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Observations of Enceladus' south pole revealed large rifts in the crust, called "tiger stripes", which exhibit higher temperatures than the surrounding terrain and are likely sources of observed eruptions. Tidal stress may periodically open the tiger stripe rifts, controlling the timing and location of eruptions. Moreover, shear motion along rifts may produce the heat to drive eruptions.

Tectonic patterns on Europa are influenced by tidal stress. An important well-organized component is associated with the orbital eccentricity, which produces a diurnally varying stress as Jupiter's apparent position in Europa's sky oscillates in longitude. Cycloidal lineaments seem to have formed as cracks propagated in this diurnally varying stress field. Maps of theoretical cycloid patterns capture many of the characteristics of the observed distribution on Europa. However, a few details of the observed cycloids distribution have not reproduced by previous models. Recently, it has been shown that Europa has a finite forced obliquity, so Jupiter's apparent positon in Europa's sky will also oscillate in latitude. We explore this new type of diurnal effect on cycloid formation. We find that stress from obliquity may be the key to explaining several characteristics of observed cycloids such as the shape of equator-crossing cycloids and the shift in the crack patterns in the Argadnel Regio region. All of those improvements of the fit between observaiton and theory seem to require Jupiter crossing Europa's equatorial plane 45 deg. to 180 deg after perijove passage. Suggestive of complex orbital dynamics that lock the direction of Europe's pericenter with the direction of the ascending node at the time these cracks were formed.

Given the non-spherical shape of Enceladus (Thomas et al., 2007), the satellite will experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus tidal bulge which, could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus libration amplitude of F < 1.5deg (Porco et al., 2006), smaller amplitudes can still have geologically significant consequences. Here we present the first detailed description of how physical libration affects tidal stresses and how those stresses then might affect geological processes including crack formation and propagation, south polar eruption activity, and tidal heating. Our goal is to provide a framework for testing the hypothesis that geologic features on Enceladus are produced by tidal stresses from diurnal physical and optical librations of the satellite.

The observed cratering records on asteroid surfaces (four so far: Gaspra, Ida, Mathilde, and Eros [1-4]) provide us with important clues to their past bombardment histories. Previous efforts toward interpreting these records have led to two basic modeling styles for reproducing the statistics of the observed crater populations. The first, and most direct, method is to use Monte Carlo techniques [5] to stochastically populate a matrix-model test surface with craters as a function of time [6,7]. The second method is to use a more general, parameterized approach to duplicate the statistics of the observed crater population [8,9]. In both methods, several factors must be included beyond the simple superposing of circular features: (1) crater erosion by subsequent impacts, (2) infilling of craters by impact ejecta, and (3) crater degradation and era- sure due to the seismic effects of subsequent impacts. Here we present an updated Monte Carlo (stochastic) modeling approach, designed specifically with small- to medium-sized asteroids in mind.

In recent years, spacecraft observations of asteroids 951 Gaspra, 243 Ida, 253 Mathilde, and 433 Eros have shown the overriding dominance of impact processes with regard to the structure and appearance of these small, irregular bodies. One currently unanswered question is: to what degree does seismic shaking from impacts affect the surface morphology of these bodies? Through detailed modeling, we begin to address this question.

In recent years, spacecraft observations of asteroids 951 Gaspra, 243 Ida, 253 Mathilde, and 433 Eros have shown the overriding dominance of impact processes with regard to the structure and surface morphology of these small, irregular bodies. In particular, impact ejecta play an important role in regolith formation, ranging from small particles to large blocks, as well as surface feature modification and obscuration. To investigate these processes, a numerical model has been developed based upon the impact ejecta scaling laws provided by Housen, Schmidt, and Holsapple, and modified to more properly simulate the late-stage ejection velocities and ejecta plume shape changes (ejection angle variations) shown in impact cratering experiments. A target strength parameter has also been added to allow the simulation of strength-dominated cratering events in addition to the more familiar gravity-dominated cratering events. The result is a dynamical simulation which models -- via tracer particles -- the ejecta plume behavior, ejecta blanket placement, and impact crater area resulting from a specified impact on an irregularly shaped target body, which is modeled in 3-dimensional polygon fashion. This target body can be placed in a simple rotation state about one of its principal axes, with the impact site and projectile/target parameters selected by the user. The gravitational force from the irregular target body (on each tracer particle) is determined using the polygonized surface (polyhedron) gravity technique developed by Werner.

