Critical crater diameter and asteroid impact seismology

Abstract— If impact stress reverberation is the primary gradational process on an asteroid at global scales, then the largest undegraded crater records an asteroid's seismological response. The critical crater diameter D_crit is defined as the smallest crater whose formation disrupts all previous craters globally up to its size; it is solved for by combining relationships for crater growth and for stress attenuation. The computation for D_crit gives a simple explanation for the curious observation that small asteroids have only modest undegraded craters, in comparison to their size, whereas large asteroids have giant undegraded craters. D_crit can even exceed the asteroid diameter, in which case all craters are “local” and the asteroid becomes crowded with giant craters. D_crit is the most recent crater to have formed on a blank slate; when it is equated to the measured diameter of the largest undegraded crater on known asteroids, peak particle velocities are found to attenuate with the 1.2–1.3 power of distance—less attenuative than strong shocks, and more characteristic of powerful seismic disturbances. This is to be expected, since global degradation can result from seismic (cm s^?1) particle velocities on small asteroids. Attenuation, as modeled, appears to be higher on asteroids known to be porous, although these are also bodies for which different crater scaling rules might apply.     

The geology of 433 Eros

Abstract— The global high‐resolution imaging of asteroid 433 Eros by the Near‐Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft has made it possible to develop the first comprehensive picture of the geology of a small S‐type asteroid. Eros displays a variety of surface features, and evidence of a substantial regolith. Large scale facets, grooves, and ridges indicate the presence of at least one global planar structure. Directional and superposition relations of smaller structural features suggest that fracturing has occurred throughout the object. As with other small objects, impact craters dominate the overall shape as well as the small‐scale topography of Eros. Depth/diameter ratios of craters on Eros average ～0.13, but the freshest craters approach lunar values of ～0.2. Ejecta block production from craters is highly variable; the majority of large blocks appear to have originated from one 7.6 km crater (Shoemaker). The interior morphology of craters does not reveal the influence of discrete mechanical boundaries at depth in the manner of craters formed on lunar mare regolith and on some parts of Phobos. This lack of mechanical boundaries, and the abundant evidence of regolith in nearly every high‐resolution image, suggests a gradation in the porosity and fracturing with depth. The density of small craters is deficient at sizes below ～200 m relative to predicted slopes of empirical saturation. This characteristic, which is also found on parts of Phobos and lunar highland areas, probably results from the efficient obliteration of small craters on a body with significant topographic slopes and a thick regolith. Eros displays a variety of regolith features, such as debris aprons, fine‐grained “ponded” deposits, talus cones, and bright and dark streamers on steep slopes indicative of efficient downslope movement of regolith. These processes serve to mix materials in the upper loose fragmental portion of the asteroid (regolith). In the instance of “ponded” materials and crater wall deposits, there is evidence of processes that segregate finer materials into discrete deposits. The NEAR observations have shown us that surface processes on small asteroids can be very complex and result in a wide variety of morphologic features and landforms that today seem exotic. Future missions to comets and asteroids will surely reveal still as yet unseen processes as well as give context to those discovered by the NEAR Shoemaker spacecraft.     

Impact cratering on porous asteroids

The increasing evidence that many or even most asteroids are rubble piles underscores the need to understand how porous structures respond to impact. Experiments are reported in which craters are formed in porous, crushable, silicate materials by impacts at 2 km/s. Target porosity ranged from 34 to 96%. The experiments were performed at elevated acceleration on a centrifuge to provide similarity conditions that reproduce the physics of the formation of asteroid craters as large as several tens of kilometers in diameter.Crater and ejecta blanket formation in these highly porous materials is found to be markedly different from that observed in typical dry soils of low or moderate porosity. In highly porous materials, the compaction of the target material introduces a new cratering mechanism. The ejection velocities are substantially lower than those for impacts in less porous materials. The experiments imply that, while small craters on porous asteroids should produce ejecta blankets in the usual fashion, large craters form without ejecta blankets. In large impacts, most of the ejected material never escapes the crater. However, a significant crater bowl remains because of the volume created by permanent compaction of the target material. Over time, multiple cratering events can significantly increase the global density of an asteroid.     

