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The varying geometry of Cassini star occultations by Saturn’s rings constrains both the size and shape of structures that block starlight. Statistics of UVIS star occultations measure structures as small as meters, on times scales of minutes to decades. We calculate the excess variance, skewness and kurtosis including the effects of irregular particle shadows, along with a granola bar model of gaps, ghosts and clumps. The widths W and separation S of rectangular clumps play an analogous role to the relative size of the particle shadows, δ. In the first model considered, our calculations are based on the moments of the transparency T in that part of the ring Asampled by the occultation, thus extending the work of Showalter and Nicholson (1990) to larger τ and δ, and to higher central moments, without their simplifying assumptions. We also calculate these statistics using an approach based on the autocovariance, autocoskewness and autocokurtosis. These new approaches compare well to the formula for excess variance from Showalter and Nicholson in the region where all are accurate, δτ≪1. Skewness for small τ has a different sign for transparent and opaque structures, distinguishing gaps from clumps. The higher order central moments are more sensitive to the extremes of the size distribution and opacity. We explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the measured optical depth is correlated with particle size. For a linear dependence Reff = 12 * (τ – 0.08) + 1.8m from Jerousek’s results, we match the curvature of normalized excess variance, the skewness and the kurtosis in the region between 78,000 and 84,600 km from Saturn. Statistics calculated from the granola bar model give different predictions from individual particles. The different τ dependence suggests that the wave crests compress the gaps more than the wakes, and produce more regularity among the clumps; and larger and more opaque self-gravity wakes in the wave crests, with transparent ghosts. The UVIS observations fall between the most regular and the most irregular granola bar models. We compare selected occultations (Eckert etal 2020) at different values of the elevation B to estimate the flattening and axial ratio of ring particles and clumps. In Ring C, we find spheres: The statistical measures from multiple occultations follow the expected dependence on sin B, e.g. Showalter & Nicholson (1990). However, in the Janus 2:1 and Mimas 5:3 density waves, the excess variance for stars β Cen, λ Sco and σ Sgr shows no B dependence. This is exactly the expectation for completely flat (H/W =0) self-gravity wakes that we have derived from the autocovariance of the wake shadows. A closer analysis of this particular case gives H/W < 0.04, different from Colwell etal (2007), suggesting wakes are more like linguine than granola bars.

We calculate the excess variance, excess skewness and excess kurtosis including the effects of cylindrical shadows, along with gaps, ghosts and clumps (all calculated for the granola bar model for rectangular clumps and gaps). The widths and separation of the clumps play an analogous role to the relative size of the particle shadows, δ. Wherever the rings have significant gaps or clumps, those will dominate the statistics over the individual ring particles shadow contribution. In the first model considered, our calculations are based on the moments of the transparency T in that part of the ring sampled by the occultation, thus extending the work of Showalter and Nicholson (1990) to larger τ and δ, and to higher central moments, without their simplifying assumptions. We also calculate these statistics using an approach based on the autocovariance, autocoskewness and autocokurtosis. This may be more intuitive, and can be extended to other transparency distributions, e.g., those provided by gaps, ghosts, clumps and granola bars. In a third method, we have refined an overlap correction for multiple shadows, which is important for larger optical depth. This correction is calculated by summing a geometric series, and is similar to the empirical formula, eq. (22) in Colwell et al (2018). These 3 new approaches compare well to the formula for excess variance from Showalter and Nicholson in the region where all are accurate, that is δτ≪1. Skewness for small τ has a different sign for transparent and opaque structures, and can distinguish gaps from clumps. The higher order central moments are more sensitive to the extremes of the size distribution and opacity. As a check, we can explain the upward curvature of the dependence of normalized excess variance for Saturn’s background C ring by the observation of Jerousek etal (2018) that the increased optical depth is directly correlated with effective particle size. For a linear dependence Reff = 12 * (τ – 0.08) + 1.8m from Jerousek’s results, we match both the curvature of normalized excess variance and the skewness in the region between 78,000 and 84,600km from Saturn. This explanation has no free parameters and requires no gaps or ghosts (Baillie etal 2013) in this region of Saturn’s C ring.

The Ultraviolet Imaging Spectrograph (UVIS) high-speed photometer (HSP) aboard the Cassini spacecraft collected stellar occultation data for stars of various brightness and viewing geometries as they were occulted by Saturn’s rings. We calculate the variance and skewness of the occultation light curves, and we analyze these statistical moments as functions of both optical depth and ring plane radius. Typical radial resolution of the occultations is 10-20 meters allowing for statistical moments to be calculated from 1000 points at 10 km radial sampling in the rings. We derived an analytic expression for skewness (S) as a function of optical depth assuming a ring composed of identical spherical particles, analogous to the normalized excess variance (E) relationship to optical depth used by Showalter and Nicholson (1990) and Colwell et al. (2018) to determine an effective particle size across the rings. We compared the results for effective particle size derived from S and E. Some regions, such as the inner B ring, return similar R-effective values, while others, such as the C ring plateaus, show distinctly different values. Skewness is a measure of the asymmetry of the distribution of photon counts in a measurement sample, while the variance is related to the spread of the distribution. Thus, agreement in the derived values of R-effective from S and E indicates an absence of clumps or local holes (nicknamed “ghosts”) in the rings that would lead to unusually small or large values of S, respectively. Regions of the rings where the values of R-effective from skewness (R_S) disagree with those derived from E (R_E) thus indicate the presence of ghosts or clumps that skew the distribution of photon counts in those regions. We use Monte-Carlo simulations of a simplified ring system composed of identical spherical particles interspersed with clumps and ghosts to determine the effects of these phenomena on S and compare to data. We also use simulated occultations through N-body simulations of the rings to calculate E and S where ghosts due to small moonlets or boulders are prevalent. We find variations in the suggested number of ghosts, presumed to be openings due to the same phenomena that create propeller structures in the A ring, across the rings, including in regions where there are no obvious optical depth signatures.

Observations of the collisional evolution of particle ensembles in a microgravity environment are necessary to characterize the processes that lead to the formation of planetesimals, km-size and larger bodies, within the protoplanetary disk. The two current theories of planetesimal formation, namely growth through binary sticking collisions and gravitational instability within the protoplanetary disk, have difficulties in explaining how particles grow beyond a centimeter in size. In this paper we describe the CubeSat Particle Aggregation and Collision Experiment (Q-PACE), a Low Earth Orbit 3U CubeSat mission that will provide a high-quality, long duration microgravity environment in which we will observe collisions between particles under conditions relevant to planetesimal formation. We have designed a series of experiments involving a broad range of particle size, density, surface properties, and collision velocities to observe collisional outcomes from bouncing to sticking as well as aggregate disruption in tens of thousands of collisions.

We present an analysis of eleven solar occultations by Saturn’s F ring observed by the Ultraviolet Imaging Spectrograph (UVIS) on the Cassini spacecraft. In four of the solar occultations we detect an unambiguous signal from diffracted sunlight that adds to the direct solar signal just before or after the occultations occur. The strongest detection was a 10% increase over the direct signal that was enabled by the accidental misalignment of the instrument’s pointing. We compare the UVIS data with images of the F ring obtained by the Cassini Imaging Science Subsystem (ISS) and find that in each instance of an unambiguous diffraction signature in the UVIS data, the ISS data shows that there was a recent disturbance in that region of the F ring. Similarly, the ISS images show a quiescent region of the F ring for all solar occultations in which no diffraction signature was detected. We therefore conclude that collisions in the F ring produce a population of small ring particles that can produce a detectable diffraction signal immediately interior or exterior to the F ring. The clearest example of this connection comes from the strong detection of diffracted light in the 2007 solar occultation, when the portion of the F ring that occulted the Sun had suffered a large collisional event, likely with S/2004 S 6, several months prior. This collision was observed in a series of ISS images (Murray et al., 2008). Our spectral analysis of the data shows no significant spectral features in the F ring, indicating that the particles must be at least 0.2 µm in radius. We apply a forward model of the solar occultations, accounting for the effects of diffracted light and the attenuated direct solar signal, to model the observed solar occultation light curves. These models constrain the optical depth, radial width, and particle size distribution of the F ring. We find that when the diffraction signature is present, we can best reproduce the occultation data using a particle population with an average effective particle size of less than 300 µm, while occultations without clear diffraction signals are best modeled using a population with an effective particle size larger than 400 µm.

