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1.
Very low values of the radio brightness temperature of the rings of Saturn indicate that their high refar reflectivity is not simply due to a gain effect in the backscattering direction. These two sets of observations are consistent with the ring particles having a very high single scattering albedo at radio wavelenghts, with multiple scattering effects being important. Comparison of scattering calculations for ice and silicate particles with the radio and radar observations imply a mean particle radius of ～1 cm. The ice bands observed in the rings' near-infrared reflectivity spectra are formed by scattering within a microstructure on the surface of the ring particles, with the scattering centers being 25–125 μm in size. The Poynting-Robertson effect has caused a significant spiraling-in of the ring particles, probably resulting in a broadening of the rings. The inferred mean size is consistent with a model in which meteoroid impacts have caused a substantial reduction in the mean particle size from its initial value. 相似文献
2.
Steven J. Ostro Gordon H. Pettengill Donald B. Campbell Richard M. Goldstein 《Icarus》1982,49(3):367-381
The relative radar reflectiveness of Saturn's classical ring sections were estimated from delay-Doppler observations made at 12.6-cm wavelength. The A and B rings are responsible for most, if not all, of the radar echo. The average radar reflectivity per unit projected area of the A ring is nearly (～90%) as large as that of the B ring. The outer half of the B ring contains the most reflective part of the ring system. There is no firm evidence for detection of radar backscattering from particles interior to the B ring, exterior to the A ring, or from the planet itself. The radar reflectivity of the C ring is certainly no more than one-half that of the B ring, and probably is much less. Unexpectedly large amounts of power at Doppler shifts near the center of the echo spectrum, previously reported at both λ3.5 and λ12.6 cm for ring-plane tilt angles δ ≥ 24.4°, are not apparent in λ3.5- or 12.6-cm spectra obtained at δ ≤ 21.4°. 相似文献
3.
The preliminary measurements by Pioneer 11 of the limb darkening and polarization of Titan at red and blue wavelenghts (M. G. Tomasko, 1980,J. Geophys. Res., 85, 5937–5942) are refined and the measurements of the brightness of the integrated disk at phase angles from 22 to 96° are reduced. At 28° phase, Titan's reflectivity in blue light at southern latitudes is as much as 25% greater than that at northern latitudes, comparable to the values observed by Voyager 1 (L. A. Sromovsky et al., 1981,Nature (London), 292, 698–702). In red light the reflectivity is constant to within a few percent for latitudes between 40°S and 60°N. Titan's phase coefficient between 22 and 96° phase angle averages about 0.014 magnitudes/degree in both colors—a value considerably greater than that observed at smaller phase from the Earth. Comparisons of the data with vertically homogeneous multiple-scattering models indicate that the single-scattering phase functions of the aerosols in both colors are rather flat at scattering angles between 80 and 150° with a small peak at larger scattering (i.e., small phase) angles. The models indicate that the phase integral, q, for Titan in both red and blue light is about 1.66 ± 0.1. Together with Younkin's value for the bolometric geometric albedo scaled to a radius of 2825 km, this implies an effective temperature in equilibrium with sunlight of 84 ± 2°K, in agreement with recent thermal measurements. The single-scattering polarizations produced by the particles at 90° scattering angle are quite large, >85% in blue light and >95% in red. A vertically homogeneous model in which the particles are assumed to scatter as spheres cannot simultaneously match the polarization observations in both colors for any refractive index. However, the observed polarizations are most sensitive to the particle properties near optical depth in each color, and so models based on single scattering by spheres can be successful over a range of refractive indices if the size of the particles increases with depth and if the cross section of the particles increases sufficiently rapidly with decreasing wavelenght. For example, with nr = 1.70, the polarization (and the photometry) are reproduced reasonably well in both colors when the area-weighted average radous of the particles, α, is given by α = (0.117 μm)(τred/0.5)0.217. While this model does not reproduce the large increase in brightness from 129 to 160° phase observed by Voyager 1, the observed increase is determined by the properties of the particles in the top few hundredths of an optical depth. Thus the addition of a very thin layer of forward-scattering aerosols on top of the above model offers one way of satisfying both the Pioneer 11 and Voyager 1 observations. Of course, other models, using bimodal size distributions or scattering by nonspherical particles, may also be capable of reproducing these data. 相似文献
4.
Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material. 相似文献
5.
Lucien Froidevaux 《Icarus》1981,46(1):4-17
The variation in infrared equilibrium brightness temperature of Saturn's A, B, and C rings is modeled as a function of solar elevation B′ with respect to the ring plane. The basic model includes estimates of minimum and maximum interparticle shadowing in a monolayer approximation. Simple laboratory observations of random particle distributions at various illumination angles provide more realistic shadowing functions. Radiation balance calculations yield the physical (kinetic) temperature of particles in equilibrium with radiation from the Sun, Saturn, and neighboring particles. Infrared brightness temperatures as a function of B′ are then computed and compared to the available 20-μm data (Pioneer results are also briefly discussed). The A and B rings are well modeled by an optically thick monolayer, or equivalently, a flat sheet, radiating from one side only. This points to a temperature contrast between the two sides, possibly due to particles with low thermal inertia. Other existing models for the B ring are discussed. The good fit for the monolayer model does not rule out the possibility that the A and B rings are many particles thick. It could well be that a multilayer ring produces an infrared behavior (as a function of tilt angle) similar to that of a monolayer. The C ring brightness increases as B′ decreases. This contrast in behavior can be understood simply in terms of the low C ring optical depth and small amount of interparticle shadowing. High-albedo particles (A?0.5) can fit the C ring infrared data if they radiate mostly from one hemisphere due to slow rotation or low thermal inertia (or both). Alternatively, particles isothermal over their surface (owing to a rapid spin, high inertia, or small size), and significantly darker (A?0.3) than the A and B ring particles, can produce a similar brightness variation with ring inclination. In any case, the C ring particles have significantly hotter physical temperatures than the particles in the A and B rings, whether or not the rings form a monolayer. 相似文献
6.
We present delay-Doppler images of Saturn's rings based on radar observations made at Arecibo Observatory between 1999 and 2003, at a wavelength of 12.6 cm and at ring opening angles of 20.1°?|B|?26.7°. The average radar cross-section of the A ring is ∼77% relative to that of the B ring, while a stringent upper limit of 3% is placed on the cross-section of the C ring and 9% on that of the Cassini Division. These results are consistent with those obtained by Ostro et al. [1982, Icarus 49, 367-381] from radar observations at |B|=21.4°, but provide higher resolution maps of the rings' reflectivity profile. The average cross-section of the A and B rings, normalized by their projected unblocked area, is found to have decreased from 1.25±0.31 to 0.74±0.19 as the rings have opened up, while the circular polarization ratio has increased from 0.64±0.06 to 0.77±0.06. The steep decrease in cross-section is at variance with previous radar measurements [Ostro et al., 1980, Icarus 41, 381-388], and neither this nor the polarization variations are easily understood within the framework of either classical, many-particle-thick or monolayer ring models. One possible explanation involves vertical size segregation in the rings, whereby observations at larger elevation angles which see deeper into the rings preferentially see the larger particles concentrated near the rings' mid-plane. These larger particles may be less reflective and/or rougher and thus more depolarizing than the smaller ones. Images from all four years show a strong m=2 azimuthal asymmetry in the reflectivity of the A ring, with an amplitude of ±20% and minima at longitudes of 67±4° and 247±4° from the sub-Earth point. We attribute the asymmetry to the presence of gravitational wakes in the A ring as invoked by Colombo et al. [1976, Nature 264, 344-345] to explain the similar asymmetry long seen at optical wavelengths. A simple radiative transfer model suggests that the enhancement of the azimuthal asymmetry in the radar images compared with that seen at optical wavelengths is due to the forward-scattering behavior of icy ring particles at decimeter wavelengths. A much weaker azimuthal asymmetry with a similar orientation may be present in the B ring. 相似文献
7.
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
8.
