find a better fit for the depth of the 2.87 μm feature. The DDA models imply a slightly different overall size distribution. We present a simple heuristic model which explains the differences between the Mie and DDA model results. We conclude that the F ring contains aggregate particles with a size distribution that is distinctly narrower than a typical power law, and that the particles are predominantly crystalline water ice. 相似文献
11.
《Icarus》1987,71(1):69-77
The gravitational influence of moonlets or satellites on the radial structure of the rings of Saturn has been calculated numerically. A drastic change in the surface mass density is obtained even after a single scattering process of the ring particles on a moonlet (satellite). The final surface density shows a significant radial structure, which has been used to estimate the radius and the mass of moonlets or satellites embedded in rings of low optical depth (E ring, Cassini division, C ring). 相似文献
12.
Preservation potential of implanted solar wind volatiles in lunar paleoregolith deposits buried by lava flows 总被引：1，自引：0，他引：1
The lunar surface is bathed in a variety of impacting particles originating from the solar wind, solar flares, and galactic cosmic rays. These particles can become embedded in the regolith and/or produce a range of other molecules as they pass through the target material. The Moon therefore contains a record of the variability of the solar and galactic particle fluxes through time. To obtain useful temporal snapshots of these processes, discrete regolith units must be shielded from continued bombardment that would rewrite the record over time. One mechanism for achieving this preservation is the burial of a regolith deposit by a later lava flow. The archival value of such deposits sandwiched between lava layers is enhanced by the fact that both the under- and over-lying lava can be dated by radiometric techniques, thereby precisely defining the age of the regolith layer and the geologic record contained therein. The implanted volatile species would be vulnerable to outgassing by the heat of the over-lying flow, at temperatures exceeding 300-700 °C. However, the insulating properties of the finely particulate regolith would restrict significant heating to shallow depths. We have therefore modeled the heat transfer between lunar mare basalt lavas and the regolith in order to establish the range of depths below which implanted volatiles would be preserved. We find that the full suite of solar wind volatiles, consisting predominantly of H and He, would survive at depths of ∼13-290 cm (for 1-10 m thick lava flows, respectively). A substantial amount of CO, CO2, N2 and Xe would be preserved at depths as shallow as 3.7 cm beneath meter-thick flows. Given typical regolith accumulation rates during mare volcanism, the optimal localities for collecting viable solar wind samples would involve stacks of thin mare lava flows emplaced a few tens to a few hundred Ma apart, in order for sufficient regolith to develop between burial events. Obtaining useful archives of Solar System processes would therefore require extraction of regolith deposits buried at quite shallow depths beneath radiometrically-dated mare lava flows. These results provide a basis for possible lunar exploration activities. 相似文献
13.
A computer simulation of the sputtering of lunar soil by solar wind protons was performed with the TRIM program. The rate of the sputtering-induced erosion of regolith particles was shown to be less than 0.2 Å per year. A preferential sputtering of Ca, Mg, and O was found along with a less intense sputtering of Fe, Si, and Ti. However, with no other selection mechanisms, surface concentrations of the atoms would differ from the volume ones by no more than 6 %. The enrichment of rims of regolith particles with iron occurs as a result of selective removal of lighter atoms from the lunar surface because of different energies of escape from the Moon's gravity. The energy distributions proved to be the same for all sorts of the sputtered atoms, except for implanted hydrogen; thus, a greater fraction of the atoms left on the lunar surface corresponds to heavier elements. According to simulation results, the concentration of reduced iron observed in the mature regolith could be attained during the time of regolith particle exposure to the present flux of solar wind (105 years). Thus, sputtering can provide the concentration of Fe0 observed in regolith. On periphery of a cloud of impact vapor the temperature is too low for an irreversible selective removal of evaporation products; thus, a meteoritic bombardment contributes to the formation of composition of the rims of regolith particles mainly through enrichment of the rims with elements from the bulk of the particles. The estimates of fluxes of backscattered solar wind protons and of sputtered protons, earlier implanted to the regolith, demonstrated that their contribution to the proton flux near the poles is only 104 cm–2 s–1. This is by two orders of magnitude smaller than the proton flux from the Earth's magnetosphere which is, therefore, the main source of protons for permanently shaded polar craters of the Moon. 相似文献
14.
Cassini UVIS star occultations by the F ring detect 13 events ranging from 27 m to 9 km in width. We interpret these structures as likely temporary aggregations of multiple smaller objects, which result from the balance between fragmentation and accretion processes. One of these features was simultaneously observed by VIMS. There is evidence that this feature is elongated in azimuth. Some features show sharp edges. At least one F ring object is opaque and may be a “moonlet.” This possible moonlet provides evidence for larger objects embedded in Saturn's F ring, which were predicted as the sources of the F ring material by Cuzzi and Burns [Cuzzi, J.N., Burns, J.A., 1988. Icarus 74, 284-324], and as an outcome of tidally modified accretion by Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171]. We see too few events to confirm the bi-modal distribution which Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171] predict. These F ring structures and other youthful features detected by Cassini may result from ongoing destruction of small parent bodies in the rings and subsequent aggregation of the fragments. If so, the temporary aggregates are 10 times more abundant than the solid objects. If recycling by re-accretion is significant, the rings could be quite ancient, and likely to persist far into the future. 相似文献
15.