The Cassini spacecraft's Ultraviolet Imaging Spectrograph (UVIS) includes a high speed photometer (HSP) that has observed stellar occultations by Saturn's rings with a radial resolution of ∼10 m. In the absence of intervening ring material, the time series of measurements by the HSP is described by Poisson statistics in which the variance equals the mean. The finite sizes of the ring particles occulting the star lead to a variance that is larger than the mean due to correlations in the blocking of photons due to finite particle size and due to random variations in the number of individual particles in each measurement area. This effect was first exploited by Showalter and Nicholson (1990) with the stellar occultation observed by Voyager 2. At a given optical depth, a larger excess variance corresponds to larger particles or clumps that results in greater variation of the signal from measurement to measurement. Here we present analysis of the excess variance in occultations observed by Cassini UVIS. We observe differences in the best-fitting particle size in different ring regions. The C ring plateaus show a distinctly smaller effective particle size, R , than the background C ring, while the background C ring itself shows a positive correlation between R and optical depth. The innermost 700 km of the B ring has a distribution of excess variance with optical depth that is consistent with the C ring ramp and C ring but not with the remainder of the B1 region. The Cassini Division, while similar to the C ring in spectral and structural properties, has different trends in effective particle size with optical depth. There are discrete jumps in R on either side of the Cassini Division ramp, while the C ring ramp shows a smooth transition in R from the C ring to the B ring. The A ring is dominated by self-gravity wakes whose shadow size depends on the occultation geometry. The spectral “halo” regions around the strongest density waves in the A ring correspond to decreases in R . There is also a pronounced dip in R at the Mimas 5:3 bending wave corresponding to an increase in optical depth there, suggesting that at these waves small particles are liberated from clumps or self-gravity wakes leading to a reduction in effective particle size and an increase in optical depth.

We present a comprehensive solution for the geometry of Saturn’s ring system, based on orbital fits to an extensive set of occultation observations of 122 individual ring edges and gaps. We begin with a restricted set of very high quality Cassini VIMS, UVIS, and RSS measurements for quasi-circular features in the C and B rings and the Cassini Division, and then successively add suitably weighted additional Cassini and historical occultation measurements (from Voyager, HST and the widely-observed 28 Sgr occultation of 3 Jul 1989) for additional non-circular features, to derive an absolute radius scale applicable across the entire classical ring system. As part of our adopted solution, we determine first-order corrections to the spacecraft trajectories used to determine the geometry of individual occultation chords. We adopt a simple linear model for Saturn’s precession, and our favored solution yields a precession rate on the sky n ^ ˙ P = 0.207 ± 0 . 006 ′ ′ yr − 1 , equivalent to an angular rate of polar motion Ω P = 0.451 ± 0 . 014 ′ ′ yr − 1 . The 3% formal uncertainty in the fitted precession rate is approaching the point where it can provide a useful constraint on models of Saturn’s interior, although realistic errors are likely to be larger, given the linear approximation of the precession model and possible unmodeled systematic errors in the spacecraft ephemerides. Our results are largely consistent with independent estimates of the precession rate based on historical RPX times (Nicholson et al., 1999 AAS/Division for Planetary Sciences Meeting Abstracts #31 31, 44.01) and from theoretical expectations that account for Titan’s 700-yr precession period (Vienne and Duriez 1992, Astronomy and Astrophysics 257, 331–352). The fitted precession rate based on Cassini data only is somewhat lower, which may be an indication of unmodeled shorter term contributions to Saturn’s polar motion from other satellites, or perhaps the result of inconsistencies in the assumed direction of Saturn’s pole in the reconstructed Cassini spacecraft ephemerides. Overall, the agreement of our results with the widely-used French et al. (1993, Icarus 103, 163–214) radius scale is excellent, with very small (≲ 0.1 km) systematic differences, although differences in a few individual feature radii are as large as 6 km. Our new solution incorporates many more features across the ring system, and the fitted orbital elements correct for the several-km biases in the radii of many ring features in the French et al. (1993) catalog that were unresolved because of the large projected diameter of the occulted star in the 28 Sgr event. The formal errors in the fitted radii are generally quite small – on the order of tens of meters. Systematic errors stemming from uncertainty in the precession rate of Saturn’s pole and its effect on the accuracy of the reconstructed Cassini trajectories are somewhat larger, but the absolute radius scale is relatively insensitive to 5- σ changes in the pole direction or precession rate, and we estimate the combined magnitude of these systematic errors and pole uncertainties to be of order 250 m. This estimate is likely to be improved once a new set of reconstructed Cassini trajectories has been developed, based on a self-consistent model for Saturn’s pole. We demonstrate the utility of the new radius scale and the associated trajectory corrections in the analysis of short-wavelength density waves in the C ring. In online supplementary material, we provide in machine-readable form the more than 15,000 individual ring measurements used in this study, as well as details of the ring orbit fits underlying this work.

The eccentric Maxwell ringlet in Saturn’s C ring is home to a prominent wavelike structure that varies strongly and systematically with true anomaly, as revealed by nearly a decade of high-SNR Cassini occultation observations. Using a simple linear “accordion” model to compensate for the compression and expansion of the ringlet and the wave, we derive a mean optical depth profile for the ringlet and a set of rescaled, background-subtracted radial wave profiles. We use wavelet analysis to identify the wave as a 2-armed trailing spiral, consistent with a density wave driven by an m = 2 outer Lindblad resonance (OLR), with a pattern speed Ω p = 1769.17 ° d−1 and a corresponding resonance radius a res = 87530.0 km. Estimates of the surface mass density of the Maxwell ringlet range from a mean value of 11 0.25 e m 0 e x g 0.25 e m 0 e x cm − 2 derived from the self-gravity model to 5 − 12 g cm − 2 , as inferred from the wave’s phase profile and a theoretical dispersion relation. The corresponding opacity is about 0.12 0.25 e m 0 e x cm 2 0.25 e m 0 e x g − 1 , comparable to several plateaus in the outer C ring (Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369–1388). A linear density wave model using the derived wave phase profile nicely matches the wave’s amplitude, wavelength, and phase in most of our observations, confirming the accuracy of the pattern speed and demonstrating the wave’s coherence over a period of 8 years. However, the linear model fails to reproduce the narrow, spike-like structures that are prominent in the observed optical depth profiles. Using a symplectic N-body streamline-based dynamical code (Hahn, J.M., Spitale, J.N. [2013]. Astrophys. J. 772, 122), we simulate analogs of the Maxwell ringlet, modeled as an eccentric ringlet with an embedded wave driven by a fictitious satellite with an OLR located within the ring. The simulations reproduce many of the features of the actual observations, including strongly asymmetric peaks and troughs in the inward-propagating density wave. We argue that the Maxwell ringlet wave is generated by a sectoral normal-mode oscillation inside Saturn with l = m = 2 , similar to other planetary internal modes that have been inferred from density waves observed in Saturn’s C ring (Hedman, M.N., Nicholson, P.D. [2013]. Astron. J. 146, 12; Hedman, M.N., Nicholson, P.D. [2014]. Mont. Not. Roy. Astron. Soc. 444, 1369–1388). Our identification of a third m = 2 mode associated with saturnian internal oscillations supports the suggestions of mode splitting by Fuller et al. (Fuller, J., Lai, D., Storch, N.I. [2014]. Icarus 231, 34–50) and Fuller (Fuller, J. [2014]. Icarus 242, 283–296). The fitted amplitude of the wave, if it is interpreted as driven by the l = m = 2 f-mode, implies a radial amplitude at the 1 bar level of ∼ 50 cm, according to the models of Marley and Porco (Marley, M.S., Porco, C.C. [1993]. Icarus 106, 508).