We have examined the lifetimes of Near-Earth asteroids (NEA's) by directly computing the collision probabilities with other asteroids and with the terrestrial planets. We compare these to the dynamical lifetimes, and to collisional lifetimes assumed by other workers. We discuss the implications of the differences. The lifetimes of NEA's are important because, along with the statistics of craters on the Earth and Moon, they help us to compute the number of NEA's and the rate at which new NEA's are brought to the vicinity of the Earth. Assuming that the NEA population is in steady-state, the lifetimes determine the flux of new bodies needed to replenish the population. Earlier estimates of the lifetimes ignored (or incompletely accounted for) the differences in the velocities of asteroids as they move in their orbits, so our results differ from (for example) Greenberg and Chapman (1983, Icarus 55, 455) and Wetherill (1988, Icarus 76, 1) by factors of 2 to 10. We have computed the collision rates and relative velocities of NEA's with each other, the main-belt asteroids, and the terrestrial planets, using the corrected method described by Bottke et. al. (1992, GRL, in press). We find that NEA's typically have shorter collisional lifetimes than do main-belt asteroids of the same size, due to their high eccentricities, which typically give them aphelia in the main belt. Consequently, they spend a great deal of time in the main belt, and are moving much slower than the bodies around them, making them 'sitting ducks' for impacts with other asteroids. They cross the paths of many objects, and their typical collision velocities are much higher (10-15 km/s) than the collision velocities (5 km/s) among objects within the main belt. These factors combine to give them substantially shorter lifetimes than had been previously estimated.

Interpretation of the impact record on Gaspra requires understanding of the effects of collisions on a target body of Gaspra's size and shape, recognition of impact features that may have different morphologies from craters on larger planets, and models of the geological processes that erase and modify impact features. Crater counts on the 140 sq km of Gaspra imaged at highest resolution by the Galileo spacecraft show a steep size-frequency distribution (cumulative power-law index near -3.5) from the smallest resolvable size (150 m diameter) up through the large feature (1.5 km diameter crater) of familiar crater-like morphology. In addition, there appear to be as many as eight roughly circular concavities with diameters greater than 3 km visible on the asteroid. If we restrict our crater counts to features with traditionally recognized crater morphologies, these concavities would not be included. However, if we define craters to include any concave structures that may represent local or regional damage at an impact size, then the larger features on Gaspra are candidates for consideration. Acceptance of the multi-km features as craters has been cautious for several reasons. First, scaling laws (the physically plausible algorithms for extrapolating from experimental data) indicate that Gaspra could not have sustained such large-crater-forming impacts without being disrupted; second, aside from concavity, the larger structures have no other features (e.g. rims) that can be identified with known impact craters; and third, extrapolation of the power-law size distribution for smaller craters predicts no craters larger than 3 km over the entire surface. On the other hand, recent hydrocode modeling of impacts shows that for given impact (albeit into a sphere), the crater size is much larger than given by scaling laws. Gaspra-size bodies can sustain formation of up to 8-km craters without disruption. Besides allowing larger impact craters, this result doubles the lifetime since the last catastrophic fragmentation event up to one billion years. Events that create multi-km craters also globally damage the material structure, such that regolith is produced, whether or not Gaspra 'initially' had a regolith, contrary to other models in which initial regolith is required in order to allow current regolith. Because the globally destructive shock wave precedes basin formation, crater size is closer to the large size extrapolated from gravity-scaling rather than the strength-scaling that had earlier been assumed for such small bodies. This mechanism may also help explain the existence of Stickney on Phobos. Moreover, rejection of the large concavities as craters based on unfamiliar morphology would be premature, because (aside from Stickney) we have no other data on such large impact structures on such a small, irregular body. The eight candidate concavities cover an area greater than that counted for smaller craters, because they are most apparent where small craters cannot be seen: on low resolution images and at the limb on high resolution images. We estimate that there are at least two with diameter greater than 4 km per 140 sq km, which would have to be accounted for in any model that claims these are impact craters.