Impact cratering and break up of the small bodies of the Solar System

We consider the largest impact craters observed on small satellites and asteroids and the impact disruption of such bodies. Observational data are considered from 21 impact-like structures on 13 satellites and 8 asteroids (target body radii in the range 0.7-265 km). If the radius of the target body is R and the diameter of the largest crater observed on this body D, the ratio D/R is then the main observational parameter of interest. This is found on the observed bodies and compared to data obtained in the laboratory. Taking the largest observed value for D/R as a proxy for the ratio Dc/R (where Dc is the diameter of the largest crater that can be formed on a body without shattering it) it was found that for the observed icy satellites Dc,icy≈1.2R and for the asteroids and the rocky satellites Dc,rocky≈1.6R. In laboratory experiments with ice targets at impactor speeds of 1 to 3 km s⁻¹ we obtained Dc,icy≈1.64R.     

A survey of possible impact structures on 25143 Itokawa

We determined the morphologies and dimensions of possible impact craters on the surface of Asteroid 25143 Itokawa from images taken by the Hayabusa spacecraft. Circular depressions, circular features with flat floors or convex floors, and circular features with smooth surfaces were identified as possible craters. The survey identified 38 candidates with widely varying morphologies including rough, smooth and saddle-shaped floors, a lack of raised rims and fresh material exposures. The average depth/diameter ratio was 0.08±0.03: these craters are very shallow relative to craters observed on other asteroids. These shallow craters are a result of (1) target curvature influencing the cratering process, (2) raised rim not being generated by this process, and (3) fines infilling the craters. As many of the crater candidates have an unusual appearance, we used a classification scheme that reflects the likelihood of an observed candidate's formation by a hypervelocity impact. We considered a variety of alternative interpretations while developing this scheme, including inherited features from a proto-Itokawa, spall scars created by the disruption of the proto-Itokawa, spall scars following the formation of a large crater on Itokawa itself, and apparent depressions due to random arrangements of boulders. The size-frequency distribution of the crater candidates was close to the empirical saturation line at the largest diameter, and then decline with decreasing diameter.     

The global effects of impact-induced seismic activity on fractured asteroid surface morphology

Impact-induced seismic vibrations have long been suspected of being an important surface modification process on small satellites and asteroids. In this study, we use a series of linked seismic and geomorphic models to investigate the process in detail. We begin by developing a basic theory for the propagation of seismic energy in a highly fractured asteroid, and we use this theory to model the global vibrations experienced on the surface of an asteroid following an impact. These synthetic seismograms are then applied to a model of regolith resting on a slope, and the resulting downslope motion is computed for a full range of impactor sizes. Next, this computed downslope regolith flow is used in a morphological model of impact crater degradation and erasure, showing how topographic erosion accumulates as a function of time and the number of impacts. Finally, these results are applied in a stochastic cratering model for the surface of an Eros-like body (same volume and surface area as the asteroid), with craters formed by impacts and then erased by the effects of superposing craters, ejecta coverage, and seismic shakedown. This simulation shows good agreement with the observed 433 Eros cratering record at a Main Belt exposure age of 400±200 Myr, including the observed paucity of small craters. The lowered equilibrium numbers (loss rate = production rate) for craters less than ∼100 m in diameter is a direct result of seismic erasure, which requires less than a meter of mobilized regolith to reproduce the NEAR observations. This study also points to an upper limit on asteroid size for experiencing global, surface-modifying, seismic effects from individual impacts of about 70-100 km (depending upon asteroid seismic properties). Larger asteroids will experience only localized (regional) seismic effects from individual impacts.     

