Attitude instability of the secondary in the synchronous binary asteroid

For synchronous binary asteroid, the configuration of the spin-axes of the two asteroids being aligned and normal to the orbital plane is unstable in case of attitude instability. Focusing on the attitude stability of the secondary, there are four contributions of this study. (1) Stability analysis using the method of periodic orbit reveals the functional dependence of the attitude stability of the secondary on some system parameters - mass ratio of the binary, mutual orbit distance, orbit eccentricity, and the secondary's elongations. The stability results obtained for a wide range of system parameters help explain the significant lack of synchronous secondaries with equatorial elongations larger than 1.5 reported by Pravec et al. (2016) and also predict a lack of synchronous secondaries with equatorial elongations about 1.1. (2) Attitude unstable secondary is found to exhibit different excited rotation states which are sensitive to the orbit eccentricity: for small eccentricities the typical state is a small amplitude tumbling (non-principal axis rotation) which can be either regular or chaotic; as the eccentricity increases, the typical state is a chaotic rolling along its longest axis, i.e., the phenomenon known as barrel instability by Cuk et al. (2021); for sufficiently large eccentricities, the synchronous state of the secondary may break within a short time interval. (3) Using the analytical approach of normal form of Hamiltonian system, the inherent mechanism behind the attitude instability is attributed to the secondary resonance between the fundamental frequencies of the principal axis rotation and the non-principal axis rotation. (4) A systematic comparison study is carried out between the full model adopted here with a finite mass ratio and the classic restricted model for planet-satellite case (Wisdom et al., 1984). The result shows that for binary asteroids with the secondary's elongation larger than 1.5, the full model is recommended.