The Excited Spin State of Dimorphos Resulting from the DART Impact

Abstract

The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of $\sim 6.5{\text{ km s}}^{-1}$, perturbing Dimorphos's orbital velocity and changing the binary orbital period. We present three independent methods (one analytic and two numerical) to investigate the post-impact attitude stability of Dimorphos as a function of its axial ratios, $a/b$ and $b/c$ ($a\ge b\ge c$), and the momentum transfer efficiency $\beta$. The first method uses a novel analytic approach in which we assume a circular orbit and a point-mass primary that identifies four fundamental frequencies of motion corresponding to the secondary's mean motion, libration, precession, and nutation frequencies. At resonance locations among these four frequencies, we find that attitude instabilities are possible. Using two independent numerical codes, we recover many of the resonances predicted by the analytic model and indeed show attitude instability. With one code, we use fast Lyapunov indicators to show that the secondary's attitude can evolve chaotically near the resonance locations. Then, using a high-fidelity numerical model, we find that Dimorphos enters a chaotic tumbling state near the resonance locations and is especially prone to unstable rotation about its long axis, which can be confirmed by ESA's Hera mission arriving at Didymos in late 2026. We also show that a fully coupled treatment of the spin and orbital evolution of both bodies is crucial to accurately model the long-term evolution of the secondary's spin state and libration amplitude. Finally, we discuss the implications of a post-impact tumbling or rolling state, including the possibility of terminating BYORP evolution if Dimorphos is no longer in synchronous rotation.

38 pages, 13 figures, Accepted for publication in Icarus

References in corpus (7)

• Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems
• Tidal Evolution of Rubble Piles
• DART Mission Determination of Momentum Transfer: Model of Ejecta Plume Observations
• Near-Earth Asteroid Satellite Spins Under Spin-Orbit Coupling
• Doubly Synchronous Binary Asteroid Mass Parameter Observability
• Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact
• Accurate modelling of the low-order secondary resonances in the spin-orbit problem

Cited by in corpus (1)

• Chaos over Order: Mapping 3D Rotation of Triaxial Asteroids and Minor Planets