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For a positive integer $n$, a graph with at least $n$ vertices is $n$-existentially closed or simply $n$-e.c. if for any set of vertices $S$ of size $n$ and any set $T\subseteq S$, there is a vertex $x\not\in S$ adjacent to each vertex of $T$ and no vertex of $S\setminus T$. We extend this concept to uniform hypergraphs, find necessary conditions for $n$-e.c. hypergraphs to exist, and prove that random uniform hypergraphs are asymptotically $n$-existentially closed. We then provide constructions to generate infinitely many examples of $n$-e.c. hypergraphs. In particular, these constructions use certain combinatorial designs as ingredients, adding to the ever-growing list of applications of designs.

The ~200 m/s impact of a single 400-kg Bjurb\"ole L/LL ordinary chondrite meteorite onto sea ice resulted in the catastrophic disruption of the projectile. This resulted in a significant fraction of decimeter-sized fragments that exhibit power law cumulative size and mass distributions. This size range is underrepresented in impact experiments and asteroid boulder studies. The Bjurb\"ole projectile fragments share similarities in shape (sphericity, and roughness at small and large scale) with asteroid boulders. However, the mean aspect ratio (3D measurement) and apparent aspect ratio (2D measurement) of Bjurb\"ole fragment is 0.83 and 0.77, respectively, indicating that Bjurb\"ole fragments are more equidimensional compared to both fragments produced in smaller scale impact experiments and asteroid boulders. These differences may be attributed either to the fragment source (projectile vs. target), to the high porosity and low strength of Bjurb\"ole, to the lower impact velocity compared with typical asteroid collision velocities, or potentially to fragment erosion during sea sediment penetration or cleaning., Comment: Data repository https://www.doi.org/10.5281/zenodo.10062980

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

The history of accretion and differentiation processes in the planetesimals is provided by various groups of meteorites. Sampling different parent body layers, they reveal the circumstances of the metal-silicate segregation and the internal structures of the protoplanets. The ungrouped achondrite Erg Chech 002 (EC 002) added to the suite of samples from primitive igneous crusts. Here we present models that utilize thermo-chronological data for EC 002 and fit the accretion time and size of its parent body to these data. The U-corrected Pb-Pb, Al-Mg, and Ar-Ar ages used imply a best-fit planetesimal with a radius of 20-30 km that formed at 0.1 Ma after CAIs. Its interior melted early and differentiated by 0.5 Ma, allowing core and mantle formation with a transient lower mantle magma ocean, and a melt fraction of <25 % at the meteorite layering depth. EC 002 formed from this melt at a depth of 0.8 km in a partially differentiated region covered by an undifferentiated crust. By simulating collisions with impactors of different sizes and velocities, we analyzed the minimum ejection conditions of EC 002 from its original parent body and the surface composition of the impact site. The magma ocean region distinct from the layering depth of EC 002 implyes that it was not involved in the EC 002 genesis. Our models estimate closure temperatures for the Al-Mg ages as 1060 K to 1200 K. A fast parent body cooling attributes the late Ar-Ar age to a local reheating by another, late impact.

A graph $G$ is {\it $n$-existentially closed} if, for all disjoint sets of vertices $A$ and $B$ with $|A\cup B|=n$, there is a vertex $z$ not in $A\cup B$ adjacent to each vertex of $A$ and to no vertex of $B$. In this paper, we investigate $n$-existentially closed line graphs. In particular, we present necessary conditions for the existence of such graphs as well as constructions for finding infinite families of such graphs. We also prove that there are exactly two $2$-existentially closed planar line graphs. We then consider the existential closure of the line graphs of hypergraphs and present constructions for $2$-existentially closed line graphs of hypergraphs., Comment: 14 pages, 2 figures

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

Shock metamorphism in ordinary chondrites allows for reconstructing impact events between asteroids in the main asteroid belt. Shock-darkening of ordinary chondrites occurs at the onset of complete shock melting of the rock (>70 GPa) or injection of sulfide and metal melt into the cracks within solid silicates (\sim 50 GPa). Darkening of ordinary chondrites masks diagnostic silicate features observed in the reflectance spectrum of S-complex asteroids so they appear similar to C/X-complex asteroids. In this work, we investigate the shock pressure and associated metamorphism pattern in rubble-pile asteroids at impact velocities of 4-10 km/s. We use the iSALE shock physics code and implement two-dimensional models with simplified properties in order to quantify the influence of the following parameters on shock-darkening efficiency: impact velocity, porosity within the asteroid, impactor size, and ejection efficiency. We observe that, in rubble-pile asteroids, the velocity and size of the impactor are the constraining parameters in recording high-grade shock metamorphism. Yet, the recorded fraction of higher shock stages remains low (<0.2). Varying the porosity of the boulders from 10% to 30% does not significantly affect the distribution of pressure and fraction of shock-darkened material. The pressure distribution in rubble-pile asteroids is very similar to that of monolithic asteroids with the same porosity. Thus, producing significant volumes of high-degree shocked ordinary chondrites requires strong collision events (impact velocities above 8 km/s and/or large sizes of impactors). A large amount of asteroid material escapes during an impact event (up to 90%); however, only a small portion of the escaping material is shock-darkened (6%)., Comment: 12 pages, 9 figures

A graph or hypergraph is said to be vertex-transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex-transitive hypergraph is maximally edge-connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex-transitive hypergraphs which are not maximally edge-connected., Comment: 8 pages