An analysis of Titan's solar phase variation as a function of wavelength together with the continuum geometric albedo makes it possible to set limits on the real part of the refractive index and on the average particle size of the aerosol component of Titan's atmosphere: . If nris known can be determined to within a few percent, and varies inversely with nr. Using this information in a two-layer model of a methane-aerosol atmosphere and comparing the result with Titan's visible and near-infrared methane spectrum leads to the conclusion that the top layer of Titan's atmosphere contains 0.01 km atm of methane and 2.5 extinction optical depths of aerosol, while the data are consistent with a bottom layer containing 2.2 km atm of methane and about 7.5 aerosol optical depths for . 相似文献
9.
Observations of the rings of Saturn at 2–4 μm reveal the presence of a 3.6-μm peak in the infrared reflectivity. This peak is consistent with a particle size of ? 50 μm, and a composition of pure H2O ice. The quoted size may only be indicative of the textural scale of frost on the surface of larger particles. The presence of small amounts of CH4 in the form of a clathrate, however, cannot be ruled out by our measurements. 相似文献
10.
The sizes, composition, and number of particles comprising the rings of Saturn may be meaningfully constrained by a combination of radar- and radio-astronomical observations. In a previous paper, we have discussed constraints obtained from radar observations. In this paper, we discuss the constraints imposed by complementary “passive” radio observations at similar wavelengths. First, we present theoretical models of the brightness of Saturn's rings at microwave wavelengths (0.34–21.0 cm), including both intrinsic ring emission and diffuse scattering by the rings of the planetary emission. The models are accurate simulations of the behavior of realistic ring particles and are parameterized only by particle composition and size distribution, and ring optical depth. Second, we have reanalyzed several previously existing sets of interferometric observations of the Saturn system at 0.83-, 3.71-, 6.0-, 11.1-, and 21.0-cm wavelengths. These observations all have spatial resolution sufficient to resolve the rings and planetary disk, and most have resolution sufficient to resolve the ring-occulted region of the disk as well. Using our ring models and a realistic model of the planetary brightness distribution, we are able to establish improved constraints on the properties of the rings. In particular, we find that: (a) the maximum optical depth in the rings is ～ 1.5 ± 0.3 referred to visible wavelengths; (b) a significant decrease in ring optical depth from λ3.7 to λ21.0 cm allows us to rule out the possibility that more than ～30% of the cross section of the rings is composed of particles larger than a meter or so; this assertion is essentially independent of uncertainties in particle adsorption coefficient; and (c) the ring particles cannot be primarily of silicate composition, independently of particle size, and the particles cannot be primarily smaller than ～0.1 cm, independently of composition. 相似文献
11.
As part of a long-term study of Saturn's rings, we have used the Hubble Space Telescope's (HST) Wide Field and Planetary Camera (WFPC2) to obtain several hundred high resolution images from 1996 to 2004, spanning the full range of ring tilt and solar phase angles accessible from the Earth. Using these multiwavelength observations and HST archival data, we have measured the photometric properties of spokes in the B ring, visible in a substantial number of images. We determined the spoke particle size distribution by fitting the wavelength-dependent extinction efficiency of a prominent, isolated spoke, using a Mie scattering model. Following Doyle and Grün (1990, Icarus 85, 168-190), we assumed that the spoke particles were sub-micron size spheres of pure water ice, with a Hansen-Hovenier size distribution (Hansen and Hovenier, 1974, J. Atmos. Sci. 31, 1137-1160). The WFPC2 wavelength coverage is broader than that of the Voyager data, resulting in tighter constraints on the nature of spoke particles. The effective particle size was reff=0.57±0.05 μm, and the size distribution was quite narrow with a variance of b=0.09±0.03, very similar to the results of Doyle and Grün (1990, Icarus 85, 168-190), and consistent with predictions of plasma cloud models for spoke production from meteoritic impacts (Goertz and Morfill, 1983, Icarus 53, 219-229; Goertz, 1984, Adv. Space Res. 4, 137-141). In all, we identified 36 spokes