DDA 36th Meeting, 10-14 April 2005
Session 4 Dynamics of Rotating Bodies
Oral, Monday, April 11, 2005, 3:05-5:25pm

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[4.04] Evolution of Mercury's Obliquity

M. Yseboodt, J.L. Margot (Cornell University)

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. In order to constrain the size of the planet's core with the framework suggested by Peale (1976), the obliquity must be known precisely. Rambaux and Bois (2004) have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin-orbit evolution of Mercury subject to planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois (2004) if we introduce the planetary perturbations abruptly, i.e. by a step function. But if we introduce the planetary effects smoothly starting from an equilibrium position corresponding to the Cassini state (where the spin axis, the normal to the invariable plane and the normal to the orbital plane are aligned), the thousand-year oscillations in the obliquity do not appear. We find an equilibrium value for the obliquity of ~1.6 arcmin for (B-A)/C = 1.2 10-4 and (C-A)/C = 2.4 10-4, which are combinations of the moments of inertia corresponding to the Mariner 10 gravity data.

Our results indicate that planetary perturbations do not force short-period oscillations in Mercury's obliquity, even though such oscillations may appear in numerical integrations involving artificial departures from the Cassini state or the sudden onset of perturbations.

Peale (2004) has shown that the periods of damping of the free motions (free precession or free libration) are short compared to the age of the solar system, such that oscillations in obliquity are expected to decay. In the absence of excitation processes, Mercury's obliquity will remain constant, suggesting that one of the important conditions for the success of Peale's experiment is realized.

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Bulletin of the American Astronomical Society, 37 #2
© 2005. The American Astronomical Soceity.