On the post-impact spin state of the secondary component of the Didymos-Dimorphos binary asteroid system

NASA’s Double Asteroid Redirection Test (DART) will be the first demonstration of a kinetic impactor for planetary defense against a small-body impact hazard. The target is the smaller component of the Didymos-Dimorphos binary asteroid system. The DART impact will abruptly change the velocity of the secondary (Dimorphos), increasing the binary eccentricity and exciting librations in the secondary. The observed change in the binary orbit period will be used to infer the “beta factor”, or the momentum transfer efficiency, an important parameter used in planetary defense. The post-impact spin and orbital dynamics are expected to be highly dependent on the momentum transferred (i.e., beta) and the shape of the secondary, which is still poorly constrained.

In this work, we explore the post-impact spin state of Dimorphos as a function of its ellipsoidal axis ratios and beta. We conducted attitude dynamics simulations with a modified 3-D spin-orbit model, accounting for the secondary’s shape and the primary’s oblateness, to understand the underlying dynamical structure of the system. In addition, we used the radar-derived polyhedral shape model of Didymos in high-fidelity Full Rigid Two-Body Problem simulations to capture the three-dimensional nature of the problem. We consider the outcomes from a simplified planar impact, where the DART momentum is transferred within the binary orbit plane and opposite the motion of Dimorphos, in addition to a more realistic case that includes full DART velocity vector (which contains out-of-plane components).

We produce the expected signatures of the 1:1 and 2:1 secondary resonances between the free and forced libration frequencies, corresponding to axial ratios of a/b = 1.414 and a/b = 1.087, respectively. For moderate values of beta (~3), we find that the libration amplitude can exceed ~40 degrees in many cases. For some axial ratios, it is even possible to achieve a libration amplitude exceeding 40 degrees with beta as low as 1. In addition, our simulations show that the secondary may be attitude unstable, and can enter a chaotic tumbling state for larger values of beta (~5), breaking from the 1:1 spin-orbit resonance.

In the simulations with a more realistic impact geometry (where some momentum is transferred out-of-plane), the results are similar. The most noticeable difference is in the cases that result in chaotic tumbling. In those runs, the characteristic timescale for entering the chaotic tumbling state is short—typically only several orbit periods. We also discuss the feasibility of detecting the post-impact spin state of Dimorphos with ground-based observations.