Benoit Noyelles, Julien Frouard, Valeri Makarov, Michael Efroimsky
Mercury is a peculiar case, in that it is locked into the 3:2 spin-orbit resonance. Its rotation period, 58 days, is exactly two thirds of its orbital period. It is accepted that the eccentricity of Mercury (0.206) favours the trapping into this resonance. More controversial is how the capture took place. A recent study by Makarov has shown that entrapment into this resonance is certain if the eccentricity is larger than 0.2, provided that we use a realistic tidal model, based on the Darwin-Kaula expansion of the tidal torque, including both the elastic rebound and anelastic creep of solids. We here revisit the scenario of Mercury's capture into the supersynchronous spin-orbit resonances. The study is based on a realistic model of tidal friction in solids, that takes into account the rheology and the self-gravitation of the planet. Developed in Efroimsky, it was employed by Makarov et al. to determine the likely spin state of the planet GJ581d, with its eccentricity evolution taken into account. It was also used in the afore-cited work to study the tidal spin-down and to find the likely end-state of a Mercury-like planet with its eccentricity fixed. We now go ahead by considering the evolution of Mercury's eccentricity. We find that the realistic tidal model, as opposed to the constant time lag and constant phase lag models, changes dramatically the statistics of the probable final spin-orbit states. First, after only one crossing of the 3:2 resonance this resonance becomes the most probable end-state. Second, if a capture into any resonance takes place, the capture is final, several crossings of the same state being forbidden. Third, within our model the trapping of Mercury happens much faster than previously believed. The swift capture justifies our treatment of Mercury as a homogeneous, unstratified body whose liquid core had not yet formed by the time of trapping.
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http://arxiv.org/abs/1307.0136
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