The recent flyby of the Galileo spacecraft en route to Jupiter contributes a unique perspective to our view of our home planet. Imaging activities conducted during the second Earth encounter provide an important opportunity to assess new methods and approaches on familiar territory. These include unique multispectral observations, low light-level imaging (searches for aurorae, lightning and artificial lights on the nightside) and experiments with multiple exposure times to extend the effective radiometric resolution and dynamic range of the camera system. Galileo imaging data has the potential to make important contributions to terrestrial remote sensing. This is because the particular set of filters included in the Solid State Imaging system are not presently incorporated in any currently operating Earth-orbiting sensor system. The visible/near-infrared bandpasses of the SSI filters are well suited to remote sensing of geological, glaciological, botanical, and meteorological phenomena. Data from this and the previous Earth encounter may provide an extremely valuable reference point in time for comparison with similar data expected from EOS or other systems in the future, contributing directly to our knowledge of global change. The highest resolution imaging (0.2 km/pixel) during the December, 1992 encounter occurred over the central Andes; a five filter mosaic of visible and near infrared bands displays the remarkable spectral heterogeneity of this geologically diverse region. As Galileo departed the Earth, cooperative imaging with the Near Infrared Mapping Spectrometer (NIMS) instrument targeted Antarctica, Australia, and Indonesia at 1.0 to 2.5 km/pixel resolutions in the early morning local times near the terminator. The Antarctic data are of particular interest, potentially allowing ice grain size mapping using the 889 and 968 nm filters and providing an important means of calibrating the technique for application to the Galilean satellites. As the spacecraft receded further, regional scale imaging provided data which, along with data from the previous encounter, will enable the production of global multispectral mosaics of Earth in each of the SSI filters.

Galileo images of Gaspra reveal it to be an irregularly shaped object (19 by 12 by 11 kilometers) that appears to have been created by a catastrophic collisional disruption of a precursor parent body. The cratering age of the surface is about 200 million years. Subtle albedo and color variations appear to correlate with morphological features: brighter materials are associated with craters especially along the crests of ridges, have a stronger 1-micrometer absorption, and may represent freshly excavated mafic materials; darker materials exhibiting a significantly weaker 1-micrometer absorption appear concentrated in interridge areas. One explanation of these patterns is that Gaspra is covered with a thin regolith and that some of this material has migrated downslope in some areas.

Three images of Venus have been returned so far by the Galileo spacecraft following an encounter with the planet on UT February 10, 1990. The images, taken at effective wavelengths of 4200 and 9900 A, characterize the global motions and distribution of haze near the Venus cloud tops and, at the latter wavelength, deep within the main cloud. Previously undetected markings are clearly seen in the near-infrared image. The global distribution of these features, which have maximum contrasts of 3 percent, is different from that recorded at short wavelengths. In particular, the 'polar collar', which is omnipresent in short wavelength images, is absent at 9900 A. The maximum contrast in the features at 4200 A is about 20 percent. The optical performance of the camera is described and is judged to be nominal.

Summaries are given of the spectral calibration, compositional parameters, nearside color, and limb and farside color of the Moon. The farside of the Moon, a large area of lunar crust, is dominated by heavily cratered terrain and basin deposits that represent the products of the first half billion years of crustal evolution. Continuing analysis of the returned lunar samples suggest a magma ocean and/or serial magmatism model for evolution of the primordial lunar crust. However, testing either hypothesis requires compositional information about the crustal stratigraphy and lateral heterogeneity. Resolution of this important planetary science issue is dependent on additional data. New Galileo multispectral images indicate previously unknown local and regional compositional diversity of the farside crust. Future analysis will focus on individual features and a more detailed assessment of crustal stratigraphy and heterogeneity.

The intermediate stage of protoplanetary accretion, where sub-km sized bodies accrete in 500-1000 km diameter bodies, is critical in determining the character of subsequent evolution. Greenberg et al. discovered that, at least through the formation of 500 km planetary embryos, the small particle dominate the population and control the velocity distribution, keeping velocities much smaller and setting up the possibility of runaway accretion, where the largest body is able to accumulate quickly a much greater mass and separate itself from the continuum of the size distribution. However, some controversy remains as to the exact methods used by Greenberg et al. I reviewed that planet formation model in detail to address these criticisms and better explain the algorithm used in the study. In particular, the algorithms for mutual velocity stirring among planetesimals and mass shifting between adjacent diameter bins are rederived in detail. I also examined the likelihood of artificial acceleration of the runaway growth phase of the intermediate stage of planetesimal formation.

