Size Distribution Of Asteroids Research Articles

Hubble Asteroid Hunter

Context. Determining the size distribution of asteroids is key to understanding the collisional history and evolution of the inner Solar System. Aims. We aim to improve our knowledge of the size distribution of small asteroids in the main belt by determining the parallaxes of newly detected asteroids in the Hubble Space Telescope (HST) archive and subsequently their absolute magnitudes and sizes. Methods. Asteroids appear as curved trails in HST images because of the parallax induced by the fast orbital motion of the spacecraft. Taking into account the trajectory of this latter, the parallax effect can be computed to obtain the distance to the asteroids by fitting simulated trajectories to the observed trails. Using distance, we can obtain the absolute magnitude of an object and an estimation of its size assuming an albedo value, along with some boundaries for its orbital parameters. Results. In this work, we analyse a set of 632 serendipitously imaged asteroids found in the ESA HST archive. Images were captured with the ACS/WFC and WFC3/UVIS instruments. A machine learning algorithm (trained with the results of a citizen science project) was used to detect objects in these images as part of a previous study. Our raw data consist of 1031 asteroid trails from unknown objects, not matching any entries in the Minor Planet Center (MPC) database using their coordinates and imaging time. We also found 670 trails from known objects (objects featuring matching entries in the MPC). After an accuracy assessment and filtering process, our analysed HST asteroid set consists of 454 unknown objects and 178 known objects. We obtain a sample dominated by potential main belt objects featuring absolute magnitudes (H) mostly between 15 and 22 mag. The absolute magnitude cumulative distribution log N(H > H0) ∝ α log(H0) confirms the previously reported slope change for 15 < H < 18, from α ≈ 0.56 to α ≈ 0.26, maintained in our case down to absolute magnitudes of around H ≈ 20, and therefore expanding the previous result by approximately two magnitudes. Conclusions. HST archival observations can be used as an asteroid survey because the telescope pointings are statistically randomly oriented in the sky and cover long periods of time. They allow us to expand the current best samples of astronomical objects at no extra cost in regard to telescope time.

The influence of a static planetary atmosphere on spin transfer during pebble accretion

Context. Pebble accretion has been used to explain the small size of Mars, the heavy element contents of the gas giants, and the size distribution of asteroids. More recently, pebble accretion has been proposed as a means to explain not only the growth but also the prograde spin preference of most larger bodies in the Solar System. Pebble accretion could induce planetary and asteroid spin equal to or exceeding the spins currently measured. However, as these planetesimals grow, they start condensing the gas of the disc around them, forming an atmosphere within their Bondi radius. Aims. We study the effect an atmosphere has on the pebble orbits and spin build-up on the planet’s surface during pebble accretion in the extreme case of a static atmosphere. Pebble feedback to the gas is not taken into account. Methods. The equations of motion for pebbles in a planar, global frame with a planet and a central star were integrated using the AIS15 integrator of REBOUND. An adiabatic atmosphere was then placed around the planet, and the spin deposited on the planet’s surface was measured. These simulations were evaluated for different distances to the star, Stokes numbers, and planet masses. Results. In general, an atmosphere dampens the spin the planet’s surface receives by absorbing part of the angular momentum of the pebbles and circularising their orbits. This could prevent the excessive spin values predicted in some 3D pebble accretion simulations without an atmosphere. For planets larger than 0.5 M⊕, a stationary atmosphere absorbs all angular momentum, leaving no spin for the surface. Significant quantities of angular momentum are stored in the inner and intermediate atmosphere (<0.3 Bondi radii). Depending on the atmospheric and disc model, this spin could be transported either to the disc through atmospheric recycling or to the planet through drag between the surface and the atmosphere. Further research is required to quantify the spin transfer within the atmosphere.

