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Comets are icy objects that orbitally evolve from the trans-Neptunian region (the Kuiper belt and beyond) into the inner Solar System, where they are heated by solar radiation and become active due to sublimation of water ice. Here we perform end-to-end simulations in which cometary reservoirs are formed in the early Solar System and evolved over 4.5 Gyr. The gravitational effects of Planet 9 (P9), hypothesized to circle the Sun on a wide orbit, are included in some of our simulations. Different models are considered for comets to be active, including a simple assumption that comets remain active for Np(q) perihelion passages with perihelion distance q<2.5 au. The orbital distribution and number of active comets produced in our model is compared to observations. The orbital distribution of ecliptic comets (ECs) is well reproduced in models with Np(2.5)=500 and without P9. With P9, the inclination distribution of model ECs is wider than the observed one. We find that the known Halley-type comets (HTCs) have a nearly isotropic inclination distribution (with only a slight preference for prograde orbits). In our model, the HTCs appear to be an extension of the population of returning Oort-cloud comets (OCCs) to shorter orbital periods. The inclination distribution of model HTCs becomes broader with increasing Np, but the existing observational data are not good enough to constrain Np from orbital fits. Np(2.5)>1000 is required to obtain a steady-state population of large active HTCs that is consistent with observations. To fit the ratio of the returning-to-new OCCs, by contrast, our model implies that Np(2.5)<10, possibly because the detected long-period comets are smaller and much easier to disrupt than observed HTCs.

This chapter of the book Planetary Ring Systems addresses the origin of planetary rings, one of the least understood processes related to planet formation and evolution. Whereas rings seem ubiquitous around giant planets, their great diversity of mass, structure and composition is a challenge for any formation scenario. Recent advances in our understanding of ring and satellite formation and destruction suggest that these processes are interconnected, so that rings and satellites may be two aspects of the same geological system. However, no single theory seems able to explain the origin of the different planetary rings known in our Solar System, and it now seems evident that rings may result from a variety of processes like giant collisions, tidal stripping of comets or satellites, as well as planet formation itself. In order to build any theory of ring formation it is important to specify physical processes that affect the long-term evolution of rings, as well as to describe the different observations that any ring formation model should explain. This is the topic of section 2. In section 3, we focus our attention on Saturn's rings and their main properties, and then discuss the pros and cons of a series of ring formation models. We also discuss the link between rings and satellites. In section 4, we extend the discussion to the other giant planets (Jupiter, Uranus, and Neptune). Section 5 is devoted to new types of rings -- the recent discovery of rings orbiting small outer Solar System bodies (Centaurs), and the possible rings around extrasolar planets. In section 6, we conclude and try to identify critical observations and theoretical advances needed to better understand the origin of rings and their significance in the global evolution of planets., Comment: This material will be published as the 18th Chapter of the book Planetary Ring Systems, edited by Matthew S. Tiscareno and Carl D. Murray. See: www.cambridge.org/9781107113824

We present a scenario for building the equatorial ridge and de-spinning Iapetus through an impact-generated disk and satellite. This impact puts debris into orbit, forming a ring inside the Roche limit and a satellite outside. This satellite rapidly pushes the ring material down to the surface of Iapetus, and then itself tidally evolves outward, thereby helping to de-spin Iapetus. This scenario can de-spin Iapetus an order of magnitude faster than when tides due to Saturn act alone, almost independently of its interior geophysical evolution. Eventually, the satellite is stripped from its orbit by Saturn. The range of satellite and impactor masses required is compatible with the estimated impact history of Iapetus., Comment: 19 pages, 3 figures; Icarus, in press

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.

Saturn is the first giant planet to be visited by an orbiting spacecraft that can transmit large amounts of data to Earth. Crater counts on satellites from Phoebe inward to the regular satellites and ring moons are providing unprecedented insights into the origin and time histories of the impacting populations. Many Voyager-era scientists concluded that the satellites had been struck by at least two populations of impactors. In this view, the Population I impactors, which were generally judged to be comets orbiting the Sun, formed most of the larger and older craters, while Population II impactors, interpreted as Saturn-orbiting ejecta from impacts on satellites, produced most of the smaller and younger craters. Voyager data also implied that all of the ring moons, and probably some of the midsized classical moons, had been catastrophically disrupted and reaccreted since they formed. We examine models of the primary impactor populations in the Saturn system. At the present time, ecliptic comets, which likely originate in the Kuiper belt/scattered disk, are predicted to dominate impacts on the regular satellites and ring moons, but the models require extrapolations in size (from the observed Kuiper belt objects to the much smaller bodies that produce the craters) or in distance (from the known active Jupiter family comets to 9.5 AU). Phoebe, Iapetus, and perhaps even moons closer to Saturn have been struck by irregular satellites as well. We describe the Nice model, which provides a plausible mechanism by which the entire Solar System might have experienced an era of heavy bombardment long after the planets formed. We then discuss the three cratering chronologies, including one based upon the Nice model, that have been used to infer surface ages from crater densities on the saturnian satellites. After reviewing scaling relations between the properties of impactors and the craters they produce, we provide model estimates of the present-day rate at which comets impact, and catastrophically disrupt, the saturnian moons. Finally, we present crater counts on the satellites from two different groups. Many of the heavily cratered terrains appear to be nearly saturated, so it is difficult to infer the provenance of the impactors from crater counts alone. More large craters have been found on Iapetus than on any other satellite. Enceladus displays an enormous range of surface ages, ranging from the old mid-latitude plains to the extremely young South Polar Terrain. Cassini images provide some evidence for the reality of Population II. Most of the observed craters may have formed in one or more cataclysms, but more work is needed to determine the roles of heliocentric and planetocentric bodies in creating the craters.

