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Context. Most small asteroids (< 50 km in diameter) are the result of the breakup of a larger parent body and are often considered to be rubble-pile objects. Similar structures are expected for the secondaries of small asteroid binaries, including Dimorphos, the smaller component of the 65 803 Didymos binary system and the target of NASA’s Double Asteroid Redirection Test (DART) and ESA’s Hera mission. The DART impact will occur on September 26, 2022, and will alter the orbital period of Dimorphos around Didymos. Aims. In this work we assume Dimorphos-like bodies with a rubble-pile structure and quantify the effects of boulder packing in its interior on the post-impact morphology, degree of shape change, and material ejection processes. Methods. We used the Bern smoothed particle hydrodynamics shock physics code to numerically model hypervelocity impacts on small, 160 m in diameter, rubble-pile asteroids with a variety of boulder distributions. Results. We find that the post-impact target morphology is most sensitive to the mass fraction of boulders comprising the target, while the asteroid deflection efficiency depends on both the mass fraction of boulders on the target and on the boulder size distribution close to the impact point. Our results may also have important implications for the structure of small asteroids.

The fraction of the asteroid population that survived since the Solar System formation has experienced numerous collisional, dynamical and thermal events, which have shaped their structures and orbital properties. Small asteroids are often considered to be rubble-pile objects, aggregates held together only by self-gravity or small cohesive forces (1; 2). The artificial impact experiment of JAXA’s Hayabusa2 mission on the surface of asteroid Ryugu (3) created a surprisingly large crater (≈14 m). This unexpected result suggests that at least the near-surface of the asteroid is controlled to a large extent by its rather weak gravity rather than strength. Due to the inability to re-create these impact conditions in laboratory experiments, this observed regime of low-gravity, low-strength cratering remained largely unexplored so far. In addition, the very large times scales involved in the crater growth made it impossible to numerically simulate these impact processes up to now. Here we use a novel approach to model the entire cratering process resulting from impacts on small, weak asteroids, which uses shock physics code calculations directly. We found that small impacts can significantly deform weak asteroids, causing global resurfacing at the same time. We also show that even very low asteroid cohesions can drastically influence the outcome of an impact and that the collisional life-time of the overall asteroid shapes is significantly lower than the traditionally used life-time based on catastrophic disruption events. Consequently, we predict that NASA’s Double Asteroid Redirection Test (DART) impact on Dimorhpos (4; 5) will not lead to a cratering event, as originally anticipated (i.e., 6; 7). Rather, the impact is going to change the global morphology of the asteroid, if the surface cohesion is less than ≈ 10 Pa. Our results, together with the future observations by the ESA’s Hera mission (8) will provide constraints regarding the evolution of the shapes and structures of small asteroids by sub-catastrophic impacts.

Introduction: NASA’s Double Asteroid Redirection Test (DART) will impact the smaller component of the 65803 Didymos asteroid system, Dimorphos, and alter its orbital period around the primary, thus demonstrating the controlled deflection capabilities of near-Earth asteroids by a kinetic impactor [1, 2]. ESA’s Hera mission [2] will arrive at Dimorphos several years after the DART impact and provide a detailed characterization of the impact outcome, including the morphometry and morphology of the crater. Recent impact experiments and numerical studies [3–5] have shown that the kinetic impact efficiency depends strongly on the target properties and structure, and is non-unique (i.e., a number of target property configurations, such as different cohesion-porosity combinations, can result in the same deflection and a measure of the deflection alone can be interpreted in different ways depending on the target and impact properties). Therefore, for a successful interpretation of the DART impact outcome it is important to understand the influence of asteroid properties on the cratering process. Moreover, the DART impact outcome analysis will be based on numerical models, which require extensive and accurate prior validation. Most previous impact experiments and the subsequent validation work of numerical models have focused on homogeneous targets [e.g., 6, 7]. However, it is unlikely that Dimorphos is homogeneous at the scale of DART impact. Here we present