Planetesimal Clearing and Size-dependent Asteroid Retention by Secular Resonance Sweeping during the Depletion of the Solar Nebula

Abstract The distribution of heavy elements is anomalously low in the asteroid main belt region compared with elsewhere in the solar system. Observational surveys also indicate a deficit in the number of small (≲50 km size) asteroids, which is two orders of magnitude lower than what is expected from the single power-law distribution that results from a collisional coagulation and fragmentation equilibrium. Here, we consider the possibility that a major fraction of the original asteroid population may have been cleared out by Jupiter’s secular resonance, as it swept through the main asteroid belt during the depletion of the solar nebula. This effect leads to the excitation of the asteroids’ orbital eccentricities. Concurrently, hydrodynamic drag and planet–disk tidal interaction effectively damp the eccentricities of sub-100 km-size and of super-lunar-size planetesimals, respectively. These combined effects lead to the asteroids’ orbital decay and clearing from the present-day main belt region (∼2.1–3.3 au). Eccentricity damping for the intermediate-size (50 to several hundreds of kilometers) planetesimals is less efficient than for small or large planetesimals. These objects therefore preferentially remain as main belt asteroids near their birthplaces, with modest asymptotic eccentricities. The smaller asteroids are the fragments of subsequent disruptive collisions at later times as suggested by the present-day asteroid families. This scenario provides a natural explanation for both the observed low surface density and the size distribution of asteroids in the main belt, without the need to invoke special planetesimal formation mechanisms. It also offers an explanation for the confined spatial extent of the terrestrial planet building blocks without the requirement of extensive migration of Jupiter, which is required in the grand-tack scenario.

How to form planetesimals from mm-sized chondrules and chondrule aggregates

The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than $\sim$100 km in size. Instead, planetesimals appear to form top-down, with large $100-1000$ km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We use a hydrodynamic code to model the interaction between solid particles and the gas inside a shearing box inside the disk, considering particle sizes from sub-millimeter-sized chondrules to meter-sized rocks. We find that particles down to millimeter sizes can form dense particle clouds through the run-away convergence of radial drift known as the streaming instability. We make a map of the range of conditions (strength of turbulence, particle mass-loading, disk mass, and distance to the star) which are prone to producing dense particle clumps. Finally, we estimate the distribution of collision speeds between mm-sized particles. We calculate the rate of sticking collisions and obtain a robust upper limit on the particle growth timescale of $\sim$$10^5$ years. This means that mm-sized chondrule aggregates can grow on a timescale much smaller than the disk accretion timescale ($\sim$$10^6 - 10^7$ years). Our results suggest a pathway from the mm-sized grains found in primitive meteorites to fully formed asteroids. We speculate that asteroids may form from a positive feedback loop in which coagualation leads to particle clumping driven by the streaming instability. This clumping, in turn reduces collision speeds and enhances coagulation.} Future simulations should model coagulation and the streaming instability together to explore this feedback loop further.

Characterization and Analysis of Near-Earth Objects via Lunar Impact Observations

Asteroid events such as the air blast above Chelyabinsk, Russia, in the spring of 2013 have highlighted the importance of understanding Earth's local asteroid population and the potential threat they pose. While much observational data exists for larger asteroids (those greater than 50 meters in diameter), comparatively little is known of the very small meteoroid population. This study utilized the non-illuminated part of the near side of the Moon as a detection screen upon which the faint flashes of small meteoroids hitting the lunar surface could be detected. Over 80 hours of observations were conducted between the fall of 2010 and the spring of 2013. The observed lunar area was determined nightly and used alongside the impact count to determine a meteoroid flux rate. Impact flashes were calibrated to extinction and color corrected reference stars to estimate the kinetic energies involved. Analysis indicated an average flux rate of 1.09×10−7km−2h−1, corresponding to 1 impactor larger than 3 centimeters in diameter observed every 30 minutes. Further, the size distribution dependence of small impactors was found to be consistent with the power law governing the larger-size meteoroid distribution. This data helps fix the low-end of the asteroid size distribution for solar system evolution models.

The Origin and Evolution of the Asteroid Belt—Implications for Vesta and Ceres

Vesta and Ceres are the largest members of the asteroid belt, surviving from the earliest phases of Solar System history. They formed at a time when the asteroid belt was much more massive than it is today and were witness to its dramatic evolution, where planetary embryos were formed and lost, where the collisional environment shifted from accretional to destructive, and where the current size distribution of asteroids was sculpted by mutual collisions and most of the asteroids originally present were lost by dynamical processes. Since these early times, the environment of the asteroid belt has become relatively quiescent, though over the long history of the Solar System the surfaces of Vesta and Ceres continue to record and be influenced by impacts, most notably the south polar cratering event on Vesta. As a consequence of such impacts, Vesta has contributed a significant family of asteroids to the main belt, which is the likely source of the HED meteorites on Earth. No similar contribution to the main belt (or meteorites) is evident for Ceres. Through studies of craters, the surfaces of these asteroids will offer an opportunity for Dawn to probe the modern population of small asteroids in a size regime not directly observable from Earth.

