Semisecular Resonances within the Long-Term Dynamical Evolution of Didymos

Binary asteroid systems evolve overtime due to various dynamical effects. The coupled dynamics of the mutual orbit and attitude of the smaller satellite within the system are affected primarily by the binary Yarkovsky–O‘Keefe–Radzievskii–Paddack (BYORP) effect and solid body tides. The former effect is driven by uneven re-radiation of solar radiation pressure from the irregularly shaped satellite, leading to secular changes in the orbit and attitude. The latter effect is due to gravitational interactions between the two asteroids, causing non-elastic deformation and energy dissipation from the system.

Solar third body effects are also important to consider when modeling the complex dynamics of these non-Keplerian systems. It has been hypothesized that apsidal precession of the mutual orbit due to these solar effects can be resonant with the system’s heliocentric orbit (Ćuk & Nesvorný, 2010; McMahon & Scheeres, 2010). This is referred to as the “evection resonance” (Touma & Wisdom, 1998). These resonances have been observed in prior numerical simulation work (Ćuk et al., 2021; Cueva et al., 2024) and can greatly influence the nature of the chaotic dynamics of these systems. For example, these resonances can excite eccentricity and induce additional libration of the satellite, in some cases driving the system attitude unstable.

In this work, we expand upon numerical simulations performed in Cueva et al. (2024) of the tidal-BYORP secular dynamical evolution of the Didymos system following the DART impact. These simulations are an improvement upon past studies (Quillen et al., 2022; Ćuk et al., 2021) as full nonplanar orbit-attitude coupled evolution over long timescales is modeled, allowing for phenomena such as barrel instability (Ćuk et al., 2021) to be possible. With this 3D capability we conduct a detailed resonance analysis, such as predicting the expected locations of these resonances and confirming whether the observed excitations are attributed to the evection resonance phenomenon, or if they are the result of other resonance types (e.g., the inclination-eccentricity “eviction resonance” (Touma & Wisdom, 1998)). We present various representative cases to show how these resonances can impart a variety of outcomes on the system’s evolution. We evaluate the strength and timescales of these resonances, and also investigate the hypothesis posed in Cueva et al. (2024) regarding whether these resonances can assist in driving the binary system towards its theoretical tidal-BYORP equilibrium semimajor axis. Lastly, we assess the influence of these resonances on prograde versus retrograde systems.