The distribution of particle sizes in Saturn's rings roughly follows a truncated inverse power-law. Though it is well known that differential optical depths provide a way to probe the parameters of size distribution (i.e. Zebker et al. [1985] Icarus, 64, 531–548), the technique is complicated by the presence of self-gravity wakes which introduce a geometric dependence to the observed optical depth. Here we present a method of extracting information about the size distribution of the particles in the gaps between the self-gravity wakes. The Cassini Visual and Infrared Mapping Spectrometer (VIMS) occultations measure starlight at an effective wavelength of 2.9 µm falling onto a single pixel with angular dimensions 0.25 mrad × 0.5 mrad while Cassini Ultraviolet Imaging Spectrograph (UVIS) occultations measure starlight at a much smaller effective wavelength of 0.15 µm and over a field of view with larger angular dimensions of 6.0 mrad × 6.4 mrad. Starlight diffracted out of the VIMS pixel by particles smaller than 1.22 λ VIMS /2 θ ∼8.86 mm, is not replaced by neighboring particles, while the UVIS instrument, with its larger field of view and smaller effective wavelength, collects all of the light diffracted by particles larger than 1.22 λ VIMS /2 θ ∼0.025 mm. Consequently, measurements by VIMS overstate the optical depth in regions where sub-centimeter-sized particles are present. Using the rectangular cross section wake model of ( Colwell et al. [2006 ], Geophys. Res. Lett., 33, L07201) and (Colwell et al. [2007] Icarus, 190, 127–144) with a new parameter to represent the excess VIMS optical depth not seen by UVIS, we combine VIMS and UVIS occultations for the first time for particle size analysis. We find a significant fraction of sub-cm particles only in the outermost portion of the A ring, and in the B1 region of the B ring. In the Trans-Encke region, we find a trend of increasing abundance of sub-cm particles as the outer edge of the A Ring is approached, consistent with previous differential optical depth studies at radio wavelengths ( Zebker et al. [1985 ] Icarus, 64, 531–548), measurements of diffraction in stellar occultations at the ring edges ( Becker et al. [2015 ] Icarus), and measurements from VIMS solar occultations ( Harbison et al. [2013 ] Icarus, 226, 1225-1240). This may be due to greater erosion of weakly bound particle aggregates by interparticle collisions in regions where satellite perturbations are strong.

Stellar occultation data from Cassini’s Ultraviolet Imaging Spectrograph (UVIS) have revealed diffraction spikes near sharp edges in Saturn’s rings. The UVIS High Speed Photometer (HSP) observes these spikes as signals at ring edges that surpass measurements of the unocculted stellar signal. In Saturn’s A ring, diffracted light can augment the direct stellar signal by up to 6% and can be detected tens of kilometers radially from the edge. The radial profile of the diffraction signal is dependent on the size distribution of the particle population near the ring edge. These diffraction signals are clearly observed at sharp edges throughout Saturn’s ring system. In this paper we focus on the clearest detections at the outer edge of the A ring and at the edges of the Encke Gap. We present a forward model in which we reconstruct the spacecraft’s observations for each stellar occultation by ring edges. The model produces a synthetic diffraction signal for a given truncated power-law particle size distribution, which we compare with the observed signal. We find an overall steepening of the power-law size distribution and a decrease in the minimum particle size at the outer edge of the A ring when compared with the Encke Gap edges. This suggests that interparticle collisions caused by satellite perturbations in the region result in more shedding of regolith or fragmentation of particles in the outermost parts of the A ring. We rule out any significant population of sub-millimeter-sized particles in Saturn’s A ring, placing a lower limitation of 1-mm on the minimum particle size in the ring.

We have conducted a comprehensive survey of 22 sharp-edged ringlets and gaps in the Cassini Division of Saturn’s rings, making use of nearly 200 high-SNR stellar and radio occultation chords obtained by the Cassini VIMS, UVIS, and RSS instruments between 2005 and 2013. We measure eccentricities from as small as a e = 80 m to nearly 30 km, free normal modes with amplitudes from ∼ 0.1 to 4.1 km, and detectable inclinations as small as a sin i = 0.2 km. Throughout the entire region, the Mimas 2.1 ILR (inner Lindblad resonance) produces systematic forced m = 2 distortions that quantitatively match the expected amplitudes, phases, and pattern speed. The narrow Russell, Jeffreys, Kuiper, Bessel, and Barnard gaps are simplest, and do not contain dense ringlets. Their outer edges are generally quite sharp and four of them are circular to within ∼0.25 km, whereas most of the inner gap edges have significant eccentricities. Three gaps are more complex, containing one or more isolated ringlets. First among these is the 361 km-wide Huygens gap, containing two ringlets. The wider Huygens ringlet has nearly identical eccentricities on the two edges, in addition to OLR-type (outer Lindblad resonance) normal modes on the inner edge and ILR-type modes on the outer edge. A secondary m = 1 (eccentric) mode is present on the outer edge of the ringlet, with a pattern speed similar to that of the B ring’s outer edge. Variations in the ringlet’s width are complex, but are statistically consistent with the expected magnitudes resulting from the random superposition of the multiple normal modes on the two edges. Also present in the Huygens gap is the very narrow so-called Strange ringlet, with a substantial eccentricity and inclination, as well as both ILR- and OLR-type normal modes. The 100 km-wide Herschel gap’s inner edge is highly eccentric, with at least seven ILR-type normal modes. The outer gap edge is also eccentric, and hosts four OLR-type normal modes, and a secondary m = 1 mode with a pattern speed quite close to that of the B ring’s outer edge. The Herschel ringlet itself is eccentric and inclined, but neither the pericenters nor the nodes are well-aligned. The third of the complex gaps is the 241 km-wide Laplace gap, containing the Laplace ringlet. Both gap edges are eccentric, with very similar pericenter longitudes and apsidal precession rates, in spite of their large radial separation. The Laplace ringlet has eccentric edges and an abundance of normal modes. Like the Herschel ringlet, the Laplace ringlet does not precess rigidly and does not conform to the usual dynamical picture of an eccentric ringlet. Normal modes are abundant in the Cassini Division. Consistently, we find free ILR-type normal modes (m > 0) at the outer edges of ringlets and the inner edges of gaps, and free OLR-type normal modes (m ≤ 0) at inner ringlet edges and outer edges of gaps, as expected from the resonant cavity model of normal modes. We estimate the surface density of ring features from the resonance locations of the normal modes. The Cassini Division exhibits apsidal precession rates that are anomalously large, compared to the predicted values based on Saturn’s zonal gravity field. The overall radial trend matches the secular contribution expected from the nearby B ring, assuming a surface mass density of Σ = 100 gm cm − 2 . However, the outer edges of the Huygens and Laplace gaps, and the outer edge of the Laplace ringlet, have conspicuously large residuals, exceeding their predicted precession rates by more than 0 . 03 ∘ d − 1 . These patterns are probably the result of forcing by nearby ring material, but at present we cannot account for them in detail.

The Ultraviolet Imaging Spectrograph (UVIS) on the Cassini spacecraft observed 275 ring stellar occultations from July 2004 until August 2017. We use stellar occultation data from the UVIS High Speed Photometer (HSP) to characterize the smallest particles at ring edges by modeling observed diffraction signatures. We identify these signatures as spikes in the signal caused by particles near the ring edge diffracting light into the detector and increasing the signal above that of the star alone. The shape and amplitude of the diffraction signature depend on the size and abundance of the smallest particles and are therefore indicative of the lower limits of the particle size distribution at the edge. We analyze the outer edge of the A ring and B ring and the edges of the Encke Gap, Keeler Gap, the so-called “Strange” ringlet (R6), Huygens ringlet and Titan ringlet. Other edges do not have sufficient contrast and sharp enough edges for this analysis at UVIS wavelengths. We find minimum particle sizes ranging from 4.5 mm to 66 mm and average power law indices ranging from 3.0–3.2. Overall, we find that the edges of the narrow ringlets in the Cassini Division and C ring exhibit fewer diffraction signatures than the outer A ring region. Our results, in conjunction with previous results by Becker et al. (2016), indicate that edges directly perturbed by satellite resonances show a greater population of sub-cm particles than the sharp edges of ringlets that are confined by other mechanisms. Our results are similarly consistent with Esposito et al. (2012), who propose that regions perturbed by satellite resonances can be explained by a predator-prey model of aggregation and fragmentation. Large aggregates may form at these strong resonant locations that may in turn accelerate the ring particles and lead to more disruptive collisions producing a population of smaller particles that result in the diffraction signatures analyzed here. This is in agreement with Bodrova et al. (2012) who find that the mean ring particle radius decreases as relative collision velocity increases.

