Spin orbit resonance cascade via core shell model: application to Mercury and Ganymede

We discuss a model describing the spin orbit resonance cascade. We assume that the body has a two-layer (core–shell) structure; it is composed of a thin external shell and an inner and heavier solid core that are interacting due to the presence of a viscous friction. We assume two sources of dissipation: a viscous one, depending on the relative angular velocity between core and shell and a tidal one, smaller than the first, due to the viscoelastic structure of the core. We show how these two sources of dissipation are needed for the capture in spin–orbit resonance. The shell and the core fall in resonance with different time scales if the viscous coupling between them is big enough. Finally, the tidal dissipation of the viscoelastic core, decreasing the eccentricity, brings the system out of the resonance in a third very long time scale. This mechanism of entry and exit from resonance ends in the 1 : 1 stable state.