Monday, January 16, 2012

1110.2658 (Valeri V. Makarov)

How terrestrial planets traverse spin-orbit resonances: A camel goes through a needle's eye    [PDF]

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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