Terrestrial planets reaching the 3:2 spin-orbit resonance

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Terrestrial planets reaching the 3:2 spin-orbit resonance

Post by Sirius_Alpha on 13th October 2011, 7:18 pm

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

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, and invariably traverses all higher resonances. 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, a Mercury-like planet can traverse the resonance only if its angle with respect to the star is close to $\pm\pi/2$, i.e., if the planet is positioned sidewise, with the longest axis almost perpendicular to the star direction. The range of spin rates and phase angles, for which an immediate passage is triggered, is very narrow, and yet, the test planet never fails to align itself into this state of unstable equilibrium before it traverses the resonance. A qualitative explanation to this peculiar dynamical process is given.

I realise this takes Mercury as the prototypical terrestrial but this has applications to planets in general. So I've put it in the extrasolar mechanics area.

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