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Particle-particle and particle-gas processes significantly impact planetary precursors such as dust aggregates and planetesimals. We investigate gas permeability ($\kappa$) in 12 granular samples, mimicking planetesimal dust regoliths. Using parabolic flights, this study assesses how gravitational compression -- and lack thereof -- influences gas permeation, impacting the equilibrium state of low-gravity objects. Transitioning between micro- and hyper-gravity induces granular sedimentation dynamics, revealing collective dust-grain aerodynamics. Our experiments measure $\kappa$ across Knudsen number (Kn) ranges, reflecting transitional flow. Using mass and momentum conservation, we derive $\kappa$ and calculate pressure gradients within the granular matrix. Key findings: 1. As confinement pressure increases with gravitational load and mass flow, $\kappa$ and average pore space decrease. This implies that a planetesimal's unique dust-compaction history limits sub-surface volatile outflows. 2. The derived pressure gradient enables tensile strength determination for asteroid regolith simulants with cohesion. This offers a unique approach to studying dust-layer properties when suspended in confinement pressures comparable to the equilibrium state on planetesimals surfaces, which will be valuable for modelling their collisional evolution. 3. We observe a dynamical flow symmetry breaking when granular material moves against the pressure gradient. This occurs even at low Reynolds numbers, suggesting that Stokes numbers for drifting dust aggregates near the Stokes-Epstein transition require a drag force modification based on permeability.

Binary asteroid formation is a highly complex process, which has been highlighted with recent observations of satellites with unexpected shapes, such as the oblate Dimorphos by the NASA DART mission and the contact binary Selam by NASA's Lucy mission. There is no clear consensus on which dynamical mechanisms determine the final shape of these objects. In turn, we explore a formation pathway where spin-up and rotational failure of a rubble pile asteroid lead to mass-shedding and a wide circumasteroidal debris disk in which the satellite forms. Using a combination of smooth-particle hydrodynamical and N-body simulations, we study the dynamical evolution in detail. We find that a debris disk containing matter corresponding to a few percent of the primary asteroid mass extending beyond the fluid Roche limit can consistently form both oblate and bilobate satellites via a series of tidal encounters with the primary body and mergers with other gravitational aggregates. Principally, satellites end up prolate (elongated) and on synchronous orbits, accreting mainly in a radial direction while tides from the primary asteroid keep the shape intact. However, close encounters and mergers can break the orbital state, leading to orbital migration and deformation. Satellite-satellite impacts occurring in this regime have lower impact velocities than merger-driven moon formation in e.g. planetary rings, leading to soft impacts between differently sized, non-spherical bodies. The resulting post-merger shape of the satellite is highly dependent on the impact geometry. Only moons having experienced a prior mild or catastrophic tidal disruption during a close encounter with the primary asteroid can become oblate spheroids, which is consistent with the predominantly prolate observed population of binary asteroid satellites., Comment: 37 pages, 24 figures, 3 tables. Accepted for publication in Icarus

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense, intended to validate kinetic impact as a means of asteroid deflection. Here we report the first determination of the momentum transferred to an asteroid by kinetic impact. Based on the change in the binary orbit period, we find an instantaneous reduction in Dimorphos's along-track orbital velocity component of 2.70 +/- 0.10 mm/s, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact. For a Dimorphos bulk density range of 1,500 to 3,300 kg/m$^3$, we find that the expected value of the momentum enhancement factor, $\beta$, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg/m$^3$, $\beta$= 3.61 +0.19/-0.25 (1 $\sigma$). These $\beta$ values indicate that significantly more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos., Comment: accepted by Nature

While no known asteroid poses a threat to Earth for at least the next century, the catalog of near-Earth asteroids is incomplete for objects whose impacts would produce regional devastation. Several approaches have been proposed to potentially prevent an asteroid impact with Earth by deflecting or disrupting an asteroid. A test of kinetic impact technology was identified as the highest priority space mission related to asteroid mitigation. NASA's Double Asteroid Redirection Test (DART) mission is the first full-scale test of kinetic impact technology. The mission's target asteroid was Dimorphos, the secondary member of the S-type binary near-Earth asteroid (65803) Didymos. This binary asteroid system was chosen to enable ground-based telescopes to quantify the asteroid deflection caused by DART's impact. While past missions have utilized impactors to investigate the properties of small bodies those earlier missions were not intended to deflect their targets and did not achieve measurable deflections. Here we report the DART spacecraft's autonomous kinetic impact into Dimorphos and reconstruct the impact event, including the timeline leading to impact, the location and nature of the DART impact site, and the size and shape of Dimorphos. The successful impact of the DART spacecraft with Dimorphos and the resulting change in Dimorphos's orbit demonstrates that kinetic impactor technology is a viable technique to potentially defend Earth if necessary., Comment: Accepted by Nature

