Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth

Abstract

In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circumterrestrial disk; however the current lunar orbital inclination of 5 • requires a subsequent dynamical process that is still debated [1][2][3] . In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition 4, 5 . Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modeling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the 1 arXiv:1802.03356v1 [astro-ph.EP] 9 Feb 2018Earth-Moon system. Our tidal evolution model supports recent high-angular momentum giant impact scenarios to explain the Moon's isotopic composition [6][7][8] and provides a new pathway to reach Earth's climatically favorable low obliquity.The leading theory for lunar origin is the giant impact 9, 10 , which explains the Moon's large relative size and small iron core. Here we refer to the giant impact theory in which the Earth-Moon post-impact angular momentum (AM) was the same as it is now (in agreement with classic lunar tidal evolution studies 11, 12 ) as "canonical". In the canonical giant impact model 13 , a Mars-mass body obliquely impacts the proto-Earth near the escape velocity to generate a circum-terrestrial debris disk. The angular momentum of the system is set by the impact, and the Moon accretes from the disk, which is predominantly (> 60 wt%) composed of impactor material. However, Earth and the Moon share nearly identical isotope ratios for a wide range of elements, and this isotopic signature is distinct from all other extraterrestrial materials 4, 5 . Because isotopic variations arise from multiple processes 4 , the Moon must have formed from, or equilibrated with, Earth's mantle 5,14 . Earth-Moon isotopic equilibration in the canonical model has been proposed by Pahlevan and Stevenson 15 , but has been questioned by other researchers 16 , who suggest that the large amount of mass exchange required to homogenize isotopes could lead to the collapse of the proto-lunar disk.Cuk and Stewart 6 proposed a new variant of the giant impact that is based on an initially high AM Earth-Moon system. In this model, a late erosive impact onto a fast-spinning proto-Earth produced a disk that was massive enough to form the Moon, and was composed primarily of material from Earth, potentially satisfying the isotopic observations. Canup 7 presented a variation of a high-2 AM origin in which a slow collision between two similar-mass bodies produces a fast-spinning Earth and disk with Earth-like composition. Subsequently, Lock et al. 8 have argued that a range of hig...

The structure of terrestrial bodies: Impact heating, corotation limits, and synestias

“…Alternatively, a synestia could be brought below the CoRoL by removing AM from the structure by tides, interactions with the host star [ Murray and Dermott , ], or three body interactions with the host star and a moon [ Goldreich , ; Touma and Wisdom , ; Ćuk and Stewart , ; Wisdom and Tian , ; Ćuk et al , ; Tian et al , ]. A significant reduction of AM by tides takes 10 3 –10 9 years, depending on the mechanism, which is generally greater than the radiative cooling timescale.…”

The Origin of the Moon Within a Terrestrial Synestia

“…Proposed solutions in the framework of the canonical model include a complex sequence of luni‐solar resonances (Touma & Wisdom, ), resonant interactions between the Moon and the circumterrestrial disk (Ward & Canup, ), and encounters between large planetesimals and the newly formed Earth‐Moon system (Pahlevan & Morbidelli, ). Recently, Chen and Nimmo () and Ćuk et al () investigated inclination damping by lunar obliquity tides, and Ćuk et al () found that lunar inclination must have been large (∼30°) prior to the point in tidal recession where the lunar orbit transitions between Cassini states (distinct dynamical solutions that govern the alignment of the lunar spin axis and orbital plane, see Peale, ). Such a large inclination prior to the Cassini state transition defies explanation by any of the previously proposed mechanisms to raise lunar inclination after a canonical giant impact.…”

“…Ćuk and Stewart () showed that an evection resonance could drive significant AM loss from the Earth‐Moon system after the Moon‐forming impact. Since Ćuk and Stewart (), additional mechanisms have been found that could remove AM during lunar tidal evolution (Ćuk et al, ; Tian et al, ; Wisdom & Tian, ). Allowing for a change of AM after the impact significantly expands the range of possible impact parameters for the Moon‐forming collision.…”

“…Ćuk and Stewart () and Canup () showed that high‐energy, high‐AM impact events can inject much more material into orbit than canonical impacts. In addition, Ćuk et al () showed that if the Earth after the impact had both high AM and high obliquity, an instability during the Laplace plane transition could both remove AM from the Earth‐Moon system and explain the Moon's present‐day orbital inclination. With these promising dynamical results, high‐AM giant impact scenarios for lunar origin warrant continued investigation.…”

“…Our model provides a promising pathway to explain all the key observables of the Moon discussed above: the isotopic similarity between Earth and the Moon; the magnitude and pattern of moderately volatile element depletion in the Moon; and the large mass of the Moon. If Earth had a large obliquity after the giant impact, then a single event may also explain the inclination of the lunar orbit and the present‐day AM of the Earth‐Moon system (Ćuk et al, ).…”