Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dps....40.5706g&link_type=abstract
American Astronomical Society, DPS meeting #40, #57.06; Bulletin of the American Astronomical Society, Vol. 40, p.502
Mathematics
Logic
Scientific paper
Principal moments of inertia of the Moon differ significantly. To explain these differences it has been suggested that the Moon may have frozen in a past deformation state when it was orbiting closer to Earth and subject to stronger tidal and rotational forces. One problem with this hypothesis has been that ratios of three moments do not match predictions for a synchronously-rotating Moon in a circular orbit. We calculate the predicted principal moments of inertia for a satellite that freezes in its deformation in a non-zero eccentricity orbit, for all resonances of spin and orbit velocity. We find that lunar moments of inertia are in very close agreement with past high-eccentricity orbits, including a synchronous state and two cases of 3:2 spin-orbit resonance. An apparent dilemma with past 3:2 spin-orbit resonance is that after accretion outer parts of the Moon were likely molten and unable to support the traditional permanent quadrupole deformation required to stabilize the resonance. Tidal torques would have despun the Moon to synchronous rotation faster than any permanent deformation could develop. An analysis of the tidal torques required to stabilize a resonance reveals that the lifetime of quadrupole deformation need only last as long as the libration damping timescale, provided that a new semi-permanent deformation replaces it within the same timescale. A source of such a deformation is the time-averaged tidal bulge raised by the Earth. It is plausible that a partially molten and deformed outer portion of the Moon with a modest relaxation time could have served as a stabilizing force for any 3:2 resonance. This process also applies to synchronous resonance and implies that lunar orientation may have been established at a very early time. This permits us to constrain the timing and formation mechanism for several major geologic lunar features, including the degree-2 shape.
Garrick-Bethell Ian
Zuber Maria T.
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