Tidal Evolution of the Earth-Moon System with a High Initial Obliquity

Abstract

A giant impact origin for the Moon is generally accepted, but many aspects of lunar formation remain poorly understood and debated. Ćuk et al. (2016) proposed that an impact that left the Earth-Moon system with high obliquity and angular momentum could explain the Moon's orbital inclination and isotopic similarity to Earth. In this scenario, instability during the Laplace Plane transition, when the Moon's orbit transitions from the gravitational influence of Earth's figure to that of the Sun, would both lower the system's angular momentum to its present-day value and generate the Moon's orbital inclination. Recently, Tian & Wisdom (2020) discovered new dynamical constraints on the Laplace Plane transition and concluded that the Earth-Moon system could not have evolved from an initial state with high obliquity. Here we demonstrate that the Earth-Moon system with an initially high obliquity can evolve into the present state, and we identify a spin-orbit secular resonance as a key dynamical mechanism in the later stages of the Laplace Plane transition. Some of the simulations by Tian & Wisdom (2020) did not encounter this late secular resonance, as their model suppressed obliquity tides and the resulting inclination damping. Our results demonstrate that a giant impact that left Earth with high angular momentum and high obliquity (θ > 61 • ) is a promising scenario for explaining many properties of the Earth-Moon system, including its angular momentum and obliquity, the geochemistry of Earth and the Moon, and the lunar inclination.

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

“…So where does all this leave us? Well, the last major generalization of Laplace's work ushered a stream of applications, mainly to extra solar settings (Muñoz & Lai 2015;Zanazzi & Lai 2016), but also to scenarios of Lunar formation which argue for an initially steeply oblique and fast spinning Earth (Ćuk et al 2016;Tian & Wisdom 2020;Ćuk et al 2021). We can foresee the same for our renewed focus on the foundations of the Laplace Surface itself, and for the rich structure of equilibria we have identified, with applications ranging from man made satellites, to exo-moons around planets on Kozai-Lidov cycles, then debris disks with enclosed planets, the whole perturbed by a wide eccentric binary.…”

“…The circle was recently closed back onto the solar system, when it was realized that origin around a fast spinning and oblique Earth, which is favored on geochemical grounds, could generate a Moon whose Laplace plane may very well be prone to TTN's eccentricity instability! (Ćuk et al 2016;Tian & Wisdom 2020;Ćuk et al 2021) The present work begins where TTN left the Laplace Surface, and relaxes yet another assumption in the original Laplace story by explicitly accounting for an eccentric binary companion, thus effectively breaking the hitherto assumed axisymmetry of the outer perturber. This level of generality is again demanded by exo-planetary systems, the disks that generate them, remnant debris disks, all in the presence of a massive wide binary companion on an eccentric (and inclined) orbit.…”