Observed geology, photometry, and geophysical data are used to examine various processes and properties that may have contributed to Maranda's evolution. Global tectonics and surface flow features constrain the possible heating mechanisms and materials. Statistics on impact craters and comparisons with other satellites suggest that the impactor-source population evolved through time and that ejecta mantling has resurfaced significant portions of the surface. It is proposed that the coronae, which are unique to Miranda, were formed by relaxation of topographic highs, by lithospheric stress driven by intensity anomalies in the asthenosphere, or by diapirs either breeching the surface or feeding large-scale volcanic flooding through preexisting crack structure.

During the Earth-Moon flyby the Galileo Solid State Imaging system obtained new information on lunar media. Imaging data in spectral bands from 0.4 to 1.0 micron wavelength provide color data for deposits on the western limb. General objectives were to determine the composition and stratigraphy of mare and related deposits for areas not previously seen well in color, and to compare the results with well-studied nearside maria. Initial results from images reduced with preliminary calibrations show that Galileo spectral reflectance data are consistent with previous earthbased observations.

A total of 107 complete or partial lightcurves are presented for 59 different asteroids over the 1982-1989 period. Unusual lightcurves with unequal minima and maxima at large amplitudes are preferentially seen for M-type asteroids. Some asteroids, such as 16 Psyche and 201 Penelope, exhibit lightcurves combining large amplitude with very unequal brightness for both maxima and both minima, even at small phase angles. An M-type asteroid is believed to consist of a metal core of a differentiated parent body that has had its rocky mantle completely removed by one or more large impacts.

Recent research on the resonant structure of the asteroid belt is reviewed. The resonant mechanism is discussed, and analytical models for the study of mean motion resonances are examined. Numerical averaging methods and mapping methods are considered. It is shown how fresh insight can be obtained by means of a new semianalytical approach.

Most of the knowledge of asteroidal regoliths is based on extensive studies of the lunar regolith and the meteorite regolith breccias and on theoretical models designed to match some characteristics of these two types of samples. Two major factors that affect the production and evolution of regolith and make these efforts problematical are changes of regolith properties with time, because of changes in the flux and velocity of impactors, and changes due to the location of the object in the solar system and the strength of the local gravity field. It is emphasized that, at present, not enough data are available on the processes operating on asteroids to be able to define the asteroidal regolith properties; such data can be obtained by missions to individual asteroids.

A 'photometric geodesy' program is selected on the basis of light-curve data from five years' observations of large, rapidly rotating asteroids, where the observing protocol was designed to obtain precise, absolute photometry at a wide variety of orbital longitudes and phase angles. A total of 257 complete or partial light-curves are obtained for 26 asteroids; the data set will allow the future determination of pole positions and shapes, as well as to constrain the geophysical traits of these bodies.

Comets were studied during their relatively quiescent phases at large distances from the sun. This program, has resulted in a variety of CCD images of comets in several visible and near-IR bands selected to sample the continuum, rather than emission features. The most extensive dataset was obtained for P/Halley during January 1985 (plus scattered earlier data), near the time the comet turned on. The data were reduced in a preliminary fashion. Other comets predicted to be relatively inactive (including Neujmin 1 and Arend-Rigaux) were most active than expected. P/Gehrels 3 was also observed.

Debris fom the single collisions between asteroids that are presently suggested as an explanation for zodiacal dust bands discovered by IRAS is distributed about the plane of the ecliptic, as particles undergo differential precession of their ascending nodes because of their semimajor axes' dispersion. On time scales of 100,000 to 1,000,000 yr, two bands are formed on each side of the ecliptic for each collision; the IRAS band pairs are probably due to collisions of aproximately 15-km diameter asteroids which occurred within the last several million yr. The model presented suggests that asteroid collisions suffice as a basis for most of the observed zodiacal emission.

The paper reveals the possibility that the moon could have formed from the long-term evolution of a circumterrestrial disk emplaced during the earth's final stages of formation. A model is presented which emphasizes silicate enrichment (or iron depletion) of lunar material within the disk. This model depends on the late-stage planetesimal population being dominated by small bodies.

