HR: 14:25h
AN: P13F-04    [Abstracts]
TI: Tidal and librational feedback in icy satellite shells
AU: * Bills, B G
EM: bbills@ucsd.edu
AF: NASA GSFC, Greenbelt Road, Greenbelt, MD 20771, United States
AU: * Bills, B G
EM: bbills@ucsd.edu
AF: Scripps Institution of Oceanography, University of California, La Jolla, CA 92093,
AU: Nimmo, F
EM: fnimmo@pmc.ucsc.edu
AF: Earth Sciences, University of California, Santa Cruz, CA 95064,
AB: Tides and librations are both dynamic responses of satellites to gravitational perturbations from their primaries, and are usually considered separately. We examine the case in which resonantly enhanced libration of a decoupled ice shell becomes large enough to influence the amount and pattern of tidal heating. This can control the thickness and moments of inertia of the shell, which thereby influences the libration. The dynamics, stability, and characteristic time scales of this feedback loop are not yet well characterized, but "anomalously active" bodies like Enceladus suggest that the conventional view of tidal heating needs to be expanded somewhat. A synchronously rotating satellite in an eccentric orbit has a tidal bulge which changes in amplitude and position, as the distance and apparent direction to the primary changes over the course of each orbital circuit. The optical librations, or oscillations in angular position of the tidal bulge, have amplitude γ = 2e, where e is the orbital eccentricity. When averaged over an orbital period, the tidal heating rate can be expressed as\[ \frac{dE}{dt}=-\frac{3}{2}\frac{k}{Q}\frac{n⁵R⁵}{G}\left( 3e²+γ ²\right) \] where k is a tidal Love number, Q is a tidal quality factor, R is the satellite mean radius, and G is the gravitational constant. The first term in parentheses reflects the contribution from radial tides, or change in amplitude of the tidal bulge, while the second term is due to change in its position. Forced librations in longitude are periodic deviations from uniform rotation which a satellite may experience due to gravitational torques in an eccentric orbit. The free libration rate ω is given by \[ ω ²=3n²(B-A)/C, \] where n is the orbital angular rate, and A < B < C are the principal moments of inertia. In most cases, the equatorial moment difference B-A for a satellite is a small fraction of the polar moment C, and the free libration period is much longer than the orbital period. In that case, the libration amplitude is small. However, if an ice shell is decoupled from the interior by a fluid layer, the libration response is controlled by the moments of inertia of the shell itself, and resonant enhancement is possible. If the amplitude of the forced libration is comparable to the optical libration, the amount and spatial pattern of tidal heating will change.
DE: 5417 Gravitational fields (1221)
DE: 5450 Orbital and rotational dynamics (1221)
SC: Planetary Sciences [P]
MN: 2007 Fall Meeting