Some active asteroids have been proposed to be the result of impact events. Because active asteroids are generally discovered serendipitously only after their tail formation, the process of the impact ejecta evolving into a tail has never been directly observed. NASA's Double Asteroid Redirection Test (DART) mission, apart from having successfully changed the orbital period of Dimorphos, demonstrated the activation process of an asteroid from an impact under precisely known impact conditions. Here we report the observations of the DART impact ejecta with the Hubble Space Telescope (HST) from impact time T+15 minutes to T+18.5 days at spatial resolutions of ~2.1 km per pixel. Our observations reveal a complex evolution of ejecta, which is first dominated by the gravitational interaction between the Didymos binary system and the ejected dust and later by solar radiation pressure. The lowest-speed ejecta dispersed via a sustained tail that displayed a consistent morphology with previously observed asteroid tails thought to be produced by impact. The ejecta evolution following DART's controlled impact experiment thus provides a framework for understanding the fundamental mechanisms acting on asteroids disrupted by natural impact., Comment: accepted by Nature

The Hayabusa2 mission impact experiment on asteroid Ryugu created an unexpectedly large crater. The associated regime of low-gravity, low-strength cratering remained largely unexplored so far, because these impact conditions cannot be re-created in laboratory experiments on Earth. Here we show that the target cohesion may be very low and the impact probably occurred in the transitional cratering regime, between strength and gravity. For such conditions, our numerical simulations are able to reproduce the outcome of the impact on Ryugu, including the effects of boulders originally located near the impact point. Consistent with most recent analysis of Ryugu and Bennu, cratering scaling-laws derived from our results suggest that surfaces of small asteroids must be very young. However, our results also show that the cratering efficiency can be strongly affected by the presence of a very small amount of cohesion. Consequently, the varying ages of different geological surface units on Ryugu may be due to the influence of cohesion.

A giant impact is commonly thought to explain the dramatic contrast in elevation and crustal thickness between the two hemispheres of Mars known as the "Martian Dichotomy". Initially, this scenario referred to an impact in the northern hemisphere that would lead to a huge impact basin (dubbed the "Borealis Basin"), while more recent work has instead suggested a hybrid origin that produces the Dichotomy through impact-induced crust-production. The majority of these studies have relied upon impact scaling-laws inaccurate at such large-scales, however, and those that have included realistic impact models have utilised over-simplified geophysical models and neglected any material strength. Here we use a large suite of strength-including smoothed-particle hydrodynamics (SPH) impact simulations coupled with a more sophisticated geophysical scheme of crust production and primordial crust to simultaneously investigate the feasibility of a giant impact on either hemisphere of Mars to have produced its dichotomous crust distribution, and utilise spherical harmonic analysis to identify the best-fitting cases. We find that the canonical Borealis-forming impact is not possible without both excessive crust production and strong antipodal effects not seen on Mars' southern hemisphere today. Our results instead favour an impact and subsequent localised magma ocean in the southern hemisphere that results in a thicker crust than the north upon crystallisation. Specifically, our best-fitting cases suggest that the projectile responsible for the Dichotomy-forming event was of radius 500-750 km, and collided with Mars at an impact angle of 15-30{\deg} with a velocity of 1.2-1.4 times mutual escape speed ($\sim$6-7 km/s)., Comment: Accepted for publication in Icarus