Charged dust orbiting through spatially periodic planetary magnetic fields will experience time-variable electromagnetic forces. When the forcing frequencies are nearly commensurate with the particle's orbital frequency, the particle undergoes large out-of-plane and radial excursions. Specific 'Lorentz' resonances, corresponding to particular spatial periodicities in the magnetic field, occur on either side of synchronous orbit. Lorentz resonance locations and strengths for the Jovian and Saturnian rings are described. The boundaries of the halo of the Jovian ring, and perhaps other ring structures, are near resonances.

Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run which are subject to three constraints: they must evolve to the current asteroid size distribution, preserve Vesta's basaltic crust, and produce at least the observed number of major Hirayama families. A 'runaway growth' initial asteroid population distribution is found to best satisfy these constraints, and a model is developed for the calculation of fragment size distribution in the disruption of large, gravitationally bound bodies in which the material strength is enhanced by hydrostatic self-compression. This model predicts that large asteroids behave as intrinsically strong bodies despite histories of collisional fracture.

Models of lunar origin in which the Moon accretes in orbit about the Earth from material approaching the Earth from heliocentric orbits must overcome a fundamental problem: the approach orbits of such material would be, in the simplest approximation, equally likely to be prograde or retrograde about the Earth, with the result that accretion of such material adds mass but not angular momentum to circumterrestrial satellites. Satellite orbits would then decay due to the resulting drag, ultimately impacting onto the Earth. One possibility for adding both material and angular momentum to Earth orbit is investigated: imbalance in the delivered angular momentum between pro and retrograde Earth passing orbits which arises from the three body dynamics of planetesimals approaching the Earth from heliocentric space. In order to study angular momentum delivery to circumterrestrial satellites, the near Earth velocities were numerically computed as a function of distance from the Earth for a large array of orbits systematically spanning heliocentric phase space.

A major question about the moon is its under abundance of iron. It is the purpose of this research to understand whether a metal-silicate fractionation of heliocentrically orbiting bodies can be achieved through collisional interactions with a circum-terrestrial swarm. Rates of diffusion are investigated and the mutual collisional destruction within the population is examined. The interactions of these differentiated planetesimals and their collisional products (both silicate mantle fragments and iron cores) with a swarm of Earth orbiting lunesimals (perhaps ejecta from the Earth) of km scale, totaling a mass of order 0.1 lunar mass, extending out 10 or 20 Earth radii are considered. It is found that such a small near Earth population of lunesimals can filter out silicate rich material, while passing iron cores, and form a moon composed partly of terrestrial material, but more substantially of the captured silicate rich portions of the planetesimals.

Understanding asteroid collisional evolution is important for characterizing the physical state of asteroids today and for learning about the processes that acted in this region of the solar system early in its history. The collisional outcome algorithm in the numerical simulation of asteroid evolution was revised to reflect pressure-strengthening. Asteroid collisions are now treated as a distribution of oblique impacts rather than as only head-on collisions. The initial and evolved size distribution of a plausible asteroid population is compared with the observed size distribution. Asteroid accretion times and reconstruction of the primordial solar nebula suggest that there was significantly more mass in this part of the solar system when the asteroids were accreting.

Numerical simulation of the early stages of planet growth show that a few bodies nearly 1000 km in diameter may have formed within approx. 100,000 yr after solid material grew into km scale planetesimals by gravitational instability. Even after such large bodies formed, the bulk of the mass of the future terrestrial planet zone resided in small bodies. Subsequent evolution is difficult to model because it requires simultaneous consideration of continuum (multitudinous small bodies) and discrete (a few large bodies) evolution. Some relevant issues include definition of accretional feeding zones, evaluation of the range of gravitational influence, viscous transport and diffusion, orbital commensurabilities, role of gas, etc. The first large bodies may have been (1) the embryos of the final planets, which grew by accreting tiny planetesimals, or (2) merely the first of many 1000+ km bodies, which grew independently and later collided to form the planets. Models of late stage accretion that assume all bodies to be initially nearly Moon sized provide insight into relevant collisional and dynamical processes. The chief point in this research is that the correct size distribution during the later stages of planet growth remains unknown.

