Stability of the planar synchronous full two-body problem-The approach of periodic orbits

We investigate the dynamical stability of the synchronous state of the planar full two-body problem (PF2BP) by employing the approach of periodic orbit in the primary's body-fixed frame. Our results indicate that the traditional model to the spin-orbit resonances by neglecting the rotational motion's influence on the orbital motion is inappropriate in the binary asteroid system because the two asteroids are close to each other, leading to strong coupling between the orbits and rotations. Focusing on the high-order spin-orbit resonance, the family genealogy of periodic orbits in the unperturbed case is broken apart by some resonances in the perturbed case. In the case of no spin-orbit resonances, the periodic orbit is near-circular and is generally but not always stable. In the case of spin-orbit resonances, the periodic orbit can be elliptic, and one branch of the periodic orbits is stable. In contrast, the other branch is unstable for small to moderate orbit eccentricities. (C) 2022 Elsevier B.V. All rights reserved.