Constraints on the role of impact heating and melting in asteroids

Abstract— Imaging of asteroids Gaspra and Ida and laboratory studies of asteroidal meteorites show that impacts undoubtedly played an important role in the histories of asteroids and resulted in shock metamorphism and the formation of breccias and melt rocks. However, in recent years, impact has also been called upon by numerous authors as the heat source for some of the major geological processes that took place on asteroids, such as global thermal metamorphism of chondrite parent bodies and a variety of melting and igneous events. The latter were proposed to explain the origin of ureilites, aubrites, mesosiderites, the Eagle Station pallasites, acapulcoites, lodranites, and the IAB, IIICD, and HE irons. We considered fundamental observations from terrestrial impact craters, combined with results from laboratory shock experiments and theoretical considerations, to evaluate the efficiency of impact heating and melting of asteroids. Studies of terrestrial impact craters and relevant shock experiments suggest that impact heating of asteroids will produce two types of impact melts: (1) large-scale whole rock melts (total melts, not partial melts) at high shock pressure and (2) localized melts formed at the scale of the mineral constituents (mineral specific or grain boundary melting) at intermediate shock pressures. The localized melts form minuscule amounts of melt that quench and solidify in situ, thus preventing them from pooling into larger melt bodies. Partial melting as defined in petrology has not been observed in natural and experimental shock metamorphism and is thermodynamically impossible in a shock wave-induced transient compression of rocks. The total impact melts produced represent a minuscule portion of the displaced rock volume of the parent crater. Internal differentiation by fractional crystallization is absent in impact melt sheets of craters of sizes that can be tolerated by asteroids, and impact melt rocks are usually clast-laden. Thermal metamorphism of country rocks by impact is extremely minor. Experimental and theoretical considerations suggest that (1) single disruptive impacts cannot raise the average global temperature of strength- or gravity-dominated asteroids by more than a few degrees; (2) cumulative global heating of asteroids by multiple impacts is ineffective for asteroids less than a few hundred kilometers in diameter; (3) small crater size, low gravity, and low impact velocity suggest that impact melt volume in single asteroidal impacts is a very small (0.01–0.1%) fraction of the total displaced crater volume; (4) total impact melt volume formed during the typical lifetime of an asteroid is a small fraction (<0.001) of the volume of impact-generated debris; and (5) much of the impact melt generated on asteroidal targets is ejected from craters with velocities greater than escape velocity and, thus, not retained on the asteroid. The inescapable conclusion from these observations and calculations is that impacts cannot have been the heat source for the origin of the meteorite types listed above, and we must turn to processes other than impact, such as decay of short-lived radionuclides or electromagnetic induction during an early T-tauri phase of the Sun to explain heating and melting of the parent bodies of these meteorites.     

Ejecta–megaregolith accumulation on planetesimals and large asteroids

Megaregolith accumulation can have important thermal consequences for bodies that lose heat by conduction, as vacuous porosity of the kind observed in the lunar megaregolith lowers thermal conductivity by a factor of 10. I have modeled global average ejecta accumulation as a function of the largest impact size, with no explicit modeling of time. In conjunction with an assumed cratering size‐distribution exponent b, the largest crater constrains the sizes of all other craters that significantly contribute to a megaregolith. The largest impactor mass ratio is a major fraction of the catastrophic‐disruption mass ratio, and in general the largest crater’s diameter is close to the target’s diameter. Total accumulation is roughly 1–5% of (and proportional to) the target’s radius. Global accumulations estimated by this approach are higher than in the classic Housen et al. (1979) study by a factor of roughly 10. This revision is caused mainly by higher (typical) largest crater size. For b ～ 2, the single largest crater typically contributes close to 50% of the total of new (nonrecycled) ejecta. Megaregolith can be destroyed by sintering, a process whose pressure sensitivity makes it effective at lower temperature on larger bodies. Planetesimals ～100 km in diameter may be surprisingly well suited (about as well suited as bodies two to three times larger in diameter) for attaining temperatures conducive to widespread melting. A water‐rich composition may be a significant disadvantage in terms of planetesimal heating, as the shallow interior may be densified by aqueous metamorphism, and will have a low sintering temperature.     