preliminary results from impact experiments and numerical simulations specifically designed to mimic asteroid surface materials and structures (e.g., layered targets, rubble piles). The experiments are performed at the Experimental Projectile Impact Chamber (EPIC) at Centro de Astrobiología CSIC-INTA, Spain. Methods: The EPIC utilizes a 20 mm calibre compressed N2 (300 bar) cannon that launches projectiles at velocities up to ≈420 m/s and at angles of 20– 90◦ from horizontal [8]. The experiments, half- or quarter-space, are recorded with high-speed cameras and the resulting crater profiles are scanned in 3D with 0.5 mm resolution. Here we use the iSALE-2D [9] and the Bern SPH [10] shock physics codes to simulate the laboratory experiments. Both iSALE-2D and SPH include material models suitable for geological materials, various equations of state and porosity compaction models. We compare numerical models with impact experiments into targets with three different structures: homogeneous, layered and heterogeneous. Results and discussion: Vertical impacts into homogeneous targets. These impact experiments were performed into dry beach sand ("slow pour" maximum compaction) and iron grit targets and the results are used to validate the ejecta curtain formation and crater size from 2D numerical models into homogeneous targets. This setup is also used as reference for comparison with more complex target settings. Layered targets. Recently visited asteroids (e.g. Itokawa, Ryugu) have been observed to have a layered structure (i.e., a layer of regolith overlying a much stronger and denser substrate). The effects of target layering on impact cratering in the strength regime have been studied extensively through laboratory experiments [e.g., 11] and simulations [e.g., 12]. However, it is possible that Dimorphos has a granular cohesionless upper layer and that cratering in this layer is gravity-controlled, much like Hayabusa2’s SCI experiment [13]. Little is known of the effects of layering in the gravity regime, however it is likely that the momentum transferred from the DART spacecraft can be both amplified or reduced, depending on Dimorphos’ layering configuration [12]. We carry out experiments with layers of different density (i.e., beach sand over iron grit) to simulate gravity-controlled cratering in layered targets. While much of the kinetic energy of the projectile is released in the weaker upper target, this material also requires relatively less energy to be cratered resulting in a concentric crater morphology. This crater morphology is well reproduced in our iSALE-2D numerical models. Complex target structures/"rubble piles". Variations in strength and density also occur in very heterogeneous objects such as rubble-pile asteroids. An irregular crater growth and, consequently, irregular ejection of material affect the asteroid deflection (e.g., unpredictable motions). Such irregularities are difficult to model numerically and require full 3D geometry, which is computationally expensive. Nevertheless, efforts to model rubble pile geometries in the context of DART are undertaken [14] and laboratory experiments are essential to validate such models. We have performed shots into targets with porous ceramic balls (simulating “boulders”) of approximately equal size and weight as the projectile embedded in a matrix of beach sand (“slow pour” maximum compaction) (Fig. 1). Experiment 1 had balls distributed uniformly and at regular intervals within the sand. Experiment 2 had the same configuration, but only in half of the target while the other half was beach sand only. Comparisons were then made with the reference shot in pure beach sand. There is now a very good fit between the reference crater (Exp3) and the part of the Experiment 2 crater developed in the pure sand target, and there is an equally good fit between the half of the crater developed in the “rubble-pile” part of the target and the crater from Experiment 1 (Fig. 2). The “boulders” in the target seem to affect the excavation flow lines, resulting in steeper ejection near the limit of the excavation cavity. This results in a more flat-floored and steep-walled crater (Fig. 2). Numerical simulation of Experiment 1 replicated the experimental result very well (Fig. 3). Balls placed in immediate proximity to the impact point were ejected and ‘rays’ were created in the ejecta blanket. Balls placed at about 3 ball diameters away from the impact point were displaced towards the crater rim, as also noted in the numerical simulation (Fig. 4). Conclusions: The impact experiments represent a first step in our work towards understanding the importance of target heterogeneities in the cratering process and impact momentum transfer. SPH simulations to reproduce these impact experiments are underway and preliminary results from the early cratering process show good agreement with the experiment.