Nonuniform cratering of the Moon and a revised crater chronology of the inner Solar System

We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth–Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.

Subaru Lightcurve Observations of Sub-km-Sized Main-Belt Asteroids

Abstract The currently known spin period vs size distribution of asteroids includes a very small number of sub-km-sized main-belt asteroids (MBAs). In order to get a better understanding of such objects, we conducted lightcurve observations using the wide-field camera (Suprime-Cam) of the 8.2 m Subaru telescope in 2001 October. We surveyed a sky field of 34$'$$\times$ 27$'$ near opposition and the ecliptic, covering a time-span of 8.3 hr for a single night, and detected 127 asteroids down to a limiting magnitude of $R$$\approx$ 24.6 mag (at a level of 90% fractional detection). Since the majority of our lightcurves consisted of data points of only a few tens, we took an approach with an emphasis on searching for a dominant period of a lightcurve using two independent periodogram codes, to ascertain the mutual consistency of the obtained results. In an attempt to estimate their period errors, we made extensive simulations using artificial lightcurve data, and found that most errors do not exceed $\sim$ 0.1 hr; this level of errors is sufficiently small for the purposes of this survey observation. Out of 68 main-belt asteroids showing reliable spin periods, 33 are found to be fast-rotator MBAs, whose spin periods range from 0.5 to 2.2 hr (hereafter asteroids with periods $\lt$ 2.2 hr are abbreviated as FRAs). This result is the first observational confirmation on the existence of FRAs among sub-km MBAs; those detected small MBAs fill up the region that used to be almost void of asteroids in the spin period vs size distribution. Regarding the shapes of those objects, which were inferred from their lightcurve amplitudes, we found a tendency that FRAs are more spherical than non-FRAs. Cumulative size distributions of the FRAs and non FRAs are also compared, but revealing no clear difference.

Asteroid occultations today and tomorrow: toward the GAIA era

Context. Observation of star occultations is a powerful tool to determine shapes and sizes of asteroids. This is key information necessary for studying the evolution of the asteroid belt and to calibrate indirect methods of size determination, such as the models used to analyze thermal infrared observations. Up to now, the observation of asteroid occultations is an activity essentially secured by amateur astronomers equipped with small, portable equipments. However, the accuracy of the available ephemeris prevents accurate predictions of the occultation events for objects smaller than ∼100 km. Aims. We investigate current limits in predictability and observability of asteroid occultations, and we study their possible evolution in the future, when high accuracy asteroid orbits and star positions (such as those expected from the mission Gaia of the European Space Agency) will be available. Methods. We use a simple model for asteroid ephemeris uncertainties and numerical algorithms for estimating the limits imposed by the instruments, assuming realistic CCD performances and asteroid size distribution, to estimate the expected occultation rate under different conditions. Results. We show that high accuracy ephemerides which will be available in the future will extend toward much smaller asteroids the possibility of observing asteroid occultations, greatly increasing the number of events and objects involved. A complete set of size measurements down to ∼10 km main belt asteroids could be obtained in a few years, provided that a small network of ground-based 1m telescopes are devoted to occultation studies.

The random walk of Main Belt asteroids: orbital mobility by non-destructive collisions

Non-destructive collisions among Main Belt asteroids have effects on their orbits due to the transmission of linear momentum. The efficiency of this mechanism depends on several parameters which are currently poorly known. The most critical aspects are (i) the inventory and size distribution of small Main Belt asteroids, with sizes well below a few kilometres; (ii) the energy threshold for collisional fragmentation and fragment dispersion and (iii) the efficiency of linear momentum transfer. In spite of these difficulties, a general statistical model of the dynamical effects of non-destructive collisions can be developed, and is presented here. Based on this model, the consequences of different assumptions concerning the asteroid size distribution and collision physics are computed and discussed. Quantitative evaluations of the collisionally induced orbital mobility in different possible scenarios are presented.

