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Small, airless bodies are covered by a layer of regolith composed of particles ranging from μm-size dust to cm-size pebbles that evolve under conditions very different than those on Earth. Flight-based microgravity experiments investigating low-velocity collisions of cm-size projectiles into regolith have revealed that certain impact events result in a mass transfer from the target regolith onto the surface of the projectile. The key parameters that produce these events need to be characterized to understand the mechanical behavior of granular media, which is composed of the surfaces of small bodies. We carried out flight and ground-based research campaigns designed to investigate these mass transfer events. The goals of our experimental campaigns were (1) to identify projectile energy thresholds that influence mass transfer outcomes in low-energy collision events between cm-size projectiles and μm-size regolith, (2) to determine whether these mass transfer events required a microgravity environment to be observed, and (3) to determine whether the rebound portion of these collision events could be replicated in a laboratory drop tower environment. We found that (1) mass transfer events occurred for projectile rebound accelerations 2 and we were unable to identify a corresponding impact velocity threshold, (2) mass transfer events require a microgravity environment, and (3) ourdrop tower experiments were able to produce mass transfer events. However, drop tower experiments do not exactly reproduce the free-particle impacts and rebound of the long-duration microgravity experiments and yielded systematically lower amounts of the overall mass transferred.

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 (local openings) and self-gravity wakes. In this model, the widths W and separation S of rectangular clumps play an analogous role to the size of the particle shadows, R. In the first model considered, our calculations are based on the moments of the transparency T in the ring region sampled by the occultation, thus extending the work of Showalter and Nicholson (1990) to larger τ and fractional area 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 calculated from higher powers of the shadow size, thus more sensitive to the extremes of the size distribution. We explain the τ dependence of the 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 in the region between 78,000 and 84,600km from Saturn.Statistics calculated from the granola bar model give different predictions from those based on individual spherical particles. The density waves clearly show compression that triggers clump growth, as predicted by the Predator-Prey model (Esposito etal. 2012, Icarus 217, 103-114). The radial profiles and observed τ dependence suggest that the wave crests compress the gaps more than the wakes, along with broader self-gravity wakes in the wave crests, including transparent ghosts. The UVIS observations fall between the most regular and the most irregular granola bar models. Analysis of ring transparency favors irregularly-spaced elongated clumps. A closer analysis of this particular case gives H/W < 0.12, smaller than Colwell etal. (2007, Icarus 190, 127-144), suggesting wakes are more like linguine than granola bars.

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 the results of a series of laboratory low-speed impacts (< 4 m s−1) of centimeter-sized spherical projectiles into simulated dry and icy regolith samples. The target material was comprised of JSC-1 (Johnson Space Center) lunar simulant grains in the size range 100–250 μm, mixed with similar-sized water ice grains. Impacts were performed under vacuum, either at room temperature for JSC-1 samples or at cryogenic temperatures (π scaling to our measured crater diameters. The water ice in our target material took two forms: grains mixed with the regolith grains and frost from air condensation coating regolith grains. In both cases, the presence of water ice in the sample led to lower ejected masses and smaller crater sizes. In addition, our measured crater sizes were several orders of magnitude larger than expected for impacts into solid rock or water ice. Using our measured scaling parameters, we applied our findings to a planetary context for the study of secondary craters on icy moons, as well as eroding collisions occurring in Saturn’s rings. We found that the deviation of our measurements from solid targets and from commonly used scaling parameters allowed us to reconcile our measurements with the models in both cases.

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 high-speed photometer of Cassini’s Ultraviolet Imaging Spectrograph (UVIS) collected data from stellar occultations across Saturn’s rings at unprecedented high resolution over a wide range of viewing geometries. Because photon counts are described by Poisson statistics, we expect a variance equal to the mean in the absence of intervening ring material. However, most ring ‘particles’ are truly aggregates of smaller particles, ranging from micron-size dust to tens of meter-sized boulders, and if the sizes of these aggregates are not small relative to the field-of-view over a single integration period, they introduce excess variance from which we can glean further information about the sizes of particles and clumps. This is particularly relevant in the A ring, where non-axisymmetric self-gravity wakes are ubiquitous. Larger elongated clumps nicknamed straw have been directly imaged in the troughs of strong density waves (Porco et al., 2005, Science, 307, 1226-1236). In this work we present a survey of the statistical moments of variance and skewness for several ring stellar occultations at two strong density waves from different ring regions, Janus 2:1 and Mimas 5:3, over a variety of viewing angles. The line-of-sight distance from Cassini to the rings affects the measurement area due to the scattered signal and diffraction, and different viewing angles provide measurements of the same ring material with different aspects to potentially reveal the three-dimensional structure of clumps. We calculate an effective particle size per integration area, R, derived by Colwell et al., (2018, Icarus, 300, 150-166) and find similar values for R in both peaks and troughs across density waves as well as within density waves and in adjacent regions. We observe strong statistical similarity between troughs and regions adjoining the waves with overall higher skewness in the A ring, indicating more clumping and greater asymmetry in this region than in the inner B ring region.