The cratering history of asteroid (2867) Steins

The cratering history of main belt asteroid (2867) Steins has been investigated using OSIRIS imagery acquired during the Rosetta flyby that took place on the 5th of September 2008. For this purpose, we applied current models describing the formation and evolution of main belt asteroids, that provide the rate and velocity distributions of impactors. These models coupled with appropriate crater scaling laws, allow the cratering history to be estimated. Hence, we derive Steins’ cratering retention age, namely the time lapsed since its formation or global surface reset. We also investigate the influence of various factors—like bulk structure and crater erasing—on the estimated age, which spans from a few hundred Myrs to more than 1 Gyr, depending on the adopted scaling law and asteroid physical parameters. Moreover, a marked lack of craters smaller than about 0.6 km has been found and interpreted as a result of a peculiar evolution of Steins cratering record, possibly related either to the formation of the 2.1 km wide impact crater near the south pole or to YORP reshaping.     

小天体离散元仿真软件的搭建与测试

小天体探测是当今太阳系探测的一大热点, 对小行星演化的研究有助于人们了解太阳系的起源. 演化研究的一项重要内容是小天体结构的演化, 即小天体在多种力学机制作用下自身形状与结构的演化. 在小天体碎石堆结构的假设之下, 一种比较常见的模拟小天体结构演化的方法是离散元仿真算法(Discrete Element Method, DEM), 目前国内外有数个团队开发了相关算法软件. 本文介绍了团队开发的《基于DEM仿真算法的多粒子系统模拟软件》的基础理论、实现方法以及加速算法, 并使用二体接触模型、声速传播仿真、小行星内部压强、小行星旋转稳定性仿真算例验证了算法的可靠性.     

Meteoritic and other constraints on the internal structure and impact history of small asteroids

Studies of the internal structure of asteroids, which are crucial for understanding their impact history and for hazard mitigation, appear to be in conflict for the S-type asteroids, Eros, Gaspra, and Ida. Spacecraft images and geophysical data show that they are fractured, coherent bodies, whereas models of catastrophic asteroidal impacts, family and satellite formation, and studies of asteroid spin rates, and other diverse properties of asteroids and planetary craters suggest that such asteroids are gravitationally bound aggregates of rubble. These conflicting views may be reconciled if 10-50 km S-type asteroids formed as rubble piles, but were later consolidated into coherent bodies. Many meteorites are breccias that testify to a long history of impact fragmentation and consolidation by alteration, metamorphism, igneous and impact processes. Ordinary chondrites, which are the best analogs for S asteroids, are commonly breccias. Some may have formed in cratering events, but many appear to have formed during disruption and reaccretion of their parent asteroids. Some breccias were lithified during metamorphism, and a few were lithified by injected impact melt, but most are regolith and fragmental breccias that were lithified by mild or moderate shock, like their lunar analogs. Shock experiments show that porous chondritic powders can be consolidated during mild shock by small amounts of silicate melt that glues grains together, and by friction and pressure welding of silicate and metallic Fe,Ni grains. We suggest that the same processes that converted impact debris into meteorite breccias also consolidated asteroidal rubble. Internal voids would be partly filled with regolith by impact-induced seismic shaking. Consolidation of this material beneath large craters would lithify asteroidal rubble to form a more coherent body. Fractures on Ida that were created by antipodal impacts and are concentrated in and near large craters, and small positive gravity anomalies associated with the Psyche and Himeros craters on Eros, are consistent with this concept. Spin data suggest that smaller asteroids 0.6-6 km in size are unconsolidated rubble piles. C-type asteroids, which are more porous than S-types, and their analogs, the volatile-rich carbonaceous chondrites, were probably not lithified by shock.     

Asteroids and meteorites: Parent bodies and delivered samples

Meteorites may be pieces of main-belt asteroids, derived by cratering collisions. The physical strength of an asteroid critically affects the quantity of ejecta that can be placed in orbits (probably resonant) that evolve to cross the Earth's. Asteroid strengths very widely due to initial composition and size (e.g., weak carbonaceous material or strong rock), subsequent geophysical evolution (e.g., formation of a strong iron core), and subsequent collisional evolution (e.g., conversion of a strong rocky body into a weak rubble pile). The meteorite yield on Earth further depends on meteorite strength, which affects longevity in space and survival through the atmosphere. We show that meteorites may be derived mainly by cratering rather than by disruptive fragmentation and from large main-belt asteroids rather than from small, Earth-approaching bodies. The model combines a wide variety of evidence from various disciplines to yield results consistent with meteorite statistics. However, no claim is made for uniqueness of this model, and many elements still admit considerable uncertainty.     