1. Introduction The AIDA international collaboration, which includes the DART (NASA) and Hera (ESA) missions, aims to test the technology of deflection by a kinetic impactor and to enhance our understanding of small bodies in general. In the context of these missions, a spacecraft, DART, will impact the secondary of the 65803 Didymos system, Dimorphos, at the end of October 2022 [1]. The impact will eject asteroid material from the target surface, leading to a measurable change in the orbital period of the binary. A second, follow-up spacecraft, Hera, will arrive at the system several years after the impact to characterize the system and the impact consequences [2]. The objective of this study, which is conducted in the context of the NEO-MAPP project, is to model the collision of the kinetic impactor with Dimorphos and to predict the outcome of the impact with respect to parameters that are measurable by spaceborne and in-situ instrumentation provided by the Hera mission. We model the impact using two different numerical schemes: a continuum approach using iSALE-2D/-3D & a smooth particle approach using Bern SPH. Although all codes solve similar forms of conservation equations and use similar constitutive models, different numerical schemes can produce systematically different results. Hence, as a first step, accurate validation tests against laboratory experiments are conducted to improve the reliability of results from numerical modelling.2. MethodiSALE-2D/-3D [3, 4] is a grid-based arbitrary Eulerian Lagrangian (ALE) code and is best suited to study crater formation and the propagation of shock waves from a high velocity impact into targets with a variety of different properties. On the other hand, Bern's grid-free Smooth Particle Hydrodynamics (SPH) [5, 6] is most appropriate to study the ejection of material and processes where the entire target body is involved. Both codes include the simulation of material compaction (iSALE: ε-α model; SPH: P-α model) and different strength models. In this study, we employ the Drucker-Prager and the Lundborg rheology models to describe the strength of the material. For both codes, the ejection behaviour is analysed as described in [7,8,9], and the ejection data is used to determine the momentum transferred to the target for deflection (momentum enhancement factor β = ejecta + impactor momentum / impactor momentum). This approach was used previously for systematic parameter studies [9] and benchmarking studies [10]. To validate our shock physics codes, we compare our results against observations from a recent laboratory study [11], where PVC projectiles with a mass of ~25 mg were accelerated to velocities of 1-2 km/s, impacting glass beads, sand and regolith simulant targets. In a second step, we continue the benchmarking work done by the Hera impact working group [12] to detect, assess and remove deviations between two different numerical schemes, iSALE (in 2D and 3D) and Bern SPH at the scale of the DART impact. 3. Validation We have simulated the crater formation in glass beads and regolith simulant with iSALE-2D at impact speeds of 2.4 km/s and 2.2 km/s, respectively. The glass beads target was modelled using a Drucker-Prager criterion with a coefficient of internal friction, f = 0.5 and an initial porosity of 35%. The regolith simulant used f ~ 0.8 and an initial porosity of 42%. We determine β-values of 2.9 and 1.4, which agree well with experimentally determined values of 2.7 and 1.3, respectively. In the glass beads target laboratory experiment, at ~0.5-1 ms after the impact, the ejecta curtain made an angle of 50-60°. In the case of the regolith simulant, at ~0.5 ms after the impact, the ejecta curtain angle was 30-40°. From our numerical models, we determined ejecta curtain angles 0.5 ms after the impact as 48° (glass beads) and 30° (regolith, Fig. 1). Both results agree with the lower bound of the experimental constraints. 