Mathematics – Probability
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p51c1464a&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P51C-1464
Mathematics
Probability
[6250] Planetary Sciences: Solar System Objects / Moon
Scientific paper
The Moon's current spin-orbit resonance results in it continuously pointing the same side towards the Earth. This is the side largely covered by dense, dark mare basalts, the pattern of which, to some, resembles the shape of a man's face. For dynamical stability, the Moon must spin about its axis of maximum moment of inertia, and point its axis of minimum inertia in direction of the Earth, leaving two options of facing the current near-side or far-side towards us. While both configurations are local potential energy minima, we show that under certain conditions, breaking and locking into resonance from a state of rapid rotation preferentially selects one configuration over the other. We analytically and numerically simulate the locking of the Moon into resonance and consider the dependence on the relevant geophysical parameters at the time of last resonance locking. The probability of each configuration depends upon the gravitational potential energy asymmetry dominated by the octupole moment of the Moon, and by the energy dissipated per tidal cycle dominated by the internal properties of the Moon. If these energies are widely separated, the two configurations are equally likely. If these energies are comparable, interesting dynamical behavior results. For example, we find that in the current orbit with the current best-estimated parameters, the Moon is more likely to fall into the higher of the two energy configurations facing the near-side towards the Earth with a preference of ~3:1.
Aharonson Oded
Goldreich Peter
Sari Re'em
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