NASA's Double Asteroid Redirection Test (DART) is the first full-scale test of an asteroid deflection technology. Results from the hypervelocity kinetic impact and Earth-based observations, coupled with LICIACube and the later Hera mission, will result in measurement of the momentum transfer efficiency accurate to ~10% and characterization of the Didymos binary system. But DART is a single experiment; how could these results be used in a future planetary defense necessity involving a different asteroid? We examine what aspects of Dimorphos's response to kinetic impact will be constrained by DART results; how these constraints will help refine knowledge of the physical properties of asteroidal materials and predictive power of impact simulations; what information about a potential Earth impactor could be acquired before a deflection effort; and how design of a deflection mission should be informed by this understanding. We generalize the momentum enhancement factor $\beta$, showing that a particular direction-specific $\beta$ will be directly determined by the DART results, and that a related direction-specific $\beta$ is a figure of merit for a kinetic impact mission. The DART $\beta$ determination constrains the ejecta momentum vector, which, with hydrodynamic simulations, constrains the physical properties of Dimorphos's near-surface. In a hypothetical planetary defense exigency, extrapolating these constraints to a newly discovered asteroid will require Earth-based observations and benefit from in-situ reconnaissance. We show representative predictions for momentum transfer based on different levels of reconnaissance and discuss strategic targeting to optimize the deflection and reduce the risk of a counterproductive deflection in the wrong direction., Comment: 30 pages, 7 figures. Planetary Science Journal, in press, accepted 2022 September 22

The Double Asteroid Redirection Test (DART) spacecraft will impact into the asteroid Dimorphos on September 26, 2022 as a test of the kinetic impactor technique for planetary defense. The efficiency of the deflection following a kinetic impactor can be represented using the momentum enhancement factor, Beta, which is dependent on factors such as impact geometry and the specific target material properties. Currently, very little is known about Dimorphos and its material properties that introduces uncertainty in the results of the deflection efficiency observables, including crater formation, ejecta distribution, and Beta. The DART Impact Modeling Working Group (IWG) is responsible for using impact simulations to better understand the results of the DART impact. Pre-impact simulation studies also provide considerable insight into how different properties and impact scenarios affect momentum enhancement following a kinetic impact. This insight provides a basis for predicting the effects of the DART impact and the first understanding of how to interpret results following the encounter. Following the DART impact, the knowledge gained from these studies will inform the initial simulations that will recreate the impact conditions, including providing estimates for potential material properties of Dimorphos and Beta resulting from DARTs impact. This paper summarizes, at a high level, what has been learned from the IWG simulations and experiments in preparation for the DART impact. While unknown, estimates for reasonable potential material properties of Dimorphos provide predictions for Beta of 1-5, depending on end-member cases in the strength regime., Comment: Accepted to PSJ Didymos-DART Focus Issue

NASA's Double Asteroid Redirection Test (DART) spacecraft is planned to impact the natural satellite of (65803) Didymos, Dimorphos, around 23:14 UTC on 26 September 2022, causing a reduction in its orbital period that will be measurable with ground-based observations. This test of kinetic impactor technology will provide the first estimate of the momentum transfer enhancement factor $\beta$ at a realistic scale, wherein ejecta from the impact provides an additional deflection to the target. Earth-based observations, the LICIACube spacecraft (to be detached from DART prior to impact), and ESA's follow-up Hera mission to launch in 2024, will provide additional characterization of the deflection test. Together Hera and DART comprise the Asteroid Impact and Deflection Assessment (AIDA) cooperation between NASA and ESA. Here the predicted dynamical states of the binary system upon arrival and after impact are presented. The assumed dynamically relaxed state of the system will be excited by the impact, leading to an increase in eccentricity and slight tilt of the orbit together with enhanced libration of Dimorphos with amplitude dependent on the currently poorly known target shape. Free rotation around the moon's long axis may also be triggered and the orbital period will experience variations from seconds to minutes over timescales of days to months. Shape change of either body due to cratering or mass wasting triggered by crater formation and ejecta may affect $\beta$ but can be constrained through additional measurements. Both BYORP and gravity tides may cause measurable orbital changes on the timescale of Hera's rendezvous., Comment: 23 pages, 13 figures, published in PSJ

Comets and small Kuiper belt objects are considered to be among the most primitive objects in the solar system as comets like C/1995 O1 Hale-Bopp are rich in highly volatile ices like CO. It has been suggested that early in the solar system evolution the precursors of both groups, the so-called icy planetesimals, were modified by both short-lived radiogenic heating and collisional heating. Here we employ 2D finite-difference numerical models to study the internal thermal evolution of these objects, where we vary formation time, radius and rock-to-ice mass fraction. Additionally we perform 3D SPH collision models with different impact parameters, thus considering both cratering and catastrophic disruption events. Combining the results of both numerical models we estimate under which conditions highly volatile ices like CO, CO2 and NH3 can be retained inside present-day comets and Kuiper belt objects. Our results indicate that for present-day objects derived from the largest post-collision remnant the internal thermal evolution controls the amount of remaining highly volatile ices, while for the objects formed from unbound post-collision material the impact heating is dominant. Finally we apply our results to present-day comets and Kuiper belt objects like 67P/Churyumov-Gerasimenko, C/1995 O1 Hale-Bopp and (486958) Arrokoth.