4. Benchmark The first benchmark study focuses on the influence of target properties on the efficiency of the momentum transfer from the DART impact, β, for materials similar to the regolith simulant. The 600 kg projectile impacts targets with varying porosities, between 10 and 50%, and cohesions from 1 to 100 kPa, at a velocity of 6 km/s. The second benchmark study focuses on the influence of the impact angle on β for the 20% porosity case with 10 kPa cohesion at an impact velocity of 7 km/s. In previous studies, we found generally good agreement between the results derived with iSALE and SPH [12, 13, 14]. However, for certain porosities the deviations between the results were larger (e.g., 20% porosity and 1 kPa cohesion), which may have been the result of discrepancies in the details of the crush curve used in each model. As a result, here we conducted new models with more consistent crush curves (Fig. 2). Varying the impact angle for a specific impact scenario and set of target properties shows a remarkably good agreement between the two codes (Fig. 3). 5. SummaryOur joint modelling and experimental approach to study the efficiency of asteroid deflection by a kinetic impactor shows that there is generally a good agreement between different numerical approaches and experimental work. The benchmark studies show that the results from the grid based iSALE (-2D/-3D) and the meshless SPH can deviate for similar initial porosities when the crush curves are not consistent, but they produce similar results when the same impact conditions are considered. AcknowledgementsWe gratefully acknowledge the developers of iSALE (www.isale-code.de). This work has received funding from the European Union’s Horizon 2020 research and innovation programme, NEO-MAPP, grant agreement No. 870377.References[1]A.F.Cheng et al.,P&SS157(2018)104-115.[2]P.Michel et al.,AdvSpaceRes.62(2018)2261-2272.[3]K.Wünnemann et al.,Icarus180(2006)514–527.[4]D.Elbeshausen et al.,Icarus204(2009)716–731.[5]M.Jutzi et al.,Icarus198(2008)242–255.[6]M.Jutzi,P&SS107(2015)3–9.[7]M.Jutzi&P.Michel,Icarus229(2014)247-253.[8]R.Luther et al.,M&PS53(2018)1705–1732.[9]S.D.Raducan et al.,Icarus329(2019)282–295.[10]A.Stickle et al.,Icarus338(2020)113446.[11]S.Chourey et al.,P&SS194(2020)105112.[12]R.Luther et al.,EPSC-DPS2019-1776(2019).[13]S.D.Raducan et al.,52th LPSC(2021)#2548id1908.[14]R.Luther et al.,7th PDC(2021)#122.

The Double Asteroid Redirection Test (DART) plans to impact the smaller component of the 65803 Didymos asteroid system [1], Dimorphos, and alter the binary orbit period of the system [2]. The experiment aims to demonstrate the controlled deflection capabilities of a near-Earth asteroid. ESA’s Hera mission [1,2] will arrive at Dimorphos four years after the DART impact and provides a detailed characterization of the impact. For a successful analysis it is important to know the influence of various parameters known to affect the cratering. Here we present some preliminary results as well as planned experiments at the Experimental Projectile Impact Chamber (EPIC) at Centro de Astrobiología CSIC-INTA, Spain, carried out in concert with observations of natural craters and numerical simulations for mutual verification of the methods and a first analysis of the effects of factors such as heterogeneities in a granular (i.e. ‘rubble-pile’) target. Introduction, aim and methods As shown by previous impact experiments and numerical simulations [3,4,5], the amount by which the target asteroid can be deflected is highly dependent on the target properties and structure, and non-unique. Thus, the knowledge of the final crater as observed by Hera is important to assess the target properties of Dimorphos [6]. However, such an analysis based on numerical models requires accurate validation of the applied numerical codes [7,8]. Previous validation work has focused on impacts into homogeneous targets [e.g. 9,10]. However, it is unlikely that asteroids are as homogeneous at this scale [cf. 11] as on the scale of previous laboratory experiments. Therefore, there is a need for impact experiments specifically designed to mimic asteroid surface materials and structures (e.g. layered targets, rubble piles). The EPIC can be used to provide the impact experiments needed. In addition, field observation of relevant natural craters, both strength-controlled (e.g. Kaali, 110m) and gravity-controlled (e.g. Lockne, 7.5km) may provide additional information. The EPIC utilizes a 20mm calibre compressed N2 (300bar) cannon that can shoot projectiles of various materials and composition (e.g., solid, clustered) at velocities of up to ~420m/s and into various target materials at impact angles from 20-90° over the horizontal. The experiments, half- or quarter-space, are recorded by high speed cameras, and the resulting craters (approx. 