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

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We investigate the resonant rotation of circumbinary bodies in planar quasi-circular orbits. Denoting nb 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± kν/2, where ν= nb - n, and k is an integer. Moreover, when the libration at natural frequency has the same magnitude as ν, 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.