Asteroidal regoliths

We develop a physical model for the evolution of regoliths on small bodies and apply it to the asteroids and meteorite parent bodies. The model considers global deposition of that fraction of cratering ejecta that is not lost to space. It follows the build up of regolith on a typical region, removed from the larger craters which are the source of most regolith blankets. Later in the evolution, larger craters saturate the surface and are incorporated into the typical region; their net ejection of materials to space causes the elevation of the typical region to decrease and once-buried regolith becomes susceptible to ejection or gardening. The model is applied to cases of both strong, cohesive bodies and to bodies of weak, unconsolidated materials. Evolution of regolith depths and gardening rates are followed until a sufficiently large impact occurs that fractures the entire asteroid. (Larger asteroids are not dispersed, however, and evolve mergaregoliths from multiple generations of surficial regoliths mixed into their interiors.) We find that large, strong asteroids generate surficial regoliths of a few kilometers depth while strong asteroids smaller than 10-km diameter generate negligible regoliths. Our model does not treat large, weak asteroids, because their cratering ejecta fail to surround such bodies; regolith evolution is probably similar to that of the Moon. Small, weak asteroids of 1- to 10-km diameter generate centimeter- to meter-scale regoliths. In all cases studied, blanketing rates exceed excavation rates, so asteroid regoliths are rarely, if ever, gardened and should be very immature measured by lunar standards. They should exhibit many of the characteristics of the brecciated, gas-rich meteorites; intact foreign clasts, relatively low-exposure durations to galactic and solar cosmic rays low solar gas contents, minimal evidence for vitrification and agglutinate formation, etc. Both large, strong asteroids and small, weak ones provide regolith environments compatible with those inferred for the parent bodies of brecciated meteorites. But from volumetric calculations, we conclude that most brecciated meteorites formed on the surfaces of, and were recycled through the interiors of, parent bodies at least several tens of kilometers in diameter. The implications of our regolith model are consistent with properties inferred for asteroid regoliths from a variety of astronomical measurements of asteroids, although such data do not constrain regolith properties nearly as strongly as meteoritical evidence Our picture of substantial asteroidal regoliths produced predominantly by blanketing differs from earlier hypotheses that asteroidal regoliths might be thin or absent and that short surface exposure of asteroidal materials is due chiefly to erosion rather than blanketing.     

Cratering rates on the Galilean satellites

We exploit recent theoretical advances toward the origin and orbital evolution of comets and asteroids to obtain revised estimates for cratering rates in the jovian system. We find that most, probably more than 90%, of the craters on the Galilean satellites are caused by the impact of Jupiter-family comets (JFCs). These are comets with short periods, in generally low-inclination orbits, whose dynamics are dominated by Jupiter. Nearly isotropic comets (long period and Halley-type) contribute at the 1-10% level. Trojan asteroids might also be important at the 1-10% level; if they are important, they would be especially important for smaller craters. Main belt asteroids are currently unimportant, as each 20-km crater made on Ganymede implies the disruption of a 200-km diameter parental asteroid, a destruction rate far beyond the resources of today's asteroid belt. Twenty-kilometer diameter craters are made by kilometer-size impactors; such events occur on a Galilean satellite about once in a million years. The paucity of 20-km craters on Europa indicates that its surface is of order 10 Ma. Lightly cratered surfaces on Ganymede are nominally of order 0.5-1.0 Ga. The uncertainty in these estimates is about a factor of five. Callisto is old, probably more than 4 Ga. It is too heavily cratered to be accounted for by the current flux of JFCs. The lack of pronounced apex-antapex asymmetries on Ganymede may be compatible with crater equilibrium, but it is more easily understood as evidence for nonsynchronous rotation of an icy carapace.     