The surfaces of many planetary bodies, including asteroids, moons, and planets, are composed of rubble-like grains held together by varying levels of gravitational attraction and cohesive forces. Future instrumentation for operation on, and interacting with, such surfaces will require efficient and effective design principles and methods of testing. Here we present results from the EMPANADA experiment (Ejecta-Minimizing Protocols for Applications Needing Anchoring or Digging on Asteroids) which flew on several reduced gravity parabolic flights. EMPANADA studies the effects of the insertion of a flexible probe into a granular medium as a function of ambient gravity. This is done for an idealized 2D system as well as a more realistic 3D sample. To quantify the dynamics inside the 2D granular material we employ photoelasticity to identify the grain-scale forces throughout the system, while in 3D experiments we use simulated regolith. Experiments were conducted at three different levels of gravity: martian, lunar, and microgravity. In this work, we demonstrate that the photoelastic technique provides results that complement traditional load cell measurements in the 2D sample, and show that the idealized system exhibits similar behaviour to the more realistic 3D sample. We note that the presence of discrete, stick-slip failure events depends on the gravitational acceleration.

Saturn's C ring and Cassini Division share many morphological traits: both contain numerous opaque, sharp–edged ringlets and gaps, broader low optical depth “background” regions, larger-optical depth regions that rise abruptly from the background (known as the C ring's plateaus and the Cassini Division's triple band feature), and linear ramps in optical depth up to the abrupt inner edges of the B ring and A ring, respectively. Throughout the majority of both regions, the surface mass density of the rings is small enough that the Toomre critical wavelength (most unstable wavelength for gravitational collapse) is comparable in size to, or smaller than, the largest individual ring particles. Thus, self-gravity wakes do not form in these regions, unlike the A and B rings where the critical wavelength is tens of meters and the self-gravity wakes introduce strong dependence of the observed optical depth on viewing geometry. In the absence of self-gravity wakes, we model the ring particle size distribution with a simple power-law, where the number of particles per unit area of the rings in the size range [a, a + da] is given by n(a)da = Ca-qda between amin and amax. We fit normal optical depths derived from the power-law size distribution parameters and the thin-layers ring model of Zebker et al. (1985) to the wavelength-dependent optical depth profiles obtained by 3 Cassini Instruments: UVIS at λ = 0.15 μm, VIMS at λ = 2.9 μm, and RSS Ka-band (λ = 9.4 mm), X-band at (λ = 3.4 cm), and S-band (λ = 13.0 cm). We find that the C ring is best characterized by five or more thin layers of particles with a mean power-law index of q ~ 3.16 in the C ring background and q ~ 3.05 in the C ring plateaus, in the rings. We find a minimum particle radius of amin ~ 4.1 mm in the background C ring and plateaus and amin ~ 6 mm in the plateaus. The cross-section-weighted effective particle radius determined using the excess variance of UVIS signal beyond Poisson counting statistics by Colwell et al. (2018) constrains the size of the largest particles in the rings. We find the largest particles contributing to the power-law size distribution, and thus to the optical depth, are amax ~ 10–15 m in the background C ring and amax ~ 5–6 m in the C ring plateaus. This substantial difference in the sizes of the largest ring particles together with the overall shallower power law index in the plateaus explains their optical depth difference relative to the background C ring. Additionally, Baillie et al. (2013) used UVIS stellar occultations to find a distribution of small-scale, low optical depth gaps in the plateaus. These regions, with radial widths of We constrain the particle densities by dividing the surface mass densities determined from the dispersion of spiral density waves by the total particle volume integrated over a square meter of the ring slab. We derive low bulk particle densities of ρ ~ 0.1–0.3 g/cm3 except in the central background C ring where we find ρ ~ 0.9 g/cm3. These low derived densities may be due to inter-particle spaces within 1–20 m particle aggregates that contribute to the measured optical depth and thus to the upper end of the size distribution. Our results are consistent with Zhang et al. (2017) who reported particles with porosities >75% made of water ice with up to 11% silicate contaminate in the central background C ring.

One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. (1982, 1989) show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. (1989) model using a granular flow model to define the shear and bulk viscosities and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings (Gr\"atz et al. 2018). Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps.

Cassini's last look at Saturn's rings During the final stages of the Cassini mission, the spacecraft flew between the planet and its rings, providing a new view on this spectacular system (see the Perspective by Ida). Setting the scene, Spilker reviews the numerous discoveries made using Cassini during the 13 years it spent orbiting Saturn. Iess et al. measured the gravitational pull on Cassini, separating the contributions from the planet and the rings. This allowed them to determine the interior structure of Saturn and the mass of its rings. Buratti et al. present observations of five small moons located in and around the rings. The moons each have distinctive shapes and compositions, owing to accretion of ring material. Tiscareno et al. observed the rings directly at close range, finding complex features sculpted by the gravitational interactions between moons and ring particles. Together, these results show that Saturn's rings are substantially younger than the planet itself and constrain models of their origin. Science , this issue p. 1046 , p. eaat2965 , p. eaat2349 , p. eaau1017 ; see also p. 1028

We present a comprehensive survey of sharp-edged features in Saturn’s C ring, using data from radio and stellar occultation experiments carried out by the Cassini spacecraft over a period of more than five years. Over 100 occultations are included in the combined data set, enabling us to identify systematic radial perturbations as small as 200 m on the edges of ringlets and gaps. We systematically examine all of the noncircular features in the C ring, refine the eccentricities, precession rates and width variations of the known eccentric ringlets, identify connections between several noncircular gap and ringlet edges and nearby satellite resonances, and report the discovery of a host of free normal modes on ring and gap edges. We confirm a close association between the Titan (or Colombo) ringlet (a = 77878.7 km) and the Titan 1:0 apsidal resonance: the apoapse of the ringlet is nearly aligned with Titan’s mean longitude, and the pattern speed closely matches Titan’s mean motion. Similar forced perturbations associated with the Titan resonance are detectable in more than two dozen other features located throughout the inner C ring as far as 3500 km from the Titan resonance. The inner edge of the Titan ringlet exhibits several strong outer Lindblad resonance (OLR-type) normal modes, and scans of the outer edge reveal inner Lindblad resonance (ILR-type) normal modes. The Maxwell ringlet (a = 87,510 km), in contrast, appears to be a freely-precessing eccentric ringlet, with post-fit RMS residuals for the inner and outer edges of only 0.23 and 0.16 km, respectively. The best-fitting edge precession rates differ by over 10 times the estimated uncertainty in the rate of the inner edge, consistent with a slow libration about an equilibrium configuration on a decadal timescale. Using self-gravity models for ringlet apse alignment, we estimate the masses and surface densities of the Titan and Maxwell ringlets. The Bond ringlet (a = 88,710 km), about 17 km wide, shows no free eccentricity but lies near two strong resonances: the Mimas 3:1 inner vertical resonance (IVR) at 88702.2 km and the Prometheus 2:1 ILR at 88713.1 km. We find no measurable perturbation from the Mimas IVR, but a clear m = 2 signature of the appropriate phase and pattern speed for the Prometheus ILR on the outer edge of the ringlet, along with free ILR-type normal modes with wave numbers m = 3 ,4, 5, 6 and 7. The Dawes gap, located at 90,210 km, and its associated embedded ringlet, also show both free and forced perturbations, and as in the case of the Maxwell gap, the outer edge of the Dawes gap appears to be sympathetically forced by the nearby ringlet. The pattern of newly identified normal modes coexisting on the sharp edges of ringlets and gaps is in excellent agreement with theoretical predictions, with ILR-type modes on outer ringlet (and inner gap) edges and OLR-type modes on inner ringlet (and outer gap) edges, representing standing waves between the resonance locations and the ring edges. Modes with larger | m | generally have narrower resonant cavities, and of the dozens of detected normal modes, none has been identified with a resonance radius that falls outside the ring material.

The long-term stability of the narrow F Ring core has been hard to understand. Instead of acting as "shepherds", Prometheus and Pandora together stir the vast preponderance of the region into a chaotic state, consistent with the orbits of newly discovered objects like S/2004S6. We show how a comb of very narrow radial locations of high stability in semimajor axis is embedded within this otherwise chaotic region. The stability of these semimajor axes relies fundamentally on the unusual combination of rapid apse precession and long synodic period which characterizes the region. This situation allows stable "antiresonances" to fall on or very close to traditional Lindblad resonances which, under more common circumstances, are destabilizing. We present numerical integrations of tens of thousands of test particles over tens of thousands of Prometheus orbits that map out the effect. The stable antiresonance zones are most stable in a subset of the region where Prometheus first-order resonances are least cluttered by Pandora resonances. This region of optimum stability is paradoxically closer to Prometheus than a location more representative of "torque balance", helping explain a longstanding paradox. One stable zone corresponds closely to the currently observed semimajor axis of the F Ring core. While the model helps explain the stability of the narrow F Ring core, it does not explain why the F Ring material all shares a common apse longitude; we speculate that collisional damping at the preferred semimajor axis (not included in the current simulations) may provide that final step. Essentially, we find that the F Ring core is not confined by a combination of Prometheus and Pandora, but a combination of Prometheus and precession.

