Momentum transfer from oblique impacts

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