A plausible cause of the late heavy bombardment

Abstract— We show that at the end of the main accretional period of the terrestrial planets, a few percent of the initial planetesimal population in the 1–2 AU zone is left on highly‐inclined orbits in the inner solar system. The final depletion of this leftover population would cause an extended bombardment of all of the terrestrial planets, slowly decaying with a timescale on the order of 60 Ma. Because of the large impact velocities dictated by the high inclinations, these projectiles would produce craters much larger than those formed by asteroids of equal size on typical current near‐Earth asteroid orbits: on the Moon, basins could have been formed by bodies as small as 20 km in diameter, and 10 km craters could be produced by 400 m impactors. To account for the observed lunar crater record, the initial population of highly‐inclined leftovers would need to be a few times that presently in the main asteroid belt, at all sizes, in agreement with the simulations of the primordial sculpting of both these populations. If a terminal lunar cataclysm (a spike in the crater record ～3.9 Ga ago) really occurred on the Moon, it was not caused by the highly‐inclined leftover population, because of the monotonic decay of the latter.     

Geophysical signature of Målingen,the minor crater of the Lockne–Målingen doublet impact structure

Målingen is the 0.7 km wide minor crater associated to the 10 times larger Lockne crater in the unique Lockne–Målingen doublet. The craters formed at 458 Ma by the impact of a binary asteroid related to the well-known 470 Ma Main Belt breakup event responsible for a large number of Ordovician craters and fossil meteorites. The binary asteroid struck a target sequence including ~500 m of sea water, ~80 m of limestone, ~30 m of dark mud, and a peneplainized Precambrian crystalline basement. Although the Lockne crater has been extensively studied by core drillings and geophysics, little is known about the subsurface morphology of Målingen. We performed magnetic susceptibility and remanence, as well as density, measurements combined with gravity, and magnetic field surveys over the crater and its close vicinity as a base for forward magnetic and gravity modeling. The interior of the crater shows a general magnetic low of 90–100 nT broken by a clustered set of high-amplitude, short wavelength anomalies caused by bodies of mafic rock in the target below the crater and as allogenic blocks in the crater infill. The gravity shows a general −1.4 mgal anomaly over the crater caused by low-density breccia infill and fractured crystalline rocks below the crater floor. The modeling also revealed a slightly asymmetrical shape of the crater that together with the irregular ejecta distribution supports an oblique impact from the east, which is consistent with the direction of impact suggested for the Lockne crater.     

Grazing Impacts Upon Earth’s Surface: Towards an Understanding of the Rio Cuarto Crater Field

The origin of the Rio Cuarto crater field, Argentina has been widely debated since the early 1990s when it was first brought to public attention. In a binary on–off sense, however, the craters are either of a terrestrial origin or they formed via a large asteroid impact. While there are distinct arguments in favour of the former option being the correct interpretation, it is the latter possibility that is principally investigated here, and five distinct impact formation models are described. Of the impact scenarios it is found that the most workable model, although based upon a set of fine-tuned initial conditions, is that in which a large, 100–150-m initial diameter asteroid, entered Earth’s atmosphere on a shallow angle path that resulted in temporary capture. In this specific situation a multiple-thousand kilometer long flight path enables the asteroid to survive atmospheric passage, without suffering significant fragmentation, and to impact the ground as a largely coherent mass. Although the odds against such an impact occurring are extremely small, the crater field may nonetheless be interpreted as having potentially formed via a very low-angle, smaller than 5° to the horizon, impact with a ground contact speed of order 5 km/s. Under this scenario, as originally suggested by Schultz and Lianza (Nature 355:234, 1992), the largest of the craters (crater A) in the Rio Cuarto structure was produced in the initial ground impact, and the additional, smaller craters are interpreted as being formed through the down-range transport of decapitated impactor material and crater A ejecta.     