30cm in dry sand) can be scanned in 3D with 0.5mm resolution. For the results shown here, we use the iSALE shock physics code [12,13] to simulate the conducted experiments from the laboratory. The strengths of iSALE are the availability of: different material models (brittle/ductile rheology), a damage model, various equations of state, and a porosity compaction model. Planned activities and preliminary results Vertical impacts into homogeneous targets Vertical impact experiments into homogeneous targets can be used to validate ejecta curtain formation and final crater size from 2D numerical models. Then, simulations can be used to determine the influence of specific material properties in systematic parameter studies, which are difficult to be conducted in the laboratory (Fig. 1). Layered targets Most small bodies in the Solar System are not homogeneous, as shown by past missions to asteroids. Several visited asteroids have been observed to be covered by a layer of regolith, which overlies a much stronger or denser substrate [14]. The effects of target layering on impact cratering in the strength regime was studied extensively through laboratory experiments [e.g. 15] and simulations [16]. While much of the kinetic energy of the projectile is released in the weaker upper target, this material also requires relatively less energy to be cratered. Likewise, differing impedances of the cover layer and the substrate (i.e., basement) could result in reflection of the shock, with a reduction of the energy transferred into the basement and, consequently, more energy available for cratering the upper layer. Therefore, the crater in the weak layer may get relatively wider than a corresponding crater in an equivalent homogeneous material. For asteroids like Dimorphos the transition crater diameter will be well above the size of the target, giving that all impacts would be strength dominated. Nevertheless, even in the case of a strength dominated substrate, a layer of granular cohesionless material will still be gravity-dominated. For example, Hayabusa2’s SCI experiment created a concentric crater morphology specific to layered targets, which is believed to have formed in the gravity regime [11]. Layering affects also large gravity-dominated craters [17]. However, little is known about impact cratering into layered targets in the gravity regime. As shown from numerical simulations into layered targets in the strength-regime, the presence of a stronger and/or denser substrate can both amplify and reduce the momentum transferred from a spacecraft for deflecting an asteroid. [6] This can have important implications for NASA’s DART mission. We have already carried out some experiments at the EPIC with layers of different density (i.e., beach sand over iron grit) to simulate gravity-controlled cratering in layered targets (Figs. 2,3). 3. Complex target structures/Rubble piles However, the variations in strength and density can also be compared to the configuration of greatly heterogeneous objects such as rubble-piles. Rubble-pile asteroids may have a highly irregular distribution of massive rock vs rubble (i.e. not in an orderly “layered” fashion), and strength and density vary locally. An irregular crater growth and, consequently, irregular ejection of material affect the asteroid deflection (e.g. unpredictable motions). Such irregularities may be difficult to model numerically and would require full 3-dimensional geometry, which is computationally expensive. Nevertheless, current efforts to model rubble pile geometries in the context of the DART impact are undertaken [18]. Laboratory experiments are highly needed to validate such models. We intend to investigate these effects experimentally for both strength and gravity dominated targets (Fig. 4). Acknowledgements Ormö was supported by grants ESP2017-87676-C5-1-R from the Spanish Ministry of Economy and Competitiveness and Fondo Europeo de Desarrollo Regional. Ormö and Herreros were supported by the Spanish State Research Agency Project No.MDM-2017-0737 Unidad de Excelencia "María de Maeztu"- Centro de Astrobiología (INTA-CSIC), and the CSIC I-LINK project LINKA20203.

