Spin-orbit coupling of the ellipsoidal secondary in a binary asteroid system

Abstract: In our Solar system, spin-orbit coupling is a common phenomenon in binary asteroid systems, where the mutual orbits are no longer invariant due to exchange of angular momentum between translation and rotation. In this work, dynamical structures in phase space are explored for the problem of spin-orbit coupling by taking advantage of analytical and numerical methods. In particular, the technique of Poincar\'e sections is adopted to reveal numerical structures, which are dependent on the total angular momentum, the Hamiltonian, mass ratio and asphericity parameter. Analytical study based on perturbative treatments shows that high-order and/or secondary spin-orbit resonances are responsible for numerical structures arising in Poincar\'e sections. Analytical solutions are applied to (65803) Didymos, (80218) ${\rm VO}_{123}$ and (4383) Suruga to reveal their phase-space structures, showing that there is a high possibility for them to locate inside secondary 1:1 spin-orbit resonance.