The current properties of small bodies provide important clues to their origin and history. However, how much small bodies were processed by past collisions and to what extent they retain a record of processes that took place during the formation and early evolution of the Solar System is still poorly understood. Here we study the degree of collisional heating and compaction by analysing the large set of previous simulations of small body break-ups by Jutzi et al. (2019), which used porous targets of 50 - 400 km in diameter and investigated a large range of impact velocities, angles as well as energies. We find that the degree of impact processing is generally larger than found in previous studies which considered smaller objects (e.g. Jutzi et al., 2017; Schwartz et al., 2018). However, there is a clear dichotomy in terms of impact processing: the escaping material always experiences stronger heating than the material bound to the largest remnant. Assuming they originate from the same parent body, some of the observed differences between the recently visited asteroids Ryugu and Bennu may be explained by a different location of the material eventually forming these asteroids in the original parent body. Our results also provide constraints on the initial size of cometary nuclei., Comment: 34 pages, 11 figures. Accepted for publication in Icarus

The overall shape, internal structure and surface morphology of small bodies such as asteroids and comets are determined to a large degree by the last global-scale impact or disruption event. Depending on the specific energy, impacts lead to a large spectrum of outcomes. Sub-catastrophic disruptions take place in an energy range between cratering impacts and catastrophic disruptions. Although less energetic than catastrophic events, they can still significantly alter the overall shape and structure of the target body. This has been demonstrated recently in the case of bi-lobe cometary nuclei (Jutzi and Benz, 2017). Here we present results of a subsequent study on the shapes of asteroids resulting from such collisions. Sizes ranging from a few hundred meters to a few kilometers are considered. We show that impacts on elongated rotating asteroids frequently lead to the formation of contact binaries. Our results confirm that this mechanism is robust and works for a large range of asteroid sizes and impact velocities. Scaling-laws for the prediction of the size and velocity dependent specific energies required for successful bi-lobe formation are presented. Based on these scaling laws, the expected frequency of such sub-catastrophic impacts is calculated and is compared to the one of catastrophic disruptions, which require much higher specific energies and are more rare. Our analysis suggest that the shapes and structures of a large fraction of small asteroids as observed today may be the result of the last major sub-catastrophic impact., Comment: 21 pages, 5 figures

Understanding the collisional fragmentation and subsequent reaccumulation of fragments is crucial for studies of the formation and evolution of the small-body populations. Using an SPH / N-body approach, we investigate the size-frequency distributions (SFDs) resulting from the disruption of 100 km-diameter targets consisting of porous material, including the effects of pore-crushing as well as friction. Overall, the porous targets have a significantly higher impact strength (Q*D) than the rubble-pile parent bodies investigated previously (Benavidez et al., 2012) and show a behavior more similar to non-porous monolithic targets (Durda et al., 2007). Our results also confirm that for a given specific impact energy, the SFDs resulting from a parent body disruption are strongly dependent on the size scale., Comment: 26 pages, 12 figures; accepted for publication in Icarus

The Cassini spacecraft revealed the spectacular, highly irregular shapes of the small inner moons of Saturn, ranging from the unique "ravioli-like" forms of Pan and Atlas to the highly elongated structure of Prometheus. Closest to Saturn, these bodies provide important clues regarding the formation process of small moons in close orbits around their host planet, but their range of irregular shapes has not been explained yet. Here we show that the spectrum of shapes among Saturn's small moons is a natural outcome of merging collisions among similar-sized moonlets possessing physical properties and orbits that are consistent with those of the current moons. A significant fraction of such merging collisions take place either at the first encounter or after 1-2 hit-and-run events, with impact velocities in the range of 1-5 times the mutual escape velocity. Close to head-on mergers result in flattened objects with large equatorial ridges, as observed on Atlas and Pan. With slightly more oblique impact angles, collisions lead to elongated, Prometheus-like shapes. These results suggest that the current forms of the small moons provide direct evidence of the processes at the final stages of their formation, involving pairwise encounters of moonlets of comparable size. Finally, we show that this mechanism may also explain the formation of Iapetus' equatorial ridge, as well as its oblate shape., Comment: https://www.nature.com/articles/s41550-018-0471-7

