Physics
Scientific paper
Dec 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufm.g53c..08p&link_type=abstract
American Geophysical Union, Fall Meeting 2005, abstract #G53C-08
Physics
1221 Lunar And Planetary Geodesy And Gravity (5417, 5450, 5714, 5744, 6019, 6250), 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics (1221), 6019 Gravitational Fields (1221), 6035 Orbital And Rotational Dynamics
Scientific paper
In determining Mercury's core structure from its rotational properties, the value of C/MR2 from the location of Cassini state 1 is crucial. (C,M,R are Mercury's moment of inertia, mass and radius.) The occupancy of Cassini state 1 means the spin axis is nearly fixed in the frame precessing with the orbit and its position would thereby determine the position of the state. Although tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(105) years, the spin might still be displaced from the Cassini state if the variations in the orbital elements induced by planetary perturbations, which change the position of the Cassini state, cause the spin to lag behind as it attempts to follow the state. The spin axis is expected to follow the Cassini state for variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. The exception would be if there are forcing terms in the perturbations that are nearly resonant with the 1000 year precession period. The precision of the radar and eventual spacecraft measurments of the position of Mercury's spin axis warrants a check on the likely proximity of the spin axis to the Cassini state. How confident should we be that the spin axis position defines the Cassini state sufficiently well for a precise determination of C/MR2? By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years (Quinn et al., 1991) and short time scale variations for 20000 years (JPL Ephemeris DE 408, Standish, 2005), we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. In this process the spin is located in the orbit frame of reference, which in turn is referenced to the inertial ecliptic plane of J2000. There are no pertubations with periods resonant with the precession period that could cause large separations. The maximum 1'' deviation is less than currently projected uncertainties in both radar and spacecraft determinations of the spin axis position.
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