or spoke complexes, predominantly on the morning (east) ansa. The photometric contrast of the spokes is strongly dependent on effective ring opening angle, Beff. Spokes were clearly visible on the north face of the rings in 1994, just prior to the most recent ring plane crossing (RPX) epoch, and on the south face shortly after RPX. However, spokes were both less abundant and fainter as the rings opened up, and no spokes were detected after 18 October 1998 (Beff=−15.43°), when a single faint spoke was seen on the morning ansa. The high resolution and photometric quality of the WFPC2 images enabled us to set a detection limit of ?1% in fractional brightness contrast for spokes for the post-1998 observations. We compare the observed trend of spoke contrast with Beff to radiative transfer calculations based on three models of the distribution of spoke material. In the first, the spoke “haze” is uniformly mixed with macroscopic B ring particles. No variation in spoke contrast is predicted for single-scattering, in this case, and only a modest decrease in contrast with Beff is predicted when multiple scattering is taken into account. In the second model, the spoke dust occupies an extended layer that is thicker than the B ring, which gives virtually identical results to a third case, when the haze layer lies exclusively above the ring. Multiple-scattering Monte Carlo calculations for these two extended haze models match the trend of spoke contrast exceptionally well. We compute the predicted spoke contrast for a wide variety of viewing geometries, including forward- and backscattering. Based on these results, spokes should be easily detectable during the Cassini mission when the rings are viewed at relatively small (|B|?10°) ring opening angles. 相似文献
12.
We have considered the steady state vertical structure of Saturn's rings with regard to whether collapse to a monolayer due to collisions between particles, the end state predicted by Jeffreys (1947a), may be prevented by any of a variety of mechanisms. Given a broad distribution of particle sizes such as a typical power law n(R) = n0R?3, it is found that gravitational scattering of small particles by large particles maintains a true ring thickness of several times the radius of the largest particles, or many times the radius of the smallest particles. Thus the “many-particle-thick” condition which best satisfies optical observations, such as the opposition effect, may be reconciled with ongoing particle collisions. If we consider the obvious sources of energy available for such a process, we find that a ring thickness of only tens of meters may be sustained over the lifetime of the solar system. This implies a maximum particle size on the order of a few meters. 相似文献
13.
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 [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 —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 , partly deconvolved from its angular dependence, between 0.5 and 1 a.u. (Fig. 6 and Table 4).The uncertainty bars on 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
14.
Thirteen-centimeter-wavelength radar observations of Mars made in 1982 at Arecibo Observatory yield accurate measurements of the full backscatter spectrum in two orthogonal polarizations. The data, which were obtained for several widely separated subradar longitudes at 24°N latitude, provide the first global view of the distribution of small-scale surface roughness on Mars. The diffuse component of the echo exhibits strong spatial variations. Areas of maximum depolarization correlate well with volcanic regions (Tharsis and Elysium), while the heavily cratered upland terrain yields relatively low depolarization. Parts of Tharsis give near-complete depolarization (polaziation ratio when viewed at oblique angles of incidence). Northern Martian plains regions (Tharsis, Elysium, and Amazonis) may comprise the most extensive area of severe decimeter-scale surface roughness in the inner Solar System. On the average, the northern Martian tropics yield higher diffuse radar cross sections (σD = 0.05–0.12) and a higher of degree disk-integrated depolarization (μc = 0.1–0.4) than is found for the Moon, Mercury, and Venus. Comparisons between the Moon and Mars using radar data, ground truth, and simple scattering models suggest that Mars possesses a relatively high average coverage by decimeter-scale rocks. Also discussed are several of the more interesting quasispecular scattering results, the most unsual of which were obtained over the Olympus Mons aureole region. 相似文献
15.