The current model of planet formation lacks a good understanding of the growth of dust particles inside the protoplanetary disk beyond mm sizes. In order to investigate the low-velocity collisions between this type of particles, the NanoRocks experiment was flown on the International Space Station (ISS) between September 2014 and March 2016. We present the results of this experiment. We quantify the damping of energy in systems of multiple particles in the 0.1 to 1 mm size range while they are in the bouncing regime, and study the formation of clusters through sticking collisions between particles. We developed statistical methods for the analysis of the large quantity of collision data collected by the experiment. We measured the average motion of particles, the moment of clustering, and the cluster size formed. In addition, we ran simple numerical simulations in order to validate our measurements. We computed the average coefficient of restitution (COR) of collisions and find values ranging from 0.55 for systems including a population of fine grains to 0.94 for systems of denser particles. We also measured the sticking threshold velocities and find values around 1 cm/s, consistent with the current dust collision models based on independently collected experimental data. Our findings have the following implications that can be useful for the simulation of particles in PPDs and planetary rings: (1) The average COR of collisions between same-sized free-floating particles at low speeds (< 2 cm/s) is not dependent on the collision velocity; (2) The simplified approach of using a constant COR value will accurately reproduce the average behavior of a particle system during collisional cooling; (3) At speeds below 5 mm/s, the influence of particle rotation becomes apparent on the collision behavior; (4) Current dust collision models predicting sticking thresholds are robust., 15 pages, 14 figures

A comprehensive investigation of all available radio and stellar occultation data for the outer edge of Saturn’s B ring, spanning the period 1980–2010, confirms that the m = 2 distortion due to the strong Mimas 2:1 inner Lindblad resonance circulates slowly relative to Mimas in a prograde direction, with a frequency Ω L = 0.1819° d −1 . Our best-fitting model implies that the radial amplitude of this distortion ranges from a minimum of 3 km to a maximum of 71 km, with short-lived minima recurring every 5.42 yrs. In addition to the dominant m = 2 pattern, the edge of the B ring also exhibits at least four other perturbations. An m = 1 component with a radial amplitude of ∼20 km rotates at a rate very close to the expected local apsidal precession rate of ϖ B ∼ 5.059 ° d −1 , while smaller perturbations are seen with m = 3 (amplitude 12.5 km), m = 4 (5.9 km), and m = 5 (5.6 km), each of which has a pattern speed consistent with that expected for a spontaneously-generated “normal mode” (French, R.G. et al. [1988]. Icarus 73, 349–378). Our results for m = 1, m = 2 and m = 3 are compatible with those obtained by Spitale and Porco (Spitale, J.N., Porco, C.C. [2010]. Astron. J. 140, 1747–1757), which were based on Cassini imaging data. The pattern speed of each normal mode slightly exceeds that expected at the mean edge radius, supporting their conclusion that they may represent a series of free modes, each of which is trapped in a narrow region between the mode’s resonant radius and the ring’s edge. However, both our model and that of Spitale and Porco fail to provide complete descriptions of this surprisingly complex feature, with post-fit root-mean-square residuals of ∼8 km considerably exceeding typical measurement errors of 1 km or less.

We use Cassini UVIS data to determine the scattering properties of Saturn’s ring particles in the FUV. We have replaced the scattering function from the classical Chandrasekhar single scattering radiative transfer equation for reflectance with a ring wake model for the A and B rings derived from stellar occultations. The free parameters in this model are the ring particle Bond albedo, AB, and the ring particle asymmetry parameter, g, which equals the cosine of the most probable scattering angle of a photon from a ring particle. The spectrum of Saturn’s rings from 140 to 190 nm shows an absorption feature due to water ice shortward of 165 nm. We compare our model values for I/F to lit-side data at 155 nm and at 180 nm for regions in both the A and B rings. We used the unmodified Chandrasekhar model for the C ring and Cassini Division, and in all cases we determined AB and g in the FUV for the first time. Values of AB vary between 0.04 and 0.091 at 180 nm and between 0.012 and 0.019 at 155 nm. The variations across the ring of AB at 180 nm is consistent with a greater abundance of non-ice contaminant in the C ring and Cassini Division and a minimum in contaminant abundance in the outer B ring. There is little variation in AB at 155 nm across the rings, which suggests that the reflectance of the water ice and non-water ice material shortward of the 165 nm absorption edge are about the same. Values of g vary between −0.68 and −0.78 at 180 nm and between −0.63 and −0.77 at 155 nm showing that the ring particles are highly backscattering in the FUV. We find that the wavelength of the absorption feature varies with ring region and viewing geometry indicating a different photon mean path length, L, through the outer layer of the ring particle (Bradley, E.T., Colwell, J.E., Esposito, L.W., Cuzzi, J.N., Tollerud, H., Chambers, L. [2010]. Icarus 206 (2), 458–466). We compared I/F from 152 to 185 nm to a radiative transfer spectral model developed by Shkuratov et al. (Shkuratov, Y., Starukhina, L., Hoffmann, H., Arnold, G. [1999]. Icarus 137, 235–246) and modified by Poulet et al. (Poulet, F., Cuzzi, J.N., Cruikshank, D.P., Roush, T., Dalle Ore, C.M. [2002]. Icarus 160, 313–324). We find that L is positively correlated with phase angle, which we attribute to multiple scattering within the particle on length scales comparable to L. We extrapolate L to zero phase angle and find values of L at zero phase ranging from ∼2 to 3 μm. This provides a direct measure of the distance from the surface of a ring particle to the first scattering center. L at zero phase is roughly constant across the rings suggesting the outermost 1.25 μm of the ring particles have the same structural properties in all ring regions. We azimuthally binned and interpolated observations of the unlit side of the A ring taken during Saturn orbit insertion to a 100 km resolution radial profile. We see halos (enhanced brightness) surrounding the Janus 4:3 and Janus 5:4 density waves. We also computed I/F across the A ring using the SOI observational geometry along with AB and the power-law index, n, derived from the retrieval approach from lit side observations. I/F determined by this technique agrees with results from the lit side analysis for the A2 ring but diverge for the inner and outer A ring, which we attribute to multiple scattering effects.

UVIS occultation data show clumping in Saturn’s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200–2000 m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator–prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the “boom-bust” economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings… including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring).

We performed a complete wavelet analysis of Saturn’s C ring on 62 stellar occultation profiles. These profiles were obtained by Cassini’s Ultraviolet Imaging Spectrograph High Speed Photometer. We used a WWZ wavelet power transform to analyze them. With a co-adding process, we found evidence of 40 wavelike structures, 18 of which are reported here for the first time. Seventeen of these appear to be propagating waves (wavelength changing systematically with distance from Saturn). The longest new wavetrain in the C ring is a 52-km-long wave in a plateau at 86,397 km. We produced a complete map of resonances with external satellites and possible structures rotating with Saturn’s rotation period up to the eighth order, allowing us to associate a previously observed wave with the Atlas 2:1 inner Lindblad resonance (ILR) and newly detected waves with the Mimas 6:2 ILR and the Pandora 4:2 ILR. We derived surface mass densities and mass extinction coefficients, finding σ = 0.22(±0.03) g cm −2 for the Atlas 2:1 ILR, σ = 1.31(±0.20) g cm −2 for the Mimas 6:2 ILR, and σ = 1.42(±0.21) g cm −2 for the Pandora 4:2 ILR. We determined a range of mass extinction coefficients ( κ = τ / σ ) for the waves associated with resonances with κ = 0.13 (±0.03) to 0.28(±0.06) cm 2 g −1 , where τ is the optical depth. These values are higher than the reported values for the A ring (0.01–0.02 cm 2 g −1 ) and the Cassini Division (0.07–0.12 cm 2 g −1 from Colwell et al. (Colwell, J.E., Cooney, J.H., Esposito, L.W., Sremcevic, M. [2009]. Icarus 200, 574–580)). We also note that the mass extinction coefficient is probably not constant across the C ring (in contrast to the A ring and the Cassini Division): it is systematically higher in the plateaus than elsewhere, suggesting smaller particles in the plateaus. We present the results of our analysis of these waves in the C ring and estimate the mass of the C ring to be between3.7(±0.9) × 10 16 kg and 7.9(±2.0) × 10 16 kg (equivalent to an icy satellite of radius between 28.0(±2.3) km and 36.2(±3.0) km with a density of 400 kg m −3 , close to that of Pan or Atlas). Using the ring viscosity derived from the wave damping length, we also estimate the vertical thickness of the C ring between 1.9(±0.4) m and 5.6(±1.4) m, comparable to the vertical thickness of the Cassini Division.

