Other
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004agufm.g33a..03p&link_type=abstract
American Geophysical Union, Fall Meeting 2004, abstract #G33A-03
Other
5417 Gravitational Fields (1227), 5450 Orbital And Rotational Dynamics, 6250 Moon (1221), 1221 Lunar Geodesy And Gravity (6250), 1227 Planetary Geodesy And Gravity (5420, 5714, 6019)
Scientific paper
If free rotational modes of significant amplitude are found in the precise measurements of Mercury's obliquity and the libration in longitude by radar speckle displacement interferometry (RSDI), and the MESSENGER and BepiColombo spacecraft, sources of excitation of the free modes will be constrained by the time scales for damping their amplitudes. The free modes consist of libration in longitude (10 year period), precession of the spin about the Cassini state (1000 year period), and wobble (500 year period), where the term free means the modes can have arbitrary amplitude and phase. The amplitude of the physical libration in longitude and the obliquity of the Cassini state together with the gravitational coefficients J2 and C22 determine the state and constrain the geometry of Mercury's core (e.g. Peale, et al. 2002). A free libration in longitude does not compromise the determination the 88 day forced libration, since the latter is simply superposed and its amplitude easily determined. But a free precession will make the determination of the obliquity of the Cassini state somewhat uncertain. The latter obliquity is crucial in constraining C/MR2, where C,M,R are moment of inertia, mass and radius of Mercury. The signature of a free precession would be finding the spin axis displaced from the plane determined by the orbit normal and the normal to the Laplacian plane and thereby not occupying the Cassini state. A free wobble will be hard to detect with the proposed measurements, but it should not compromise the determination of the core properties. Already RSDI has determined that Cm/C<0.7 with 95% confidence by measuring a large physical libration amplitude of 60± 5 arcsec (Margot et al. 2004), which is consistent with Mercury having a molten core. Cm is the moment of inertia of the mantle alone. That means we must add the dissipation at the core-mantle interface to the traditional tidal friction in determining the damping times of the free modes. We model the torque between a liquid core and solid mantle as being simply proportional to the difference in the angular velocities and relate the constant of proportionality to the kinematic viscosity of the core material by comparing with known spin-up time scales. Representative time scales in years for damping the free modes are as follows with subscripts ℓ,p,w indicating longitude, precession and wobble respectively, and T,C indicating tide and core: τ {ℓ T}=9.3e5,; τ {ℓ C}=2.1e5 (1.7e5 for tides and core acting together), τ pT}=6.4e6,;τ {pC}=1.0e5,;τ_ {wT=3.7e6,; τ wC=3.5e8. The damping times of all the free modes with both tidal and core-mantle dissipation acting together are short compared with the age of the solar system, so we would expect all such amplitudes to be undetectable, at least for the near future, and the state and geometry of the core to be discernible with the radar and spacecraft measurements. Otherwise, we must seek still unspecified processes for their excitation. The obvious choice of a relatively recent collision by an asteroid or comet is improbable because of the short damping time scales.
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