Fundamentally distinct outcomes of asteroid collisional evolution and catastrophic disruption

The outcomes of asteroid collisional evolution are presently unclear: are most asteroids larger than 1 km size gravitational aggregates reaccreted from fragments of a parent body that was collisionally disrupted, while much smaller asteroids are collisional shards that were never completely disrupted? The 16 km mean diameter S-type asteroid 433 Eros, visited by the NEAR mission, has surface geology consistent with being a fractured shard. A ubiquitous fabric of linear structural features is found on the surface of Eros and probably indicates a globally consolidated structure beneath its regolith cover. Despite the differences in absolute scale and in lighting conditions for NEAR and Hayabusa, similar features should have been found on 25143 Itokawa if present. This much smaller, 320 m diameter S-asteroid was visited by the Hayabusa spacecraft. Comparative analyses of Itokawa and Eros geology reveal fundamental differences, and interpretation of Eros geology is illuminated by comparison with Itokawa. Itokawa lacks a global lineament fabric, and its blocks, craters, and regolith may be inconsistent with formation and evolution as a fractured shard, unlike Eros. An object as small as Itokawa can form as a rubble pile, while much larger Eros formed as a fractured shard. Itokawa is not a scaled-down Eros, but formed by catastrophic disruption and reaccumulation.     

The shape of asteroids: Theoretical considerations

Theoretical consideration and observations by other authors indicate that small asteroids are capable of maintaining irregular shapes, notably the shape of a cigar and even of a dumb-bell. This paper presents a model which describes the changes in the shape of an asteroid due to collisions of smaller objects (meteoroids) with the asteroid. The following assumptions must be approximately valid: (1) collisions are not uncommon; (2) collisions between a (relatively) large asteroid and small objects (meteroids) are more common than collisions between asteroids; (3) the cumulative probability of the collision of a meteoroid on a point on the surface of an asteroid is proportional to the zenith angle of the horizon as seen by that point; (4) obliquities of all but the major asteroids are random, so that there is not a preferred side on which collisions occur; (5) a considerable percentage of collision ejecta achieves escape velocity; and (6) the rate of erosion of each point on the surface of an asteroid is proportional to the cumulative probability of collision.Generalized conclusions that are obtained from the computer running of the model indicate that both cigars and dumb-bells are possible outcomes. Sharp corners are smoothed away, the radius of curvature of rounded surfaces increases to the point of going from convexity to concavity, and flat surfaces develop into gentle concavities.Collisions of an asteroid with an object of sufficient size such that the impact causes the breakage of the asteroid or the formation of a large crater, are not discussed in this paper. Previous work, however, suggests that the crater will undergo geomorphological changes of different geometry than a similar crater on the Moon.     

The origin of SNC meteorites: An alternative to Mars

Shergottites, Nakhlites, and Chassignites (SNC) are a small group of achondrites with crystallization ages of approximately 1.3 AE. Although it has recently been postulated the these meteorites came from Mars, the dynamical difficulties of ejecting large meteorites from a major planet have caused us to examine the alternative possibility that they crystallized from an impact melt formed on a large asteroid. The kinetic energy necessary to produce a crater of a given size is estimated; it is postulated that 25% of this energy is partitioned into heat, and the heat is distributed in this model in a pattern suggested by the impact melt distribution in Brent Crater and the radioactivity distribution in Cactus nucelear explosion crater. The time evolution of the temperature by heat conduction for several locations around the crater is computed. Crystallization times for the more deeply buried impact melts are form 5 × 10⁴ years for 60-km-diameter craters and increase for larger craters. These times are long enough for the observed cumulate textures to develop. Once solidified, these rocks may be ejected from the asteroid by subsequent cratering events. Since asteroidal escape velocities are low, ejection may be accomplished by shock pressures too low to produce petrologically detectable shock features. The SNC meteorites could thus have originated in the asteroid belt, their young crystallization ages being due to melting induced by impacts occurring on asteroids long after condensation from the solar nebula. This scenario avoids the dynamical difficulties of a major planet origin, but raises questions of how the SNC's acquired their chemical and REE characteristics. To date, there seems to be no internally consistent model for the origin of these strange meteorites. The impact melt hypothesis is offered as a rational alternative to a Martian origin. Neither hypothesis explains all the problems.