Problems which have arisen in formulating a mutually consistent picture of Mercury's evolution are outlined. It appears that one or more of the following widely adopted assumptions are wrong about Mercury: (1) its original composition at least approximately resulted from equilibrium condensation; (2) its magnetic field arises from a still-active dynamo; (3) its thermal evolution should have yielded early core formation followed by cooling and a global contraction approaching 20 km in the planet's radius; (4) Mercury's surface is basaltic and the intercrater plains are of volcanic origin. It is suggested that Mercury's role in comparative planetology be reevaluated in the context of an alternative timescale based on the possibility that Mercury was subjected to a continuing source of cratering projectiles over recent aeons, which have not impacted the other terrestrial planets. Although such vulcanoids have not yet been discovered, the evolution of Mercury's orbit due to secular perturbations could well have led to a prolonged period of sweeping out any intra-Mercurian planetesimals that were originally present. Mercury's surface could be younger than previously believed, which explains why Mercury's core is still molten.

Satellite masses are derivation with emphasis on implications for bulk densities and albedos is reviewed. In the Uranian system the inner satellites have lower densities and/or higher albedos than the outer ones. However, uncertainties are great enough that all five satellites may have nearly equal densities. In such a case the albedo would decrease with semimajor axis. A more severe constraint is placed on Miranda's mass, and hence on its density and albedo. The recent radiometric value for Triton's diameter, combined with mass determinations, yields a density greater than 4 gm/cu cm.

The growth of Neptune and Uranus and the origin of the Oort comet cloud are simulated numerically, applying the planetesimal-growth model developed by Greenberg et al. (1978) for the terrestrial planets. The results of 12 experiments are presented in graphs and tables and discussed in detail. In the model which best fits observations, the planets grow relatively quickly from icy planetesimals of diameter 10 km or less which form by gravitational clumping of grains as they settle nonhomologously to the midplane of the solar system; the comets then represent unaltered remnants of the original planetesimal populations in the zone.

Each of the Galilean satellites, as well as most other satellites whose initial rotations have been substantialy altered by tidal dissipation, has been widely assumed to rotate synchronously with its orbital mean motion. Such rotation would require a small permanent asymmetry in the mass distribution in order to overcome the small mean tidal torque. Since Io and Europa may be substantially fluid, they may not have the strength to support the required permanent asymmetry. Thus, each may rotate at the unknown but slightly nonsynchronous rate that corresponds to zero mean tidal torque. This behavior may be observable by Galileo spacecraft imaging. It may help explain the longitudinal variation of volcanism on Io and the cracking of Europa's crust.

Although Saturn's rings are within the Roche zone, the accretion of centimeter-sized particles into large aggregates many meters in diameter occurs readily, on a time scale of weeks. These aggregates are disrupted when tidal stresses exceed their very low strengths; thus most of the mass of the ring system is continually processed through a population of large 'dynamic ephemeral bodies', which are continually forming and disintegrating. These large aggregates are not at all like the idealized ice spheres often used in modeling Saturn's ring dynamics. Their coefficient of restitution is low, hence they form a monolayer in the ring plane. The optically observable characteristics of the rings are dominated by the swarm of centimeter-sized particles.

Stony-iron meteorites formed at the core/mantle interfaces of small asteroidal parents. The mesosiderites formed when the thick crust of a largely molten parent body (100-200 km in diameter) foundered and sank through the mantle to the core. Pallasites formed in smaller parent bodies (50-100 km) in which olivine crystals from the partially molten mantle sank to the core/mantle interface and rafted there. Subsequent collisions stripped away the rocky mantles of both kinds of parent bodies, exposing the stony-iron surfaces of their cores to direct impacts, which continue to knock off meteorite fragments.

Attention is given to the properties of, and dynamical processes affecting individual particles of Saturn's rings. Because particles tend to be gravitationally bound when located on the surfaces of larger particles, and since net tidal stresses within the particles are small, particle collisions should produce accretion in Saturn's rings. Rapid accretionary processes within the rings are counterbalanced by tidal disruption of the larger accreted aggregates, which are presently designated 'dynamic ephemeral bodies'. The coefficient of restitution is probably very low, implying that the large particles containing most of the rings' mass are in a monolayer, although the small particles responsible for most of the rings' visible cross section form a layer many particles thick. Kinematic viscosity and interparticle erosive process models should incorporate these properties.