Introduction: Earth is continuously impacted by space debris and small asteroids, and, while large asteroid impacts are very rare, they have the potential to cause severe damage. NASA's Double Asteroid Redirection Test (DART) aims to be the first mission to test a controlled deflection of a Near-Earth binary asteroid [1, 2], by impacting the smaller component of the 65803 Didymos asteroid system, Dimorphos. The impact will thereby alter the binary orbit period by an amount detectable from Earth [3]. ESA's Hera mission [3, 4], that will arrive at Dimorphos several years after the DART impact. It will rendezvous with the asteroid system and perform detailed characterisation of Dimorphos's volume and surface properties, as well as measure the DART impact outcome, such as change in the binary system orbit and the volume and morphology of the DART impact crater. In high velocity impacts on an asteroid the change in momentum of the asteroid ΔP can be amplified by the momentum of crater ejecta that exceeds the escape velocity, which is often expressed in terms of the parameter β=ΔP/mU, where mU is the impactor momentum [5]. The amount by which crater ejecta enhances asteroid deflection-that is, the normalised momentum of the crater ejecta that escapes the gravitational attraction of the target body (β-1)-has been found to vary significantly depending on the target asteroid's properties and composition [6]. Previous numerical simulations [7, 8] have quantified the sensitivity of the asteroid deflection to target material properties. To allow for a large variety of material properties to be studied, these simulations employed a two-dimensional shock physics code with an axially-symmetric mesh geometry, which restricted the studies to vertical impacts only. However the DART spacecraft will impact the surface of Didymoon at an oblique angle [3]. Here we investigate the influence of impact angle on the ejecta momentum transfer with the aim of developing an empirical scaling relationship for β as a function of impact angle. Numerical methods: We used the iSALE3D shock physics code [9] to numerically simulate the DART impact in two and three dimensions. The DART spacecraft structure was modelled as a porous aluminium sphere, impacting a 20% porous, homogeneous basaltic regolith target at 7 km/s. The cohesive strength of the damaged material was 10 kPa. Influence of the impact angle on the net momentum: Consistent with previous laboratory-scale oblique impact experiments [10, 11] and DART impact models [12], our simulations show that the ejecta from oblique impacts displays higher speeds and lower ejection angles in the downrange direction, and lower speeds and higher ejection angles in the uprange direction of the impact. Figure 1 compares the surface topography of a vertical DART impact, at a 90o angle of incidence to the target plane, and an oblique DART impact at a 45o angle. The time-frames of the oblique impact Figure 1b show a highly asymmetric ejecta distribution at early times of the cratering process The asymmetry of the ejecta can have important implications for momentum transfer vector. The net momentum of the target after the impact is the vector sum of the impactor momentum and the crater ejecta momentum enhancement vectors. The projectile imparts an its momentum along the impact direction; that is, downrange and into the target. As most of the ejecta momentum is launched in the downrange direction, the net momentum imparted to the target, which acts in the opposite direction, acts downward and slightly uprange. The vector sum of the impactor momentum and the momentum enhancement vectors is in between the individual vectors, implying that the ejecta momentum acts to increase the vertical component of momentum transfer and reduce the horizontal downrange component. Figure 2 shows the direction of the total momentum imparted to the asteroid, as a function of time, measured relative to the downrange horizontal direction, for four different impact angles. As the crater grows towards its final diameter (at about 1 s), the uprange direction of the ejecta momentum becomes more perpendicular to the surface. The direction of the net momentum imparted to the target also changes, from the downrange direction, towards the vertical direction. In the scenarios simulated here, for impacts into a 10 kPa target, the direction of the net momentum at the end of the crater growth is about 83o for the 60o impact, ~77o for the 45o impact and ~66o for the 30o impact. In the simulations presented here, crater growth is halted by the target's strength before the total momentum direction becomes vertical. However, it is expected that with increasing cratering efficiency (e.g. decreasing strength), the ejecta momentum will make a larger contribution towards the total momentum vector. Towards an ejecta scaling relationship for oblique impacts: Ejecta scaling relationships are useful to predict the ejecta distribution and momentum transfer for vertical impacts. However, most planetary impacts are oblique and stationary point-source scaling [6] becomes inadequate. An aim of this work is to develop an ejecta scaling relationship for oblique impacts, based on numerical simulation data. Three-dimensional simulations of the DART impact at vertical, 60o, 45o and 30o impact angles provide information about the ejecta mass-velocity distribution as a function of impact angle and azimuth. The momentum carried away by the ejecta from a vertical impact, β-1, can be found from integrating the mass, dM, within the radial distance range from n1 to n2R/a [1]. Here we apply this semi-analytical equation on a per azimuth basis and then sum each azimuthal ejecta distribution to derive β-1 values from all ejecta in oblique impact scenarios (Fig. 3). Acknowledgements: We gratefully acknowledge the developers of iSALE (www.isale-code.de) and STFC for funding (Grant ST/N000803/1).