Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque

Abstract

In this paper, we make a detailed study of the spin-orbit dynamics of Mercury, as predicted by the realistic model that has been recently introduced in a series of papers mainly by Efroimsky and Makarov. We present numerical and analytical results concerning the nature of the librations of Mercury's spin in the 3:2 resonance. The results provide evidence that the librations are quasi-periodic in time, consisting of a slowoscillation, with an amplitude of order of arcminutes, superimposed on the 88-d libration. This contrasts with recent astronomical observations and hence suggests that the 3:2 resonance in which Mercury has been trapped might have been originally described by a large-amplitude quasi-periodic libration that, only at a later stage, with the formation of a molten core, evolved into the small-amplitude libration that is observed today.