Asteroid (162173) Ryugu is the target object of Hayabusa2, an asteroid exploration and sample return mission led by Japan Aerospace Exploration Agency (JAXA). Ground-based observations indicate that Ryugu is a C-type near-Earth asteroid with a diameter of less than 1 km, but the knowledge of its detailed properties is still very limited. This paper summarizes our best understanding of the physical and dynamical properties of Ryugu based on remote sensing and theoretical modeling. This information is used to construct a design reference model of the asteroid that is used for formulation of mission operations plans in advance of asteroid arrival. Particular attention is given to the surface properties of Ryugu that are relevant to sample acquisition. This reference model helps readers to appropriately interpret the data that will be directly obtained by Hayabusa2 and promotes scientific studies not only for Ryugu itself and other small bodies but also for the Solar System evolution that small bodies shed light on., Comment: 62 pages, 10 figures, 8 tables. Submitted to Space Science Reviews, on 6 April 2018

Giant impacts have been suggested to explain various characteristics of terrestrial planets and their moons. However, so far in most models only the immediate effects of the collisions have been considered, while the long-term interior evolution of the impacted planets was not studied. Here we present a new approach, combining 3-D shock physics collision calculations with 3-D thermochemical interior evolution models. We apply the combined methods to a demonstration example of a giant impact on a Mars-sized body, using typical collisional parameters from previous studies. While the material parameters (equation of state, rheology model) used in the impact simulations can have some effect on the long-term evolution, we find that the impact angle is the most crucial parameter for the resulting spatial distribution of the newly formed crust. The results indicate that a dichotomous crustal pattern can form after a head-on collision, while this is not the case when considering a more likely grazing collision. Our results underline that end-to-end 3-D calculations of the entire process are required to study in the future the effects of large-scale impacts on the evolution of planetary interiors., Comment: 29 pages, 10 figures, accepted for publication in Icarus

We model large-scale ($\approx$2000km) impacts on a Mars-like planet using a Smoothed Particle Hydrodynamics code. The effects of material strength and of using different Equations of State on the post-impact material and temperature distributions are investigated. The properties of the ejected material in terms of escaping and disc mass are analysed as well. We also study potential numerical effects in the context of density discontinuities and rigid body rotation. We find that in the large-scale collision regime considered here (with impact velocities of 4km/s), the effect of material strength is substantial for the post-impact distribution of the temperature and the impactor material, while the influence of the Equation of State is more subtle and present only at very high temperatures., Comment: 24 pages, 11 figures; accepted for publication in Icarus

We examine the relevance of tidal heating for large Trans-Neptunian Objects, with a focus on its potential to melt and maintain layers of subsurface liquid water. Depending on their past orbital evolution, tidal heating may be an important part of the heat budget for a number of discovered and hypothetical TNO systems and may enable formation of, and increased access to, subsurface liquid water. Tidal heating induced by the process of despinning is found to be particularly able to compete with heating due to radionuclide decay in a number of different scenarios. In cases where radiogenic heating alone may establish subsurface conditions for liquid water, we focus on the extent by which tidal activity lifts the depth of such conditions closer to the surface. While it is common for strong tidal heating and long lived tides to be mutually exclusive, we find this is not always the case, and highlight when these two traits occur together., Comment: Submitted to Icarus

We define a set of procedures to numerically study the fate of ejecta produced by the impact of an artificial projectile with the aim of deflecting an asteroid. Here we develop a simplified, idealized model of impact conditions that can be adapted to fit the details of specific deflection-test scenarios, such as what is being proposed for the AIDA project. Ongoing studies based upon the methodology described here can be used to inform observational strategies and safety conditions for an observing spacecraft. To account for ejecta evolution, the numerical strategies we are employing are varied and include a large N-Body component, a smoothed-particle hydrodynamics (SPH) component, and an application of impactor scaling laws. Simulations that use SPH-derived initial conditions show high-speed ejecta escaping at low angles of inclination, and very slowly moving ejecta lofting off the surface at higher inclination angles, some of which re-impacts the small-body surface. We are currently investigating the realism of this and other models' behaviors. Next steps will include the addition of solar perturbations to the model and applying the protocol developed here directly to specific potential mission concepts such as the proposed AIDA scenario., Comment: 19 pages, 11 figures, accepted for publication in Advances in Space Research, Special Issue: Asteroids & Space Debris

