1110.2658 (Valeri V. Makarov)
Valeri V. Makarov
The dynamical evolution of terrestrial planets resembling Mercury in the
vicinity of spin-orbit resonances is investigated using comprehensive harmonic
expansions of the tidal torque with accurate expressions for the
frequency-dependent quality factors and Love numbers. The torque equations are
integrated numerically with a small step in time, taking into account the
oscillating triaxial torque components but neglecting the layered structure of
the planet and assuming a zero obliquity. We find that a Mercury-like planet
with its current value of orbital eccentricity (0.2056) is always captured in
the 3:2 resonance. The probability of capture in the higher 2:1 resonance is
approximately 0.23. These results are confirmed by a semi-analytical estimation
of capture probabilities as functions of eccentricity. The circumstances of a
resonance passage are remarkable, in that it happens very quickly, in a sudden
lunge. Considering the phase space parameters at the times of periastron, the
range of spin rates and phase angles, for which an immediate passage is
triggered, is very narrow, and yet, a planet like Mercury rarely fails to align
itself into this state of unstable equilibrium before it traverses the 2:1
resonance.
View original:
http://arxiv.org/abs/1110.2658
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