The three major categories of models of lunar origin which explain the Moon's properties are complete and a more general scenario is presented. The model presented is as the Earth grew by planetesimal bombardment, a circumterrestrial cloud of particles was created from a combination of impact ejected mantle material and planetismals captured directly into orbit around the Earth. The compositional properties are explained two ways: (1) a few big late planetismals of diverse composition are captured in orbit and/or hit the Earth; and (2) the circumterrestrial swarm acts as a filter, preferentially capturing small weak silicate bodies, while passing large iron planetismals.

When orbital properties constituted most of our knowledge of Saturn's satellites, resonances provided important clues to physical properties and history. With the discoveries of the 1980s, including close-up direct observations of physical and geological properties, resonances are more important than ever. This chapter reviews the kinetics of the various classes of resonances represented among the classical and newly discovered satellites and describes how resonances have played a fundamental role in shaping the Saturn system as it is seen today.

A major question about the Moon is its under abundance of iron. The proposal of whether a metal-silicate fractionation of heliocentric bodies could be achieved through collisional interactions with a circumterrestrial swarm is examined. The whole scenario works only if there is a way to maintain the hypothesized circumterrestrial swarm, which otherwise would collisionally diffuse on a time scale of 100 yr (much of it collapsing on the Earth); the source of angular momentum to maintain the swarm remains a mystery.

Attention is drawn to current attempts to present the results of theoretical dynamical studies of the planetary rings, and to propagate observational results on ring structure and physical properties that are relevant to dynamical interpretations. Like earlier, optical models, dynamical models tend to assume simplified, single sized, smooth, and round, ring-constituting particles; a tendency is noted which confuses particles dominating optical properties with those that dominate dynamics.

Asteroid physical strengths, which critically affect the quantity of ejecta that can be placed in orbits evolving so as to cross that of the earth, vary widely due to initial composition and size, and subsequent geophysical and collisional evolutions. The meteorite yield on earth additionally depends on meteorite strength, which affects longevity in space and survival through the atmosphere. It is presently shown that meteorites may be primarily derived by cratering rather than disruptive fragmentation, and from large, main-belt asteroids rather than from small, earth-approaching bodies. The model presented combines a variety of evidence from various disciplines to yield results that are consistent with meteorite statistics, although no claim is made for the uniqueness of the model and many of its elements remain uncertain.

A discussion is presented on the gravitational interaction between ring systems and nearby satellites. A shepherd satellite lacking damping mechanisms will force oscillations in the motion of a ring particle that are symmetrical with respect to the encounter geometry. If such damping mechanisms as density wave propagation or a dissipative medium are present, a lag in particle response provides the asymmetry that exerts a net torque on the rings. While the torque on a given particle depends on the degree of damping, that dependence disappears when the torque is averaged over a range of orbits spanning resonances if the degree of damping is within a certain range. A torque that is much lower than the standard formula results from excessively weak or strong damping.

A cascaded resonance structure where planetesimal growth was accelerated at 2:1 interior and 1:2 exterior resonances, with an early-formed Jupiter producing runaway growth of planetary embryos, is hypothesized in a solar system formation model. The planetary embryos produce their own resonances, and these in turn lead to additional embryos in a process that successively propagates inwardly and outwardly to generate a resonant configuration of embryos. The early presence of Jupiter would in this way have imposed a harmonic structure on the accumulating planetesimal swarm. The positions of the planetary embryos can be moved into a degree of agreement with most of the present planetary positions which is comparable to that given by the Titius-Bode law, for the case of an accretion disk whose surface density obeys a power law of index -1.2.

The orbital motions of the Galilean satellites exert dramatic control over their physical properties (most notably Io's) through tidal heating. In turn, tidal dissipation in the satellites, as well as in Jupiter, has governed the evolution of the orbits and, in particular, of the Laplace resonance. If the system started out of the resonance and evolved into it, forced eccentricities would have increased with time. Hence, the tidal melting of Io and the cracking of Europa'a surface may have occurred relatively recently. This theory requires that Jupiter's tidal dissipation factor be greater than about two million, a rather low value (high rate of tidal dissipation) compared with most models of Jovian interior processes. Alternatively, the system may have started even deeper in the resonance than it is today, a scenario which is consistent with larger values of the tidal dissipation factor. This model, with its correspondingly large initial forced eccentricities, would imply (1) that Io melted early and fast, and may have remained molten with only a thin solid skin until the present and (2) that the water mantles of both Europa and Ganymede remained largely molten for considerably longer than Callisto did, but later froze as their eccentricities and tidal heating decreased.

