Spin-orbit coupling and chaotic rotation for circumbinary bodies. Application to the small satellites of the Pluto-Charon system

We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting $n_b$ and $n$ the orbital mean motion of the inner binary and of the circumbinary body, respectively, we show that spin-orbit resonances exist at the frequencies $n\pm k\nu/2$, where $\nu = n_b - n$, and $k$ is an integer. Moreover, when the libration at natural frequency has the same magnitude as $\nu$, the resonances overlap and the rotation becomes chaotic. We apply these results to the small satellites in the Pluto-Charon system, and conclude that their rotations are likely chaotic. However, the rotation can also be stable and not synchronous for small axial asymmetries.