Origin of chaos in the Prometheus-Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.