The size distribution of asteroids in cometary orbits and related populations

Aims. In this work we study the cumulative size distribution of the population of asteroids in cometary orbits (ACOs), aiming to discriminate its cometary or asteroidal origin. Methods. The cumulative luminosity function was determined based on the absolute magnitudes of the ACOs. The cumulative size distribution was then derived and compared to that of possible sources of ACOs, such as the Trojans and Hilda asteroids and Jupiter family comets. The size distribution of the two sub-populations, NEOs and non-NEOs, identified by Licandro et al. (2005) were also analyzed. Results. The derived cumulative size distribution index of the ACO population is 2.55 ± 0.04. The two subpopulations have distinct indexes: −2.20 ± 0.04 and −2.45 ± 0.04 for the NEOs and non-NEOs, respectively. The first value is similar to that of the Trojans and Hilda asteroids and the second to the Jupiter family comets. The obtained values suggest that the non-NEO sub-population of ACOs can be composed of a significant fraction of dormant Jupiter family comets. On the other hand, the NEO sub-population is mostly formed by scattered objects from diverse sources, including main belt asteroids.

Collisional evolution of the asteroid belt

A new synthesis of asteroid collisional evolution is motivated by the question of whether most asteroids larger than ∼1 km size are strengthless gravitational aggregates (rubble piles). NEAR found Eros not to be a rubble pile, but a shattered collisional fragment, with a through-going fracture system, and an average of about 20 m regolith cover. Of four asteroids visited by spacecraft, none appears likely to be a rubble pile, except perhaps Mathilde. Nevertheless, current understanding of asteroid collisions and size-dependent strength, and the observed distribution of rotation rates versus size, have led to a theoretical consensus that many or most asteroids larger than 1 km should be rubble piles. Is Eros, the best-observed asteroid, highly unusual because it is not a rubble pile? Is Mathilde, if it is a rubble pile, like most asteroids? What would be expected for the small asteroid Itokawa, the MUSES-C sample return target? An asteroid size distribution is synthesized from the Minor Planet Center listing and results of the Sloan Digital Sky Survey, an Infrared Space Observatory survey, the Small Main-belt Asteroid Spectroscopic Survey and the Infrared Astronomical Satellite survey. A new picture emerges of asteroid collisional evolution, in which the well-known Dohnanyi result, that the size distribution tends toward a self-similar form with a 2.5-index power law, is overturned because of scale-dependent collision physics. Survival of a basaltic crust on Vesta can be accommodated, together with formation of many exposed metal cores. The lifetimes against destruction are estimated as 3 Gyr at the size of Eros, 10 Gyr at ten times that size, and 40 Gyr at the size of Vesta. Eros as a shattered collisional fragment is not highly unusual. The new picture reveals the new possibility of a transition size in the collisional state, where asteroids below 5 km size would be primarily collisional breakup fragments whereas much larger asteroids are mostly eroded or shattered survivors of collisions. In this case, well-defined families would be found in asteroids larger than about 5 km size, but for smaller asteroids, families may no longer be readily separated from a background population. Moreover, the measured boulder size distribution on Eros is re-interpreted as a sample of impactor size distributions in the asteroid belt. The regolith on Eros may result largely from the last giant impact, and the same may be true of Itokawa, in which case about a meter of regolith would be expected there. Even a small asteroid like Itokawa may be a shattered object with regolith cover.

Solar System Objects Observed in the Sloan Digital Sky Survey Commissioning Data

We discuss measurements of the properties of D13,000 asteroids detected in 500 deg2 of sky in the Sloan Digital Sky Survey (SDSS) commissioning data. The moving objects are detected in the magnitude range 14 r* 21.5, with a baseline of D5 minutes, resulting in typical velocity errors of D3%. Extensive tests show that the sample is at least 98% complete, with a contamination rate of less than 3%. We —nd that the size distribution of asteroids resembles a broken power law, independent of the heliocentric distance: D~2.3 for 0.4 km, and D~4 for 5

How Many Rubble Piles Are in the Asteroid Belt?

