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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[4.03] Mercury's Core

S. J. Peale (UCSB)

In determining Mercury's core structure from its rotational properties, the location of Cassini state 1 is crucial. Convincing radar evidence indicates that the mantle rests on a liquid layer (Margot et al. 2005), but there are no empirical constraints on the moment of inertia C/MR2, which constraints must wait for the determination of the gravitational coefficients J2 and C22 from the MESSENGER orbiting spacecraft, and an accurate determination of the obliquity of the Cassini state. Tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(105) years, so the spin should occupy the Cassini state and thereby define its obliquity---unless there has been a recent excitation of a free precession of the spin. Another way the spin might be displaced from the Cassini state is if the variations in the orbital elements, which change the position of the Cassini state, cause the spin axis to lag behind as it attempts to follow the state. Fortunately, the solid angle the spin axis encloses as it precesses around the Cassini state is an adiabatic invariant, and it is conserved if the orbital element variations are slow compared to the precession rate. As the precession period is O(1000) years, and the time scales of orbital parameter variations are O(105) years, the spin axis should remain very close to the Cassini state if it were ever close. But how close is close? The increasing precision of the radar and eventual spacecraft measurements warrants a check on the likely proximity of the spin axis to the Cassini state. By numerically following the positions of the spin axis and Cassini state with orbital parameters varying with time scales and amplitudes comparable to the real variations, we show that the spin should remain within 1\arcsec of the Cassini state once dissipative torques bring it there. The current spin axis position should thus define the Cassini state sufficiently to put reasonably tight constraints on the core structure---unless there has been an excitation of a free precession.

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