Global scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, dilatation, stripping of mantle and crust, and seismic degradation. Deciphering the complicated record of global scale impacts, in asteroids and meteorites, will lead us to understand the original planet-forming process and its resultant populations, and their evolution in time as collisions became faster and fewer. We provide a brief overview of these ideas, and an introduction to models., Comment: A chapter for Asteroids IV, a new volume in the Space Science Series, University of Arizona Press (Patrick Michel, Francesca E. DeMeo, William F. Bottke, Eds.)

In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this review, we describe numerical simulations of asteroid collisions that reproduced the main properties of families, accounting for both the fragmentation of an asteroid at the time of impact and the subsequent gravitational interactions of the generated fragments. The simulations demonstrate that the catastrophic disruption of bodies larger than a few hundred meters in diameter leads to the formation of large aggregates due to gravitational reaccumulation of smaller fragments, which helps explain the presence of large members within asteroid families. Thus, for the first time, numerical simulations successfully reproduced the sizes and ejection velocities of members of representative families. Moreover, the simulations provide constraints on the family dynamical histories and on the possible internal structure of family members and their parent bodies., Comment: Chapter to appear in the (University of Arizona Press) Space Science Series Book: Asteroids IV

We present recent improvements of the modeling of the disruption of strength dominated bodies using the Smooth Particle Hydrodynamics (SPH) technique. The improvements include an updated strength model and a friction model, which are successfully tested by a comparison with laboratory experiments. In the modeling of catastrophic disruptions of asteroids, a comparison between old and new strength models shows no significant deviation in the case of targets which are initially non-porous, fully intact and have a homogeneous structure (such as the targets used in the study by Benz&Asphaug (1999). However, for many cases (e.g. initially partly or fully damaged targets, rubble-pile structures, etc.) we find that it is crucial that friction is taken into account and the material has a pressure dependent shear strength. Our investigations of the catastrophic disruption threshold $Q^*_{D}$ as a function of target properties and target sizes up to a few 100 km show that a fully damaged target modeled without friction has a $Q^*_{D}$ which is significantly (5-10 times) smaller than in the case where friction is included. When the effect of the energy dissipation due to compaction (pore crushing) is taken into account as well, the targets become even stronger ($Q^*_{D}$ is increased by a factor of 2-3). On the other hand, cohesion is found to have an negligible effect at large scales and is only important at scales $\lesssim$ 1km. Our results show the relative effects of strength, friction and porosity on the outcome of collisions among small ($\lesssim$ 1000 km) bodies. These results will be used in a future study to improve existing scaling laws for the outcome of collisions (e.g. Leinhardt&Stewart, 2012)., Comment: Accepted for publication in Planetary and Space Science

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision., Comment: Chapter to appear in the Space Science Series Book: Asteroids IV. Includes minor corrections

Numerical simulations of asteroid break-ups, including both the fragmentation of the parent body and the gravitational interactions between the fragments, have allowed us to reproduce successfully the main properties of asteroid families formed in different regimes of impact energy, starting from a non-porous parent body. In this paper, using the same approach, we concentrate on a single regime of impact energy, the so-called catastrophic threshold usually designated by Q*D, which results in the escape of half of the target's mass. Thanks to our recent implementation of a model of fragmentation of porous materials, we can characterize Q*D for both porous and non-porous targets with a wide range of diameters. We can then analyze the potential influence of porosity on the value of Q*D, and by computing the gravitational phase of the collision in the gravity regime, we can characterize the collisional outcome in terms of the fragment size and ejection speed distributions, which are the main outcome properties used by collisional models to study the evolutions of the different populations of small bodies. We also check the dependency of Q*D on the impact speed of the projectile. In the strength regime, which corresponds to target sizes below a few hundreds of meters, we find that porous targets are more difficult to disrupt than non-porous ones. In the gravity regime, the outcome is controlled purely by gravity and porosity in the case of porous targets. In the case of non-porous targets, the outcome also depends on strength. We then propose some power-law relationships between Q*D and both target's size and impact speed that can be used in collisional evolution models., Comment: 18 pages, 19 Figures. Accepted for publication in Icarus