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

A giant impact origin for the Moon is generally accepted, but many aspects of lunar formation remain poorly understood and debated. \'Cuk 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 and 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 and 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 ($\theta > 61^{\circ}$) 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.