Cassini has identified a geologically active province a the south pole of Saturn's moon Enceladus. The shape of Enceladus suggests a possible intense heating epoch in the past by capture into a 1:4 secondary spin/orbit resonance.

We use several independent constraints on the number of ecliptic comets (aka JFCs) to determine impact cratering rates from Jupiter to Pluto. Long period comets and asteroids are currently unimportant on most worlds at most sizes. The size- number distribution of comets smaller than 20 km is inferred from size-number distributions of impact craters on Europa, Ganymede, and Triton; while the size- number distribution of comets bigger than 50 km is equated to the size-number distribution of Kuiper Belt Objects. The gap is bridged by interpolation. It is notable that small craters on Jupiter's moons indicate a pronounced paucity of small impactors, while small craters on Triton imply a collisional population rich in small bodies. However it is unclear whether the craters on Triton are of heliocentric or planetocentric origin. We therefore consider two cases for Saturn and beyond: a Case A in which the size-number distribution is like that inferred at Jupiter, and a Case B in which small objects obey a more nearly collisional distribution. Known craters on Saturnian and Uranian satellites are consistent with either Case, although surface ages are much younger in Case B, especially at Saturn and Uranus. At Neptune and especially at Saturn our cratering rates are much higher than rates estimated by Shoemaker and colleagues, presumably because Shoemaker's estimates mostly predate discovery of the Kuiper Belt. We also estimate collisional disruption rates of moons and compare these to estimates in the literature .

We present a progress report of a continuing study of the coupling between outer planetary system architecture and inner planetary system formation. Additional information is contained in the original extended abstract.

We use a Monte Carlo method to confirm that cratering asymmetries between the leading and trailing hemispheres of synchronously-rotating satellites should be very large; indeed we find that previous work has tended to underestimate the asymmetry.

Atmospheres are found enveloping those planets and satellites best able to hold them. The obvious conclusion is that volatile escape must have played nearly as great a role as volatile supply. A consequence of this view is that volatile supplies were probably much greater than the atmospheres that remain. The likeliest candidates are sources associated with the main events of planetary accretion itself such as volatile-rich planetesimals, or direct gravitational capture of nebular gases. Late asteroidal or cometary volatile-rich veneers are attractive, but they present quantitative difficulties. Comets in particular are inadequate, because the associated mass of stray comets that would have been scattered to the Oort Cloud or beyond is excessive. This difficulty applies to Uranus-Neptune planetesimals as well as to a putative massive early Kuiper Belt. Another potential problem with comets is that the D/H ratio in the three comets for which this has been measured is about twice that of Earth's oceans. Objects falling from a much augmented ancient asteroid belt remain a viable option, but timing is an issue: Can the depopulation of the asteroid belt be delayed long enough that it makes sense to talk of asteroids as a late veneer? Early accretion of asteroids as objects scattered into the maw of infant Earth makes more sense. Another appealing candidate population of volatile-rich objects for the inner solar system would be scattered planetesimals associated with the accretion of Jupiter, for two reasons: (1) Before there was Jupiter, there was no object in the solar system capable of expelling comets efficiently, and (2) the cross section of the inner solar system to stray objects was Greater when there were m many planetesimals.

After the Moon-forming impact, the Earth and Moon would have been subject to impacts by asteroids, comets, and leftovers of accretion. All are plausible sources of the impactors that produced the Late Heavy Bombardment (LHB). The LHB might have included a "Lunar Cataclysm," or cratering spike, near 3.9 Ga. A mechanism for such a cataclysm involving asteroid showers following the breakup of a large main-belt asteroid has recently been proposed. However, this model, while reasonable, requires a massive main belt or unlikely breakup event.

The reason why Titan has a thick atmosphere while its Jovian clones Ganymede and Callisto have nothing is addressed. It is argued that this contrast is a predictable consequence of impact erosion, i.e., the escape of atmospheric gases as a consequence of hypervelocity impact, the average impact velocity of stray bodies on Titan being lower than on Ganymede and Callisto. A model to examine this hypothesis is presented.

The current status of efforts to model light scattering in the Uranian and Saturnian rings is briefly reviewed, with an emphasis on the treatment of thin, vertically warped, or clumpy rings. Consideration is given to observations of an opposition surge in the rings (indicating that they are physically thick) and possible reasons for the failure of classical models to predict the forward-scattering characteristics of the B and inner A rings of Saturn, the quadrupole brightness variations in the A ring, the increase in reflectivity with optical depth in the A and B rings, the increase in brightness with solar and observer angle in the B ring, and systematic brightness variations in images of the inner Cassini division. It is pointed out that some of these discrepancies are eliminated by the use of a ray-tracing simulation code which determines the singly scattered light from a layer one or many particles thick.

The formalism of Borderies, Goldreich, and Tremaine (1984), as simplified by Shu and Stewart (1985), is used to develop a theory for the viscous damping of nonlinear density waves in particulate disks of moderate collision frequency. The specific application is to Saturn's rings, but the development is general enough to allow application to a wider context (e.g., to gas clouds in a spiral galaxy). A Krook formulation is used rather than a Boltzmann formulation to treat the statistical effects of inelastic collisions. Issues that have arisen as a result of the study include a self-induced Q barrier in the first wavelength or two of the Mimas 5:3 density wave train and the surprising discovery that Saturn's B ring may behave almost as a superfluid, with hardly any viscous losses.