We present a forward modeling approach for determining, in part, the ring particle spatial distribution in the vicinity of sharp ring or ringlet edges. Synthetic edge occultation profiles are computed based on a two-parameter particle spatial distribution model. One parameter, h , characterizes the vertical extent of the ring and the other, δ , characterizes the radial scale over which the ring optical depth transitions from the background ring value to zero. We compare our synthetic occultation profiles to high resolution stellar occultation light curves observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) for occultations by the Titan ringlet and Huygens ringlet edges. More than 100 stellar occultations of the Huygens ringlet and Titan ringlet edges were studied, comprising 343 independent occultation cuts of the edges of these two ringlets. In 237 of these profiles the measured light-curve was fit well with our two-parameter edge model. Of the remaining edge occultations, 69 contained structure that could only be fit with extremely large values of the ring-plane vertical thickness ( h > 1 km) or by adopting a different model for the radial profile of the ring optical depth. An additional 37 could not be fit by our two-parameter model. Certain occultations at low ring-plane incidence angles as well as occultations nearly tangent to the ring edge allow the direct measurement of the radial scale over which the particle packing varies at the edge of the ringlet. In 24 occultations with these particular viewing geometries, we find a wide variation in the radial scale of the edge. We are able to constrain the vertical extent of the rings at the edge to less than ∼300 m in the 70% of the occultations with appropriate viewing geometry, however tighter constraints could not be placed on h due to the weaker sensitivity of the occultation profile to vertical thickness compared to its sensitivity to δ . Many occultations of a single edge could not be fit to a single value of δ , indicating large temporal or azimuthal variability, although the azimuthal variation in δ with respect to the longitudes of various moons in the system did not show any discernible pattern.

The Cassini spacecraft's Ultraviolet Imaging Spectrograph (UVIS) includes a high-speed photometer (HSP) that has observed more than 100 stellar occultations by Saturn's rings. Here, we document a standardized technique applied to the UVIS-HSP ring occultation datasets delivered to the Planetary Data System as higher level data products. These observations provide measurements of ring structure that approaches the scale of the largest common ring particles (~5 m). The combination of multiple occultations at different viewing geometries enables reconstruction of the three-dimensional structure of the rings. This inversion of the occultation data depends on accurate calibration of the data so that occultations of different stars taken at different times and under different viewing conditions can be combined to retrieve ring structure. We provide examples of the structure of the rings as seen from several occultations at different incidence angles to the rings, illustrating changes in the apparent structure with viewing geometry.

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.

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., Sremcevic, 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 σ = 42 – 54 g cm - 2 , which corresponds to a mass of 0.5 × 10 19 kg – 0.7 × 10 19 kg . We infer a minimum surface density of σ = 240 – 480 g cm - 2 for Saturn’s B ring, which corresponds to a minimum mass estimate of 4 × 10 19 kg – 7 × 10 19 kg . 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.

We analyze density waves in the Cassini Division of Saturn's rings revealed by multiple stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph. The dispersion and damping of density waves provide information on the local ring surface mass density and viscosity. Several waves in the Cassini Division are on gradients in the background optical depth, and we find that the dispersion of the wave reflects a change in the underlying surface mass density. We find that over most of the Cassini Division the ring opacity (the ratio of optical depth to surface mass density) is nearly constant and is ∼5 times higher than the opacity in the A ring where most density waves are found. However, the Cassini Division ramp, a 1100-km-wide, nearly featureless region of low optical depth that connects the Cassini Division to the inner edge of the A ring, has an opacity like that of the A ring and significantly less than that in the rest of the Cassini Division. This is consistent with particles in the ramp originating in the A ring and being transported into the Cassini Division through ballistic transport processes. Damping of the waves in the Cassini Division suggests a vertical thickness of 3–6 m. Using a mean opacity of 0.1 cm2/g we find the mass of the Cassini Division, excluding the ramp, is 3.1 × 10 16 kg while the mass of the Cassini Division ramp, with an opacity of 0.015 cm2/g, is 1.1 × 10 17 kg . Assuming a power-law size distribution for the ring particles, the larger opacity of the main Cassini Division is consistent with the largest ring particles there being ∼5 times smaller than the largest particles in the ramp and A ring.

Heliospheric neutral hydrogen scatters solar Lyman-alpha radiation from the Sun with '27-day' intensity modulations observed near Earth due to the Sun's rotation combined with Earth's orbital motion. These modulations are increasingly damped in amplitude at larger distances from the Sun due to multiple scattering in the heliosphere, providing a diagnostic of the interplanetary neutral hydrogen density independent of instrument calibration. This paper presents Cassini data from 2003-2004 obtained downwind near Saturn at approximately 10 AU that at times show undamped '27-day' waves in good agreement with the single-scattering models of Pryor et al., 1992. Simultaneous Voyager 1 data from 2003- 2004 obtained upwind at a distance of 88.8-92.6 AU from the Sun show waves damped by a factor of -0.21. The observed degree of damping is interpreted in terms of Monte Carlo multiple-scattering calculations (e.g., Keller et al., 1981) applied to two heliospheric hydrogen two-shock density distributions (discussed in Gangopadhyay et al., 2006) calculated in the frame of the Baranov-Malama model of the solar wind interaction with the two-component (neutral hydrogen and plasma) interstellar wind (Baranov and Malama 1993, Izmodenov et al., 2001, Baranov and Izmodenov, 2006). We conclude that multiple scattering is definitely occurring in the outer heliosphere. Both models compare favorably to the data, using heliospheric neutral H densities at the termination shock of 0.085 cm(exp -3) and 0.095 cm(exp -3). This work generally agrees with earlier discussions of Voyager data in Quemerais et al., 1996 showing the importance of multiple scattering but is based on Voyager data obtained at larger distances from the Sun (with larger damping) simultaneously with Cassini data obtained closer to the Sun.

Collisions between planetary ring particles and in some protoplanetary disk environments occur at speeds below 10 m/s. The particles involved in these low-velocity collisions have negligible gravity and may be made of or coated with smaller dust grains and aggregates. We undertook microgravity impact experiments to better understand the dissipation of energy and production of ejecta in these collisions. Here we report the results of impact experiments of solid projectiles into beds of granular material at impact velocities from 0.2 to 2.3 m/s performed under near-weightless conditions on the NASA KC-135 Weightless Wonder V. Impactors of various densities and radii of 1 and 2 cm were launched into targets of quartz sand, JSC-1 lunar regolith simulant, and JSC-Mars-1 martian regolith simulant. Most impacts were at normal or near-normal incidence angles, though some impacts were at oblique angles. Oblique impacts led to much higher ejection velocities and ejecta masses than normal impacts. For normal incidence impacts, characteristic ejecta velocities increase with impactor kinetic energy, KE, as approximately KE0.5. Ejecta masses could not be measured accurately due to the nature of the experiment, but qualitatively also increased with impactor kinetic energy. Some experiments were near the threshold velocity of 0.2 m/s identified in previous microgravity impact experiments as the minimum velocity needed to produce ejecta [Colwell, J.E., 2003. Icarus 164, 188–196], and the experimental scatter is large at these low speeds in the airplane experiment. A more precise exploration of the transition from low-ejecta-mass impacts to high-ejecta-mass impacts requires a longer and smoother period of reduced gravity. Coefficient of restitution measurements are not possible due to the varying acceleration of the airplane throughout the experiment.

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.

