Leveraging Observations to Model the Dynamics of the Didymos System After the DART Impact

On September 26, 2022, NASA’s DART spacecraft impacted Dimorphos, the secondary in the Didymos binary asteroid system, in the first test of a kinetic impact for planetary defense [1–3]. Since the impact, observations have sought to characterize the change in the binary mutual orbit and have measured a reduction in the orbit period by about 33 minutes [1], corresponding to a change in velocity of about 2.7 mm/s [3]. We will utilize these observations to inform numeric models of the fully spin-orbit-coupled dynamics of the Didymos system. Our numerical framework is the General Use Binary Asteroid Simulator (GUBAS), which incorporates the coupled dynamics and has been well established in the literature [4-6].

By adjusting system parameters, we match our simulation results to ground-based measurements of the mutual orbit. This approach will provide more information about the system that is not necessarily directly observable from the ground. Owing to the strong spin-orbit coupling of the system, traditional Keplerian elements are misleading [7]. Instead, we will introduce a set of “observable elements” that are consistent with external observations [8]. Our first objective is to characterize the change in semimajor axis caused by the impact. This change is approximately a linear function of the separation distance at impact. The next objective is a discussion of the system’s eccentricity, which linearly depends on the system’s eccentricity prior to the impact. However, the net change in eccentricity is largely independent of the pre-impact eccentricity. We will also discuss how the onset of secondary tumbling may be observable in ground-based observations [9], including the measured eccentricity. The third objective is to accurately account for the mutual orbit’s apsidal precession. This can provide insight into the primary’s J2 coefficient, and by extension its internal density distribution. Accurately accounting for the system’s precession can also slightly change the calculated velocity change (delta-V) due the impact. Lastly, by modeling the secular evolution of the orbit [10], we discuss implications for the upcoming Hera mission’s rendezvous with the system, specifically damping of libration and eccentricity.

[1] Thomas, C. A. et al. Nature, in Press (2023)

[2] Daly, R. T. et al. Nature, in Press (2023)

[3] Cheng, A. F. et al. Nature, in Press (2023)

[4] Davis, A. B. et al. Icarus (2020)

[5] Agrusa, H. F. et al. Icarus (2020)

[6] Richardson, D. C. et al. PSJ (2022)

[7] Scheeres, D. J. et al. CMDA (2009)

[8] Meyer, A. J. et al. AAS/DDA (2021)

[9] Meyer, A. J. et al. PSJ (2021)

[10] Meyer, A. J. et al. Icarus (2023)