Spin-orbit coupling of the primary body in a binary asteroid system

Spin-orbit coupling is widespread in binary asteroid systems and it has been widely studied for the case of ellipsoidal secondary. Due to angular momentum exchange, dynamical coupling is stronger when the orbital and rotational angular momenta are closer in magnitudes. Thus, the spin-orbit coupling effects are significantly different for ellipsoidal secondaries and primaries. In the present work, a high-order Hamiltonian model in terms of eccentricity is formulated to study the effects of spin-orbit coupling for the case of ellipsoidal primary body in a binary asteroid system. Our results show that the spin-orbit coupling problem for the ellipsoidal primary holds two kinds of spin equilibrium, while there is only one for the ellipsoidal secondary. In particular, 1:1 and 2:3 spin-orbit resonances are further studied by taking both the classical pendulum approximation as well as adiabatic approximation (Wisdom's perturbative treatment). It shows that there is a critical value of total angular momentum, around which the pendulum approximation fails to work. Dynamical structures are totally different when the total angular momentum is on two sides of the critical value.