We analyze stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph and find large variations in the apparent normal optical depth of the B ring with viewing angle. The line-of-sight optical depth is roughly independent of the viewing angle out of the ring plane so that optical depth is independent of the path length of the line-of-sight. This suggests the ring is composed of virtually opaque clumps separated by nearly transparent gaps, with the relative abundance of clumps and gaps controlling the observed optical depth. The observations can be explained with a model of self-gravity wakes like those observed in the A ring. These trailing spiral density enhancements are due to the competing processes of self-gravitational accretion of ring particles and Kepler shear. The B ring wakes are flatter and more closely packed than their neighbors in the A ring, with height-to-width ratios ∼ 10 m ) scan of one part of the B ring during a grazing occultation shows a dominant wavelength of 160 m due to structures that have zero cant angle. These structures are seen at the same radial wavelength on both ingress and egress, but the individual peaks and troughs in optical depth do not match between ingress and egress. The structures are therefore not continuous ringlets and may be a manifestation of viscous overstability.

Experimental investigations are reported on the charging of dust particles resting on conducting and insulating surfaces beneath plasma. The experiment is configured to give insight into the behavior of dust on planetary surfaces exposed to solar wind plasma. In the experiments, the surfaces are agitated so that the particles drop through a small hole into a Faraday cup that measures the charge on each dust particle. Both conducting (Ni) and insulating dusts (SiO2, Al2 O3 and JSC-1 lunar regolith simulant) are investigated. The conducting surface is given a bias voltage above the floating potential to create conditions in which the electron flux is dominant or a bias voltage below the floating potential for which the ion flux is dominant. The dust charges more positively in ion-flux-dominant conditions and more negatively in electron-flux-dominant conditions. The insulating dusts retain the charge for a long period of time ( > 1 h) after the plasma is turned off. The charge decays more quickly if the surface is agitated, causing the dust to roll around, or if there is ultraviolet illumination. The conducting dust often has a lower level of charge than the insulating dust because the charge is conducted from the dust particle into the conducting surface. Conducting and insulating dusts on an insulating surface have approximately the same level of charge

We have performed detailed dynamical modeling of the structure of a faint dust band observed in coadded IRAS data at an ecliptic latitude of 17$^{\circ}$ that convincingly demonstrates that it is the result of a relatively recent (significantly less than 1 Ma) disruption of an asteroid and is still in the process of forming. We show here that young dust bands retain information on the size distribution and cross-sectional area of dust released in the original asteroid disruption, before it is lost to orbital and collisional decay. We find that the Emilkowalski cluster is the source of this partial band and that the dust released in the disruption would correspond to a regolith layer $\sim$3 m deep on the $\sim$10 km diameter source body's surface. The dust in this band is described by a cumulative size-distribution inverse power-law index with a lower bound of 2.1 (implying domination of cross-sectional area by small particles) for dust particles with diameters ranging from a few $\mu$m up to a few cm. The coadded observations show that the thermal emission of the dust band structure is dominated by large (mm--cm size) particles. We find that dust particle ejection velocities need to be a few times the escape velocity of the Emilkowalski cluster source body to provide a good fit to the inclination dispersion of the observations. We discuss the implications that such a significant release of material during a disruption has for the temporal evolution of the structure, composition, and magnitude of the zodiacal cloud., Comment: Published by ApJ, 16 pages, 14 figures

The Planetary Atmospheres Minor Species Sensor (PAMSS) is an intracavity laser absorption spectrometer that uses a mid-infrared quantum cascade laser in an open external cavity for sensing ultra-trace gases with parts-per-billion sensitivity. PAMSS was flown on a balloon by Near Space Corporation from Madras OR to 30 km on 17 July 2014. Based on lessons learned, it was modified and was flown a second time to 32 km by World View Enterprises from Pinal AirPark AZ on 8 March 2015. Successes included continuous operation and survival of software, electronics, optics, and optical alignment during extreme conditions and a rough landing. Operation of PAMSS in the relevant environment of near space has significantly elevated its Technical Readiness Level for trace-gas sensing with potential for planetary and atmospheric science in harsh environments.

The Cassini spacecraft Ultraviolet Imaging Spectrograph (UVIS) obtained observations of Jupiter's auroral emissions in H-2 band systems and H Lyman-alpha from day 275 of 2000 (October 1), to day 81 of 2001 (March 22). Much of the globally integrated auroral variability measured with UVIS can be explained simply in terms of the rotation of Jupiter's main auroral arcs with the planet. These arcs were also imaged by the Space Telescope Imaging Spectrograph (STIS) on Hubble Space Telescope (HST). However, several brightening events were seen by UVIS in which the global auroral output increased by a factor of 2-4. These events persisted over a number of hours and in one case can clearly be tied to a large solar coronal mass ejection event. The auroral UV emissions from these bursts also correspond to hectometric radio emission (0.5-16 MHz) increases reported by the Galileo Plasma Wave Spectrometer (PWS) and Cassim Radio and Plasma Wave Spectrometer (RPWS) experiments. In general, the hectometric radio data vary differently with longitude than the UV data because of radio wave beaming effects. The 2 largest events in the UVIS data were on 2000 day 280 (October 6) and on 2000 days 325-326 (November 20-21). The global brightening events on November 20-21 are compared with corresponding data on the interplanetary magnetic field, solar wind conditions, and energetic particle environment. ACE (Advanced Composition Explorer) solar wind data was numerically propagated from the Earth to Jupiter with an MHD code and compared to the observed event. A second class of brief auroral brightening events seen in HST (and probably UVIS) data that last for similar to 2 min is associated with aurora] flares inside the main auroral ovals. On January 8, 2001, from 18:45-19:35 UT UVIS H-2 band emissions from the north polar region varied quasiperiodically. The varying emissions, probably due to amoral flares inside the main auroral oval, are correlated with low-frequency quasiperiodic radio bursts in the 0.6-5 kHz Galileo PWS data. (c) 2005 Elsevier Inc. All rights reserved.

We investigate the electrostatic transport of charged dust in the photoelectron layer over the dayside surface of an asteroid. Micron-sized dust particles may be levitated above the surface in the photoelectron layer. Horizontal transport within the layer can then lead to net deposition of dust into shadowed regions where the electric field due to the photoelectron layer disappears. We apply a 2D numerical model simulating charged dust dynamics in the near-surface daytime plasma environment of Asteroid 433 Eros to the formation of dust deposits in craters. We find that dust tends to collect in craters and regions of shadow. This electrostatic dust transport mechanism may contribute to the formation of smooth dust ponds observed by the NEAR-Shoemaker spacecraft at Eros. The size distribution of transported dust depends on the particle density and work function, and the work function of the surface and solar wind electron temperature and density. With reasonable values for these parameters, μm-sized and smaller particles are levitated at Eros. Micrometeoroid bombardment is not a sufficient source mechanism for electrostatic transport to create the Eros dust ponds. Laboratory measurements of dust in a plasma sheath show that dust launched off the surface by direct electrostatic levitation can provide a sufficient source for transport to produce the observed Eros ponds.

The Cassini Ultraviolet Imaging Spectrograph (UVIS) is part of the remote sensing payload of the Cassini orbiter spacecraft. UVIS has two spectrographic channels that provide images and spectra covering the ranges from 56 to 118 nm and 110 to 190 nm. A third optical path with a solar blind CsI photocathode is used for high signal-to-noise-ratio stellar occultations by rings and atmospheres. A separate Hydrogen Deuterium Absorption Cell measures the relative abundance of deuterium and hydrogen from their Lyman-α emission. The UVIS science objectives include investigation of the chemistry, aerosols, clouds, and energy balance of the Titan and Saturn atmospheres; neutrals in the Saturn magnetosphere; the deuterium-to-hydrogen (D/H) ratio for Titan and Saturn; icy satellite surface properties; and the structure and evolution of Saturn’s rings.

