Stability Analysis on the Moon’s Rotation in a Perturbed Binary Asteroid

Numerical calculation provides essential tools for deep space exploration, which are indispensable to mission design and planetary research. In a specific case of binary asteroid defense such as the DART mission, an accurate understanding of the possible dynamical responses and the system’s stability and engineers’ prerequisite. In this paper, we discuss the numeric techniques for tracking the year-long motion of the secondary after being perturbed, based upon which its rotational stability is analyzed. For long-term simulations, we compared the performances of several integrating schemes in the scenario of a post-impact full two-body system, including low- and high-order Runge–Kutta methods, and a symplectic integrator that combines the finite element method with a symplectic integral format. For rotational stability analysis of the secondary, we focus on the rotation of the secondary around its long-axis. We calculated a linearised error propagation matrix and found that, in the case of tidal locking of the secondary to the primary, the rotation is stable; as the perturbation amplitude of the spin angular velocity of the secondary increases, the rotation will lose stability and will be prone to being unstable in the long-axis direction of the secondary. Furthermore, we investigated the one-year-long influences of the non-spherical perturbations of the primary and the secondary.