HR: 16:30h
AN: G42C-03 INVITED     [PDF]
TI: Mercury's Interior From Geodesy of Librations
AU: * Peale, S J
EM: peale@io.physics.ucsb.edu
AF: UCSB, Dept. of Physics, Santa Barbara, CA 93106 United States
AB: Mercury offers a unique opportunity to use the equilibrium rotation state and librations about this state to investigate properties of its interior. In equilibrium, Mercury rotates at a uniform rate $\dot\psi=3n/2$ ($n=$ orbital mean motion) in a Cassini state with the spin axis displaced slightly from the orbit normal (obliquity near 1.6 arcmin), which displacement is induced by the precession of the orbit on the Laplacian plane. The spin axis, orbit normal, and normal to the Laplacian plane remain coplanar while the former two precess about the latter with the period of the orbital precession. If displaced slightly from this state, Mercury's spin will exhibit a free precession about the state with period near 1300 years and a free libration in longitude with period near 12 years. Tidal dissipation will damp both free precession and libration on time scales $<<$ the solar system age, so we expect to find Mercury very close to its equilibrium Cassini state where it remains during slow orbital variations because of an adiabatic invariant. The gravitational torque on the axial asymmetry is the restoring torque for the free librations when averaged over the orbit. This same torque causes a small forced libration in longitude (amplitude 20 to 40 arcsec) with an 88 day period due to the torque's periodic reversal around the orbit . It is desirable to determine Mercury's obliquity $\theta$ and the amplitude of its forced libration in longitude $\phi$ to very high accuracy, because their determination along with accurate values of the gravitational harmonic coefficients $C_{20}$ and $C_{22}$ can reveal whether or not Mercury's core is molten by determining the ratio $C_m/C$. $C_m$ and $C$ are the maximum principal moments of inertia for the mantle and entire planet respectively, where both moments of inertia are determined independently. This assertion relies on the axial asymmetry being due to the mantle alone, where the 88 day forced libration in longitude will have twice the amplitude if the mantle is decoupled from the interior by a molten layer than it would have if the planet is a rigid body. The precise measurements necessitated by the small values of both the obliquity and the forced libration amplitude as well as similarly precise determination of $C_{20}$ and $C_{22}$ will be possible from either of two spacecraft, MESSENGER from the U.S. and BepiColombo from Europe, which will orbit Mercury during the next decade. More astounding, a radar technique called Radar Speckle Differential Interferometry (RSDI) (Holin, 1992) is capable of arcsec accuracy in determining both the obliquity and the forced libration amplitude from the ground, where feasibility has been demonstrated (Margot {\it et al.} 2002). The RSDI and spacecraft techniques will be described. Assumptions necessary for success of the experiment will be detailed, and recent numerical calculations of Mercury's spin evolution will be discussed. Some caveats will be pointed out, but as the assumptions are likely to be satisfied, there is a high probability that precise geodesy will yield the desired information about Mercury's interior.
DE: 1227 Planetary geodesy and gravity (5420, 5714, 6019)
DE: 5450 Orbital and rotational dynamics
DE: 6235 Mercury
DE: 6949 Radar astronomy
DE: 8147 Planetary interiors (5430, 5724)
SC: Geodesy [G]
MN: 2003 Fall Meeting