A circumbinary approach to the study of spin-orbit resonances around irregular shaped bodies. Application to the Quaoar system

Abstract

We propose to model spin-orbit resonances that appear in ring systems around minor bodies of the Solar System using a circumbinary approximation. In our model, the ellipsoidal/irregular shape of the minor body is replaced by a binary dumbbell, i.e., two equal masses evolving in circular orbits around their center of mass. This allows us to apply the equations of motion of the restricted circumbinary N-body problem, duly adjusted to mimic the rotation of the central body and its quadruple momentum. The equations also allow for the simple inclusion of other perturbing bodies, like small satellites, enabling the analysis of the simultaneous effect of spin-orbit resonances and mean motion resonances on the ring dynamics. The goal of the circumbinary model is to substitute the study of a given spin-orbit resonance by a surrogate mean motion resonance, allowing for the application of well established numerical and semianalytical models to map the topology and stability of these resonances. We discuss the differences between the circumbinary model and a triaxial ellipsoid. The model is also extended to study the problem of a mass anomaly. We present some applications to the dynamics of Quaoar's ring system, indicating that spin-orbit resonances do not seem to play any relevant role in the present dynamics of the ring particles.