Tidal Evolution of the Evection Resonance/Quasi-Resonance and the Angular Momentum of the Earth-Moon System

TL;DR

This study investigates how tidal interactions and the evection resonance/quasi-resonance influence the Earth's and Moon's angular momentum, revealing that the timing of resonance escape affects the final angular momentum, which often remains higher than current levels.

Contribution

It introduces a constant-time delay tidal model to analyze lunar orbital evolution through evection and quasi-resonance, highlighting the impact of Earth's mantle cooling on angular momentum transfer.

Findings

Early exit from evection leads to quasi-resonance, regulating lunar eccentricity.

Angular momentum transfer depends on tidal dissipation ratios and Earth's mantle state.

Post-resonance angular momentum often exceeds current Earth-Moon system value.

Abstract

Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moon's orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earth's heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value.