The geometry of encounters between two bodies on independent Keplerian orbits around a third body is considered by a novel analysis, which avoids approximations made in previous studies. For the case of most of the applications considered, the formulas for collision frequencies and orbital element rates of change due to close approaches which comprise the method agree with past results. It is shown that the method can be extended to such other applications as the consideration of oscillations in orbital elements due to secular perturbations, and the computation of probabilities of escape from the system.

The fundamental geological and geophysical properties of asteroids were studied by theoretical and simulation studies of their collisional evolution. Numerical simulations incorporating realistic physical models were developed to study the collisional evolution of hypothetical asteroid populations over the age of the solar system. Ideas and models are constrained by the observed distributions of sizes, shapes, and spin rates in the asteroid belt, by properties of Hirayama families, and by experimental studies of cratering and collisional phenomena. It is suggested that many asteroids are gravitationally-bound "rubble piles.' Those that rotate rapidly may have nonspherical quasi-equilibrium shapes, such as ellipsoids or binaries. Through comparison of models with astronomical data, physical properties of these asteroids (including bulk density) are determined, and physical processes that have operated in the solar system in primordial and subsequent epochs are studied.

A three-dimensional numerical model is used to study the dynamical environment of Phobos and Deimos. Surface gravity, escape speeds, and ejecta impact contours are calculated both for the satellites at their present orbit distances, and for orbit distances they may have had in the past. Impact loci for Stickney ejecta are also calculated and compared with the observed groove locations in order to evaluate a possible secondary-impact origin for the grooves on Phobos. Attention is also given to the possible influence of the dynamical environment on shaping the satellites' surfaces.

The Laplace resonance among the Galilean satellites Io, Europa, and Ganymede is traditionally reduced to a pendulum-like dynamical problem by neglecting short-period variations of several orbital elements. However, some of these variations that can now be neglected may once have had longer periods, comparable to the 'pendulum' period, if the system was formerly in deep resonance (pairs of periods even closer to the ratio 2:1 than they are now). In that case, the dynamical system cannot be reduced to fewer than nine dimensions. The nine-dimensional system is linearized here in order to study small variations about equilibrium. When tidal effects are included, the resulting evolution is substantially the same as was indicated by the pendulum approach, except that evolution out of deep resonance is found to be somewhat slower than suggested by extrapolation of the pendulum results. This slower rate helps support the hypothesis that the system may have evolved from deep resonance.

It is noted that expressions for the apsidal precession rates to second order on J2 appear in the literature in at least three apparently mutually contradictory forms. The expressions are reconciled by accounting for subtle differences in the definitions of orbital elements.

Before the recent Pioneer probes, our knowledge of Jupiter's gravitational field was obtained from the motions of satellites and asteroids. The study of orbital perturbations of asteroids near the 2:1 commensurability yielded a value of the mass of the Jupiter system at least as precise as that obtained by the artificial probes. Precession of the inner satellites' orbits placed constraints on the harmonic coefficients J2 and J4. A correction to the satellite determination of J4 lowers its mean value closer to the Pioneer result. The orbital grouping among the outer satellites and the resonance among the Galilean satellites are described in detail, but the origins of these phenomena are not understood. However, recent research suggests that the explanation will be intimately associated with models of the origin and evolution of the planet itself.

Three of Uranus' satellites are involved in an interaction similar to the Laplace relation among the Galilean satellites of Jupiter. However, there are no pair-wise commensurabilities in the Uranus system as there are among the Galilean satellites. Thus analysis by Fourier expansion of disturbing functions becomes too unwieldy for practical calculation. Instead, the unexpanded perturbations are numerically averaged over a time scale short compared to the important variations in the Laplace relation. Perturbations of Miranda's orbit are estimated to be of observable magnitude for reasonable masses of Ariel and Umbriel.