We present the results of the second flight of the Collisions Into Dust Experiment (COLLIDE-2), a space shuttle payload that performs six impact experiments into simulated planetary regolith at speeds between 1 and 100 cm/s. COLLIDE-2 flew on the STS-108 mission in December 2001 following an initial flight in April 1998. The experiment was modified since the first flight to provide higher quality data, and the impact parameters were varied. Spherical quartz projectiles of 1-cm radius were launched into quartz sand and JSC-1 lunar regolith simulant targets 2-cm deep. At impact speeds below ∼20 cm/s the projectile embedded itself in the target material and did not rebound. Some ejecta were produced at ∼10 cm/s. At speeds >25 cm/s the projectile rebounded and significant ejecta was produced. We present coefficients of restitution, ejecta velocities, and limits on ejecta masses. Ejecta velocities are typically less than 10% of the impact velocity, and the fraction of impact kinetic energy partitioned into ejecta kinetic energy is also less than 10%. Taken together with a proposed aerodynamic planetesimal growth mechanism, these results support planetesimal growth at impact speeds above the nominal observed threshold of about 20 cm/s.

Theoretical and observational progress in studies of Saturn's ring system since the mid-1980s is reviewed, focussing on advances in configuration and dynamics, composition and size distribution, dust and meteoroids, interactions of the rings with the planet and the magnetosphere, and relationships between the rings and various satellites. The Cassini instrument suite of greatest relevance to ring studies is also summarized, emphasizing how the individual instruments might work together to solve outstanding problems. The Cassini tour is described from the standpoint of ring studies, and major ring science goals are summarized.

In an effort to better understand the early stages of planet formation, we have developed a 1.5U payload that flew on the International Space Station (ISS) in the NanoRacks NanoLab facility between September 2014 and March 2016. This payload, named NanoRocks, ran a particle collision experiment under long-term microgravity conditions. The objectives of the experiment were (a) to observe collisions between mm-sized particles at relative velocities of $, Comment: 8 pages, 8 figures

Current models of the formation of km-sized planetary building blocks, or planetesimals, by collisional accretion require unrealistically low collision velocities or ad hoc assumptions about sticking in order for growth to occur. Collision velocities in the protoplanetary nebula increase with increasing particle size, leading to bouncing and fragmentation of colliding bodies rather than growth. We describe a new and efficient mechanism in planetesimal accretion which leads to net growth in spite of fragmentation, at least for small planetesimals. Our experimental results show that nebular gas flow returns protoplanetary dust grains to a growing planetesimal, resulting in accretion for impact speeds up to at least 10–15 ms−1. This new threshold velocity is three orders of magnitude higher than the threshold velocity for accretion between macroscopic ice spheres and ten times higher than the sticking velocity for micron-sized dust particles.

The narrow rings of Uranus and Neptune exist in a system of observed and hypothesized small moons. Catastrophic fragmentation of these moons by comet impact has been proposed as the mode of origin of those rings, and earlier efforts to model the process showed that small moons are destroyed by impact on short timescales, leading to rapid collisional erosion of any primordial satellite system (Colwell and Esposito, 1992). We reexamine the question of impact fragmentation of small satellites in the light of new observational data on the population of Kuiper Belt and Centaur objects that produce the impacting flux and new theoretical and computational studies of catastrophic fragmentation. We find that the impacting flux used by Colwell and Esposito (1992) is consistent with the new observations of Kuiper Belt objects and calculations of their transport into the solar system. However, new fragmentation criteria from modeling of the asteroid belt and hydrocode simulations lengthen the model collisional lifetimes of satellite systems. The observed distribution of rings, dust bands, and moons at Uranus and Neptune suggest a catastrophic disruption model with a relatively weak dependence on target radius.

Photoelectric charging measurements are presented of dust grains in vacuum for isolated grains and for grains near a photoemissive surface. Isolated grains reach a positive-equilibrium floating potential, dependent upon the work function of the particle, which causes the emitted electrons to be returned. Grains dropped past a photoemitting surface reach a negative floating potential for which the sum of the emitted and collected currents is zero. The particles tested are 90-106 microm in diameter and are composed of Zn, Cu, graphite, and glass.

The satellite Enceladus is obviously the main source of Saturn's E ring. Up to now, different mechanisms of how particles are delivered from this satellite have been suggested. In this paper, we try to answer the question of whether these different launch processes can be distinguished by the cosmic dust analyzer (CDA) aboard the Cassini spacecraft. To this aim, the dynamics of dust particles just launched from the surface of Enceladus is studied numerically. We have integrated the equations of motion for a wide range of initial conditions including ejecta from interplanetary and E ring impactors onto Enceladus. According to our simulations, Cassini will encounter a significant dust stream about the time of closest approach to Enceladus. The duration and intensity of this expected enhanced impact rate onto the CDA depends on the way the particles are ejected from the satellite. The counting rate yields information about the distribution of ejecta sources on the surface of Enceladus. For instance, an anisotropy of the ejecta between the leading and the trailing hemispheres of Enceladus should be detectable, and impactors of different origin should be distinguishable. Furthermore, the vertical component of the ejecta velocities can explain the vertical extent of the E ring.

We describe the Collisions Into Dust Experiment (COLLIDE), a microgravity experiment to study the outcome of very low velocity (1–100 cm/sec) collisions into a simulated regolith. The experiment was flown on the Space Shuttle in April 1998 and included six independent impact experiments into a lunar soil simulant. Results of these impact experiments showed very little dust ejecta was produced in the impacts, which were highly inelastic. We present normal and tangential coefficients of restitution for impacts into simulated regolith at speeds between 15 and 90 cm/sec. We find normal coefficients of restitution of 2 to 3%, significantly lower than is suggested by extrapolation from low-velocity impact experiments with ice, but consistent with higher velocity impacts into powder. Our microgravity experiment confirms the ground-based result of Hartmann (1978, Icarus 33 , 50–62) that the presence of a regolith increases the efficiency of planetary accretion. The absence of dust ejecta suggests higher energy collisions are necessary to release the dust observed in planetary rings.

We present and use a new rough-surface thermal model to aid in the analysis of new mid-infrared spectral measurements of Mercury from 5–12.5 μm. The model calculates spatially resolved thermal emission from slowly rotating, airless bodies. The Mercury data contain the first spectral measurements of Mercury between 5–7.5 μm, a region not accessible from ground-based telescopes, and are also the first observations of Mercury to be made while flying on the Kuiper Airborne Observatory (KAO). They were obtained with the High- efficiency Infrared Faint Object Grating Spectrometer (HIFOGS). Our rough surface thermal model which best fit the KAO data has a Hapke θ of 20°. A strong 5-μm emission feature was present during both observing periods. We suggest the 5-μm excess may be a result of near surface thermal gradients in regolith materials with a 30 to 100-μm grainsize, but cannot entirely rule out an observational artifact resulting from our instrumentation or the telescope on the KAO. Other features in the spectra are consistent with a feldspathic and feldspathoidal surface composition.

Interplanetary and interstellar dust grains entering Jupiter's magnetosphere form a detectable diffuse faint ring of exogenic material. This ring is composed of particles in the size range of 0.5 to 1.5 micrometers on retrograde and prograde orbits in a 4:1 ratio, with semimajor axes 3 < a < 20 jovian radii, eccentricities 0.1 < e < 0.3, and inclinations i ≲ 20 degrees or i ≳ 160 degrees. The size range and the orbital characteristics are consistent with in situ detections of micrometer-sized grains by the Galileo dust detector, and the measured rates match the number densities predicted from numerical trajectory integrations.

The lightcurves and derived production rates of volatiles such as water for short-period comets show asymmetries around perihelion. These asymmetries do not follow a specific trend, and short-period comets are as likely to be brighter preperihelion as postperihelion. This and images of the nucleus of Comet P/Halley suggest that the activity of comet nuclei is driven by a small number of active regions. Lightcurve asymmetries may then be understood by changing geometry of the active regions with respect to the Sun. Solutions of the heat diffusion equation for a short-period comet with active regions covering the full range of spin axis orientations show that active regions can produce asymmetries of several orders of magnitude in the sublimation rate of water from the nucleus. These large and sudden swings in activity are reduced if the active zone lies within a crater or topographical depression on the nucleus. Simulation of the sublimation rate of H 2 O from craters on a comet nucleus show that topography can qualitatively change the dependence of water production on heliocentric distance. The effect of negative relief topography is to slow the loss of heat from the nucleus and maintain higher sublimation rates than from a flat surface active region experiencing winter. In the absence of topography, a single active region can lead to sublimation rates that vary over several orders of magnitude on short time scales. Negative relief topography reduces the magnitude and speed of these seasonal changes in comet activity, with rougher surfaces having smaller seasonal variations. The magnitude of seasonal changes in comet activity can be used with the results of this model to place upper limits on the amount of surface roughness at known active regions.