Impact modeling for the Double Asteroid Redirection Test (DART) mission

Highlights

• For homogeneous asteroid models, the DART impact outcome is primarily driven by a small number of material properties.

• Asteroid porosity and material strength at low pressure have the largest influence on the DART impact outcome.

• The momentum enhancement factor in the DART impact is predicted to be ~1.5–2.

Abstract

We present results from numerical simulations of the DART impact using the CTH shock physics code with 2D homogenous asteroid models. A design of experiments approach was used to create a run matrix of 28 simulations varying 17 different material model inputs for the impactor and target. The resulting values of the momentum transfer efficiency factor β and the crater width and depth were analyzed to determine the relative sensitivity of each parameter for predicting the DART impact outcome. We found that β and crater width/depth ratio are primarily influenced by a small number of material model input parameters, a result which greatly reduces the parameter space required for more expensive 3D simulations.

Introduction

The Asteroid Impact Deflection Assessment (AIDA) collaboration is a joint ESA-NASA planetary defense collaboration that will include the first full-scale test of an asteroid deflection by kinetic impactor [1]. The AIDA collaboration comprises two independent spacecraft, the NASA-sponsored Double Asteroid Redirection Test (DART) and the ESA-led Hera. In September 2022 the DART spacecraft will impact the secondary member of the binary asteroid system 65,803 Didymos (Didymos-B) at a speed of ~6.7 km/s and mass ~500 kg (Fig. 1). The resulting period change in the orbit of Didymos-B will be measured using Earth-based observations. Hera will arrive post-impact and perform detailed measurements to characterize Didymos-B.

Post-impact, the measured period change of Didymos-B will be used to compute the momentum transferred to the asteroid by the DART spacecraft. It is expected that the momentum change induced by DART could be larger than the incoming spacecraft momentum due to ejecta escaping from Didymos-B. This momentum enhancement effect is well-known and has been studied using both models and experiments [e.g., [2], [3], [4]] and is commonly parameterized by a momentum enhancement factor β, where

$$\beta =p_{target}/p_{impactor}=1+p_{ejecta}/p_{impactor},$$

and p_target is the momentum change of the target post-impact, p_impactor is the initial momentum of the impactor, and p_ejecta is the momentum carried by escaping ejecta. The properties of Didymos-B are poorly known and the local conditions of the specific impact site on the body influence the impact event; these factors result in high uncertainty in the expected momentum transfer of the DART impact. Early modeling efforts have found that β could reasonably be as low as ~1 or greater than 5 in end-member cases [5,6].

Studies of kinetic impactors have shown that the momentum enhancement factor β varies significantly with impact velocity, impact geometry, target internal structure and material properties [e.g., 7,8]. In order to apply the results of the DART impact to the design of future kinetic deflection missions, the relationship between β and asteroid properties must be well-understood.

Numerical simulations will be the primary tool used for interpretation of the measured period change of Didymos-B in terms of the momentum enhancement factor β resulting from the DART impact and its broader implications for kinetic deflection of asteroids. The Impact Simulation Working Group, which is part of the DART Investigation Team, is tasked with using impact modeling both pre- and post-impact to estimate the range of impact outcomes, including β, crater morphology, and ejecta properties, to calculate the relationships between the measured deflection and the asteroid physical properties, and to infer properties of Didymos-B based on post-impact measurements. Initial studies by the Impact Simulation Working Group have also included a benchmarking campaign [9] to characterize the variability in results from different numerical impact models used by the community, which showed that when using similar material properties the impact models produced similar results for crater size and momentum transfer. Previous studies have shown that numerical impact models can reproduce crater sizes, ejecta masses, and momentum transfer measured in laboratory experiments [e.g., 10,11]; however, application of these models for momentum transfer in planetary impacts at orders of magnitude larger scale cannot be easily tested. The DART impact will provide rare and valuable planetary-scale validation data for these numerical impact models, increasing confidence in the use of numerical models for design of kinetic impactor missions.

Because the physical properties of Didymos-B are poorly known, using numerical models to interpret the DART impact outcome will require running simulations over a wide range of potential material properties and internal structures. In this paper we present results from a sensitivity study of the effect of bulk material properties on the DART impact outcome using homogeneous asteroid target models. This purposes of this study are (1) to determine a range of potential outcomes for the DART impact, (2) to determine which model inputs are significant predictors of the DART impact outcome, and (3) to reduce the parameter space required for future, more complex simulations.

Like other asteroids [e.g., 12], Didymos-B may be a “rubble pile” agglomeration of rocks with sizes ranging from pebbles to boulders along with loosely consolidated sediments, rather than a relatively homogeneous rocky object. Due to computing limitations, it is not possible to separately model individual grains or pebbles within a full-scale planetary impact simulation (though large boulders can be individually modeled). Agglomerations of smaller particles are typically modelled as a continuous matrix with an average porosity and bulk strength properties. Simulations of impacts with rubble pile asteroids have shown that the impact outcome is highly dependent on the local impact site materials: whether the kinetic impactor hits sediment or competent rock has a significant influence on the total momentum transferred to the asteroid [8]. In the future, results of this study can be used to relate continuum approximations of rubble pile models to bulk properties, and also to facilitate comparisons of DART impact simulations performed with different impact modeling codes. Different codes contain different implementations of common asteroid material models, and not all model inputs have a one-to-one correspondence; therefore, knowledge of which model inputs are significant for DART momentum transfer will greatly simplify these types of comparisons.