We have developed a new version of the code built by Campo Bagatin et al. (1994a, Planet. Space Sci. 42, 1079–1092; 1994b, ibid., 42, 1099–1107) and Campo Bagatin (1998, Ph.D. thesis, University of Valencia) to model the collisional evolution of the asteroid size distribution. The new code distinguishes between “intact,” unfractured asteroids that did not undergo catastrophic collisions and asteroids converted by energetic collisions into reaccumulated bodies, or “rubble piles.” The distinction can also be made on a physical ground by assigning different collisional parameters to the two kinds of objects, with the objective of simulating the different responses to energetic impacts that rubble piles may have—due to their different structure—in comparison to unshattered bodies. Rubble–piles abundance when such targets are supposed to transfer less kinetic energy to the fragments turns out to be generally higher than monolithic asteroids. We have run a number of simulations of the collisional evolution process to assess the size range where reaccumulated bodies should be expected to be abundant in the main asteroid belt. We find that this diameter range goes from about 10 to 100 km, but may extend to smaller or larger bodies, depending on the prevailing collisional response parameters, such as the strength of the material, the strength scaling law, the fraction of kinetic energy of the impact transfered to the fragments, and the reaccumulation model. Both the size range and the resulting fraction of rubble piles vary widely, depending on the input parameters, which reflects the large uncertainties still present in the modelization of high-velocity impact outcomes. In particular, the simulations that take into account the derived “hydrocode” scaling laws (Davis et al. 1994, Planet. Space Sci. 42, 599–610) show that nearly 100% of the main belt asteroids larger than a few kilometers should be reaccumulated objects. On the other hand, the present code shows that the scaling law recently proposed by Durda et al. (1998, Icarus 135, 431–440) produces almost no rubble pile. This scaling law was proposed to match the actual population of asteroids, which it fails to do if collisional processes are accounted for in a self-consistent way.

Collisional reaccumulation of asteroids

AbstractWe have developed a new version of the code developed by Campo Bagatin (1994a, b) to model the collisional evolution of the asteroid size distribution. The new code distinguishes between “intact”, unfractured asteroids and asteroids converted by energetic collisions into “piles of rubble”. We have run a number of simulations of the collisional evolution process to assess the size range where reaccumulated bodies should be expected to be abundant in the main asteroid belt. We find that this diameter range ranges from about 10 to 100 km, but may extend to smaller or larger bodies depending on the prevailing collisional response parameters.

Collisional Models and Scaling Laws: A New Interpretation of the Shape of the Main-Belt Asteroid Size Distribution

Numerical models of the collisional evolution of the main-belt asteroids lead to a new interpretation of the shape of the observed size distribution. Using recent hydrocode predictions of shattering and disruption criteria as starting points, we adjust the size–strength scaling relation for asteroidal strengths within our collisional model until a best least-squares fit to the observed size distribution is obtained. We show for the first time general agreement between the predictions of hydrocodes, results of numerical collisional models, and the observed size distribution of the main-belt population.

The Collisional Evolution of the Asteroid Belt and Its Contribution to the Zodiacal Cloud

We present a number of results from a numerical model of asteroid collisional evolution. Our results verify those of Dohnanyi (1969,J. Geophys. Res.74,2531–2554) and allow us to place constraints on the impact strengths of asteroids. The slope of the equilibrium size–frequency distribution is found to be dependent upon the shape of the size–strength scaling law. We find that pure size-independent and strain-rate scaling laws yield model size distributions which fail to match the observed mainbelt size distribution. An empirical modification has been made to the size–strength scaling law which allows us to match the observed asteroid size distribution and indicates a more gradual transition from strain-rate to gravity scaling. This result is not sensitive to the mass or shape of the initial asteroid population, but rather to the form of the strength scaling law: scaling laws have definite observational consequences. Asteroid families with material properties that differ from that of the average background population may evolve a size distribution with a different equilibrium slope than that of the background. Wave-like deviations from a strict power-law equilibrium size distribution result if the smallest particles in the population are removed at a rate significantly greater than that needed to maintain a Dohnanyi equilibrium slope. We find, however, that the observed small particle cutoff in the interplanetary dust complex is too gradual to support a significant wave. We suggest that any deviations from an equilibrium size distribution in the asteroid population are the result of stochastic cratering and fragmentation events which must occur during the course of collisional evolution. By determining the ratio of the area associated with the mainbelt asteroids to that associated with the prominent Hirayama asteroid families, our analysis indicates that the entire mainbelt asteroid population produces 3.4 ± 0.6 times as much dust as the prominent families alone. This result is compared with the ratio of areas needed to account for the zodiacal background and the IRAS dust bands as determined by analysis of IRAS data. We conclude that the entire asteroid population is responsible for at least one third of the dust in the entire zodiacal cloud.

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance inter asteroid al collisions. A numerical model is used, based on collision al physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collision al physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth’s cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.

