Physics
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.p12a..08b&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #P12A-08
Physics
5417 Gravitational Fields (1221), 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics (1221)
Scientific paper
The obliquity of Titan, which is the angular separation between its spin and orbit poles, is small but certainly non-zero. An accurate measurement of this angle will provide constraints on the moments of inertia of the body and thereby yield valuable information about the composition and state of the interior. Cassini radar measurements should allow determination of this quantity. For a perfectly rigid body, the obliquity varies in response to gravitational torques and has a current value which depends upon both rate of change and initial conditions. In that case, the moments of inertia are determined from two sources: the harmonic degree two gravity field, and observations of the rate of spin pole precession. If Titan were in that category, the prospects for determination of the moments of inertia would be rather bleak, as the precession rate is likely to be small enough to avoid detection during the Cassini mission. However, an alternative approach is likely applicable. For bodies, like the Moon, in which tidal dissipation has been sufficiently vigorous, the spin pole will be driven into a generalized Cassini state. In such a state, the spin pole and orbit pole remain coplanar with the invariable pole, about which the orbit pole precesses. In that case, the obliquity is very nearly constant, and the dynamical information is encoded in the obliquity value itself, rather than the spin pole precession rate. We suggest that Titan is sufficiently dissipative that is has likely attained such a state. The relevant invariable pole is close to the spin pole of Saturn. A plausible range of polar moment values for Titan is (0.3≤ C/M R2≤ 0.4), where M and R are the mass and mean radius of the body. The upper bound corresponds to a homogeneous body, while the lower bound is more centrally condensed than the Earth. The corresponding range of tidally damped obliquity values is (0.07° ≤ ǎrepsilon ≤ 0.13° ) It is anticipated that the Cassini radar measurements will eventually yield constraints on the spin pole orientation with an accuracy no worse than 0.01°. This accuracy is set by the angular resolution of the radar at the surface of Titan. These observations of Titan's obliquity should provide an estimate of its moments of inertia which is independent of the method based on measurement of gravitational moments alone, which is forced to assume hydrostatic equilibrium.
Bills Bruce G.
Nimmo Francis
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