Excitation of Lunar Eccentricity by Planetary Resonances

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The present free eccentricity (e) of the Moon's orbit is 0.052, and direct measurements using lunar laser-ranging (Williams et al. 2001) have shown it to be currently slowly increasing due to dominance of Earth's ocean tides over lunar satellite tides. Since the tidal e-excitation is just a side effect of orbital expansion, its significance for lunar e must have been greatest during the Hadean eon (4.5-4 Gyr ago). Therefore, tidal excitation is unlikely to have produced the present e of the Moon, as the efficiency of ocean tides must have been much lower in the distant past (Bills and Ray 1999 and references therein), and the Moon's e was likely damped, rather than excited, at this epoch.
Kaula and Yoder (1976) proposed that lunar e might have been excited by a temporary capture in the Jovian evection resonance (at 53 R_E, when the lunar apsidal precession period equaled one Jovian year). We perfomed numerical integrations of that resonance passage, and found that the secular variations of Earth's orbit make capture impossible, but lead to hundreds of resonance passages as the resonance slightly shifts its location. These passages lead to a "random-walk" type changes in lunar eccentricity. If the pre-resonance eccentricity of the Moon was 0.005-0.01, the average post-resonance one is about 0.03-0.04 (with the tidal excitation subsequently bringing e up to its present level). We also discovered another planetary resonance of similar strength at about 46 R_E, involving the 1:2 commensurability with the 8-year 3:5 inequality between Earth and Venus. This resonance is strong enough to enhance small lunar eccentricities by a factor of few. A pre-resonance free e of 0.001 can plausibly be a product of tidal excitation, allowing for a total circularization of lunar orbit at some point in the past.

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