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.

We advocate for a mission concept study for a space telescope dedicated to solar system science in Earth orbit. Such a study was recommended by the Committee on Astrobiology and Planetary Science (CAPS) report "Getting Ready for the Next Planetary Science Decadal Survey." The Mid-Decadal Review also recommended NASA to assess the role and value of space telescopes for planetary science. The need for high-resolution, UV-Visible capabilities is especially acute for planetary science with the impending end of the Hubble Space Telescope (HST); however, NASA has not funded a planetary telescope concept study, and the need to assess its value remains. Here, we present potential design options that should be explored to inform the decadal survey., Whitepaper submitted to Planetary Science and Astrobiology Decadal Survey

We now know that the outer solar system is host to at least six diverse planetary ring systems, each of which is a scientifically compelling target with the potential to inform us about the evolution, history and even the internal structure of the body it adorns. These diverse ring systems represent a set of distinct local laboratories for understanding the physics and dynamics of planetary disks, with applications reaching beyond our Solar System. We highlight the current status of planetary rings science and the open questions before the community to promote continued Earth-based and spacecraft-based investigations into planetary rings. As future spacecraft missions are launched and more powerful telescopes come online in the decades to come, we urge NASA for continued support of investigations that advance our understanding of planetary rings, through research and analysis of data from existing facilities, more laboratory work and specific attention to strong rings science goals during future mission selections.

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.

The Strata-1 experiment studies the mixing and segregation dynamics of regolith on small bodies by exposing a suite of regolith simulants to the microgravity environment aboard the International Space Station (ISS) for one year. This will improve our understanding of regolith dynamics and properties on small asteroids, and may assist in interpreting analyses of samples from missions to small bodies such as OSIRIS-REx, Hayabusa-1 and -2, and future missions to small bodies. The Strata-1 experiment consists of four evacuated tubes partially filled with regolith simulants. The simulants are chosen to represent models of regolith covering a range of complexity and tailored to inform and improve computational studies. The four tubes are regularly imaged while moving in response to the ambient vibrational environment using dedicated cameras. The imagery is then downlinked to the Strata-1 science team about every two months. Analyses performed on the imagery includes evaluating the extent of the segregation of Strata-1 samples and comparing the observations to computational models. After Strata-1's return to Earth, x-ray tomography and optical microscopy will be used to study the post-flight simulant distribution. Strata-1 is also a pathfinder for the new “1E” ISS payload class, which is intended to simplify and accelerate emplacement of experiments on board ISS.

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.

In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

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

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.

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.

In this study, a spherical projectile vertical impact into a granular bed was numerically investigated with 3D Discrete Element Method (DEM) and validated with experiments. We vary the impact velocity (0.9–3.6 m/s) and size of particles in the bed (1–3 mm) and study the changes in ejecta velocity distribution for different impacts. We find good agreement for the total ejecta mass and for the velocity distribution of the ejecta between simulations and experiments, validating the numerical model and method for predicting the outcomes of low-velocity impacts into granular media. In addition, we analyzed the influences of granular bed size, solid volume fraction and particle density using the DEM and present the results of these simulations that could not readily be reproduced experimentally. The experimentally validated DEM thus enables exploration of parameter spaces that are impractical for experimental study.

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.

In September 2017, the Cassini spacecraft will point itself toward the surface of Saturn and end its 13-year mission of solving many of the mysteries of the ringed planet's system with a crash. This book is a dramatic, beautifully illustrated journey of discovery through the Saturn system. Cassini's instruments have revealed never seen before details including the only extraterrestrial lakes known in the solar system and have provided unprecedented views of the rings. It is a non-technical book for everyone who loves astronomy.

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.

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.

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

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.