Asteroid collisional evolution: results from current scaling algorithms

Acritical element for the understanding of asteroid collisional evolution is the scaling law needed to link laboratory impact experiments to the fragmentation of asteroidal bodies, ranging in size from meters to several hundreds of km. Early workers generally assumed a simple energy scaling, augmented by gravitational self-compression. Recent work on scaling theories has produced algorithms for computing the specific energy, Q ∗ , required to fragment bodies of various sizes, based on two approaches: the strain-rate scaling theory of Housen and Holsapple ( Icarus, 84, 226, 1990), based on dimensional analysis, and the 2-D hydrocode ealculations of Ryan and Melosh (1994). The strain-rate scaling predicts a deerease of about an Order of magnitude when going from laboratory sized bodies, 10 cm, to bodies a few tens of km in size, whereas for larger sizes Q ∗ , grows due to gravitational self- compression. The hydrocode results show an even stronger dependence on size, with a Q ∗ decrease of 2–3 orders of magnitude between 10 cm and 25 km, depending on the properties of the material. One possible way to discriminate among these different scaling laws is to examine which of them (if any) can predict the observed size distribution of asteroids from arbitrary starting populations and simultaneously satisfy other constraints on asteroid collisional history, such as the preservation of Vesta's basaltic crust. We have now explored this problem using the asteroid collisional evolution model of Davis et al. ( Asteroids II, pp. 805–826, University of Arizona Press, Tuscon, 1989), modified to take the different scaling algorithms as an input option. These model calculations show that a comparatively large value of Q ∗ is neede to match the observed size distribution and to preserve Vesta's crust. Simple energy scaling with gravitational self-compression in agreement with the laboratory experiments of Housen et al. ( Iearus 94, 180, 1991) does the best of reproducing the observed asteroid belf. Strain-rate scaling could also match the observations; however, extension of our knowledge of the main-belt population down to sizes of ∼ 1 km would test this agreement. The hydrocode scaling results generally predict weak asteroids and do not reproduce the size distribution, nor do they allow Vesta's crust to be preserved except in a highly improbable fashion. The hydrocode scaling of Q ∗ however, provides only a shattering threshold; work to derive the corresponding scaling law for the energy partitioning coefficient, needed to model the dispersal/reaccumulation of fragments, is under way.

The Injection of Asteroid Fragments into Resonances

Asteroidal fragments, coming from the main asteroid belt through chaotic dynamical routes, represent the likely source of most meteorites and near-Earth asteroids (NEAs). Many numerical experiments carried out over the past decade point to two specific source locations: the 3:1 mean motion resonance with Jupiter near 2.5 AU and the inner edge of the belt near 2.1 AU, where the dynamics is dominated by the g = g 6 (or v 6 ) secular resonance. We have tried to model and assess in a quantitative way the first part of the meteorite/NEA delivery process, namely the ejection of fragments from cratering and breakup events undergone by the existing asteroids as a consequence of impacts and the chance insertion of the escaping fragments into the "dangerous" strips of the phase space close to the resonances. For every parent asteroid, the efficiency of this process depends on several factors: (i) the mass vs ejection velocity distribution of the fragments, (ii) the escape velocity of the parent body, (iii) the Δ V required to approach a resonance surface, (iv) the width of the strip surrounding the resonance surfaces where chaotic eccentricity increases are possible, and (v) the amount of ejected material per unit time. The assumed number vs size distribution of asteroids at diameters <30 km is also critical in determining the overall flux. The results show that: (1) a large fraction of meteorites and NEAs could be generated by a small (≈1%) and possibly nonrepresentative fraction of the known asteroid population, mostly made of relatively large bodies located in the neighborhood of the two resonances; (2) both the 3:1 and the g = g 6 resonance are potentially effective channels for fragment collection and delivery, although they sample in a different way the orbital elements and the physical properties (size and taxonomic type) of the parent objects; and (3) the g = g 6 resonance is an efficient fragment collector not only near the inner edge of the belt, but also for several moderate-inclination (15° to 20°) asteroids at semimajor axes of about 2.4 and 2.7 AU. As for meteorite origin, within the existing uncertainties our model is consistent with the observed meteoroid flux on the Earth and suggests that a few large and possibly peculiar S-type asteroids and Vesta are the parent bodies of ordinary chondrites and basaltic achondrites, respectively. However, a poor knowledge of several key parameters and a lack of understanding of how a significant fraction of the asteroid fragments are launched at velocities of hundreds of meters per second prevent us from making claims stronger than those for the consistency of our model.