We present infrared (20 μm) observations of Saturn's rings for a solar elevation angle of 10° and phase angle of 6°. Scans across the rings yield information about the cooling of particles during eclipse and the subsequent heating along their orbits. All three rings exhibit significant cooling during eclipse, as well as a 20-μm brightness asymmetry between east and west ansae, the largest asymmetry occuring in the C ring (the brightest ring). The eclipse cooling is a simple and adequate explanation for 20-μm brightness asymmetries between the ansae of Saturn's rings. The relatively large C ring asymmetry is thought to be primarily due to the short travel time of the particles in that ring from eclipse exit to east ansa. We compare the B ring data to the theoretical models of H.H. Aumann and H.H. Kieffer (1973, Astrophys. J.186, 305–311) in order to set constraints on the average particle size and thermal inertia. The rather rapid heating after exit from eclipse points to low-conductivity-particle surfaces, similar to the water frost surfaces of Galilean satellites. If the surface conductivity is indeed low, one cannot determine an upper limit for the particle size through such infrared observations, since only the uppermost millimeters experience a thermal response during eclipse. However, based on these infrared data alone, it is clear that particles of radius equal to a few millimeters or less cannot occupy a significant fraction of the ring surface area, because-regardless of thermal inertia-their thermal response is much faster than observed. 相似文献
16.
Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains (d∼λ for the C ring particles, d∼1-10 μm for the other rings). 相似文献
17.
This paper presents the results of N-body simulations of moonlets embedded in broad rings, focusing specifically on the saturnian A ring. This work adds to previous efforts by including particle self-gravity and particle size distributions. The discussion here focuses primarily on the features that form in the background particles as a result of the moonlet. Particle self-gravity tends to damp out features produced by embedded moonlets and this damping is enhanced if the moonlet is simply the largest member of a continuous size distribution. Observable features around an embedded moonlet appear to require that the largest ring particles be no more massive than 1/30 the mass of the moonlet. These results, compared with current and future Cassini observations, will provide insight into the nature of the particle population in the saturnian rings. Some time is also spent analyzing the way in which the background particles cluster around the moonlet. The accretion of small particles onto the moonlet can be limited by disruptive collisions with the largest ring particles in the particle size distribution. 相似文献
18.
The so-called “Charming Ringlet” (R/2006 S3) is a low-optical-depth, dusty ringlet located in the Laplace gap in the Cassini Division, roughly 119,940 km from Saturn center. This ringlet is particularly interesting because its radial position varies systematically with longitude relative to the Sun in such a way that the ringlet’s geometric center appears to be displaced away from Saturn’s center in a direction roughly toward the Sun. In other words, the ringlet is always found at greater distances from the planet’s center at longitudes near the sub-solar longitude than it is at longitudes near Saturn’s shadow. This “heliotropic” behavior indicates that the dynamics of the particles in this ring are being influenced by solar radiation pressure. In order to investigate this phenomenon, which has been predicted theoretically but not observed this clearly, we analyze multiple image sequences of this ringlet obtained by the Cassini spacecraft in order to constrain its shape and orientation. These data can be fit reasonably well with a model in which both the eccentricity and the inclination of the ringlet have “forced” components (that maintain a fixed orientation relative to the Sun) as well as “free” components (that drift around the planet at steady rates determined by Saturn’s oblateness). The best-fit value for the eccentricity forced by the Sun is 0.000142 ± 0.000004, assuming this component of the eccentricity has its pericenter perfectly anti-aligned with the Sun. These data also place an upper limit on a forced inclination of 0.0007°. Assuming the forced inclination is zero and the forced eccentricity vector is aligned with the anti-solar direction, the best-fit values for the free components of the eccentricity and inclination are 0.000066 ± 0.000003 and 0.0014 ± 0.0001°, respectively. While the magnitude of the forced eccentricity is roughly consistent with theoretical expectations for radiation pressure acting on 10-to-100-μm-wide icy grains, the existence of significant free eccentricities and inclinations poses a significant challenge for models of low-optical-depth dusty rings. 相似文献
19.
Harris (Icarus24, 190–192) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than by tidal stress. While this conclusion is probably true, estimated radius limits must be revised upward from Harris' values of a few kilometers by at least an order of magnitude. Accretion of particles within Roche's limit is also possible. These considerations affect theories concerning the evolution of Saturn's rings, of the Moon, and of possible former satellites of Mercury and Venus. In the case of Saturn's rings, comparison of various theoretical scenarios with available observational evidence suggests that the rings formed from the breakup of larger particles rather than from original condensation as small particles. This process implies a distribution of particle sizes in Saturn's rings possibly ranging up to ～100 km but with most cross-section in cm-scale particles. 相似文献
20.
The small physical thickness of Saturn's rings requires that radio occultation observations be interpreted using scattering models with limited amounts of multiple scatter. A new model in which the possible order of near-forward scatter is strictly limited allows for the small physical thickness, and can be used to relate Voyager 1 observations of 3.6-and 13-cm wavelength microwave scatter from Saturn's rings to the ring particle size distribution function n(a), for particles with radius 0.001 ≤ a ≤ 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in Saturn's rings, which exhibit approximately inverse-cubic power-law behavior, with large-size cutoffs in particle radius ranging from about 5 m in ring C to about 10 m in parts of ring A. The power-law index is about 3.1 in ring C, about 2.8 in the Cassini division, and increases systematically with radial location in ring A from 2.7 at 2.10Rs to slightly more than 3.0 at 2.24Rs. Corresponding mass densities are 32–43 kg/m2 in ring C, 188 kg/m2 in the Cassini division, and 244–344 kg/m2 in ring A, under the assumption that the material density of the particles is 0.9 g/cm3. These values are a factor of 1 to 2 lower than first-order mass loading estimates derived from resonance phenomena. In view of the uncertainties in the measurements and in the linear density wave model, and the strong arguments for icy particles with specific gravity not greater than about 1, we interpret this discrepancy as being indicative of possible differences in the regions studied, or systematic errors in the interpretation of the scattering results, the density wave phenomena, or some combination of the above. 相似文献