Interferometric observations of Saturn and its rings made at the Owens Valley Radio Observatory at a wavelength of 3.71 cm ar fit to models of the Saturn brightness structure. The models have allowed us to estimate the brightness temperatures and optical thicknesses of the A, B, and C rings as well as the brightness temperature of the planetary disk. The most accurate results are the ratios of the ring temperatures to the planet temperature of 0.030 ± 0.012, 0.050 ± 0.010, and 0.040 ± 0.014 for the A, B, and C rings, respectively. The best estimates of the ring optical thicknesses are τA = 0.2 ± 0.1, τB = 0.9 ± 0.2, and τC = 0.1 ± 0.1. The actual brightness temperatures, which are affected by the absolute calibration errors, are Tplanet = 178 ± 8, TA = 5.2 ± 2.0, TB = 9.1 ± 1.8, and TC = 7.1 ± 2.6°K. The particle single-scattering albedo that would be most consistent with the observations is slightly less than one, but probably greater than 0.95. The observations are consistent with particles which conservatively scatter the thermal emission from Saturn to the Earth and emit no thermal emission of their own. The 3.71-cm optical depths which we have estimated are very close to the visible wavelength optical depths. This similarity indicates that the ring particles must be at least a few centimeters in size, although we feel that the particles may well be much larger than this in view of the closeness of the visible and microwave optical depths. Particles which are nearly conservative scatterers at our wavelength and at least a few centimeters in size must be composed of a material which is either a very good reflector of microwaves or a very poor absorber of them. At this time, water ice seems to be the most likely candidate since it is a very poor absorber of microwaves and has been detected in the rings spectroscopically. 相似文献
16.
Steven J. Ostro Gordon H. Pettengill Irwin I. Shapiro Donald B. Campbell Richard R. Green 《Icarus》1979,40(3):355-358
Radar observations of asteroid 1 Ceres were made at a 12.6-cm wavelength from the Arecibo Observatory in March/April 1977. The measurements, made with a received circular polarization orthogonal to that transmitted, yield a radar cross section of (0.04 ± 0.01)πR2, for R = 510 km. The corresponding radar reflectivity is less than that measured for any other celestial body. Within the accuracy of measurement, no significant variation of cross section with rotational phase is apparent. The shape of the power spectrum suggests that Ceres is rougher at the scale of the observing wavelength than the Moon and inner planets, but smoother than the outer three Galilean satellites. 相似文献
17.
18.
Observations of 3.5- and 12.6-cm radar echoes from the rings of Saturn suggest that no significant difference in scattering properties exists in this wavelength interval. The echoes are largely unpolarized at both wavelengths, and yield a radar cross section at 3.5 cm of 7.32 ± 0.84 × 109 km2 for each polarization. The combined radar cross sections for both polarizations correspond to 1.37 ± 0.16 times the optically observed projected A- and B-ring areas (excluding that part of the rings shadowed by the planet). The shape of the echo spectrum is compatible with a homogeneous ring scattering model, except in having excess power at frequencies near the center of the spectrum. A number of possible explanations for the observed scattering properties are explored. 相似文献
19.
Essam A. Marouf G. Leonard Tyler Howard A. Zebker Richard A. Simpson Von R. Eshleman 《Icarus》1983,54(2):189-211
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 by integral inversion and inverse scattering methods, again assuming a many-particle-thick slab-type radiative transfer model. Distributions n(a) valid over 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 for all four locations. No single power law distribution is consistent with the data over the entire interval , although a power law-type model is consistent with the data over a limited size range of , 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 , 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
20.
Models of Saturn's B ring have been investigated which include the shadowing mechanism, realistic phase functions for the ring particles, and the effects of multiple scattering and a particle size dispersion. These models are based on the assumption that the rings form a layer many particles thick. A power law relation dn ∝ ??s is used for the size dispersion law of the ring particles, where dn is the number of particles with radii between ? and ? + d?. In the calculation of the infrared brightness temperature of the rings, the effect of mutual heating among the ring particles is considered quantitatively for the first time. The parameters of the polydisperse s = 2 model can be chosen to satisfy both optical (λ ? 1.1 μ) and infrared data, but the situation could be much clarified if a good phase curve for the rings were available in the red, if the ring brightness were known accurately for λ > 1 μ, and if it could be established whether the ring particles are rotating synchronously. 相似文献