Resonances in the Early Evolution of the Earth-Moon System

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 1-3 . 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 2018 Earth-Moon system. Our tidal evolution model supports recent high-angular momentum giant impact scenarios to explain the Moon's isotopic composition 6-8 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-

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

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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 .

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“…This is at odds with lunar formation from a flat disk in Earth's equatorial plane, which should produce a Moon with no inclination. Hypotheses that have been proposed to explain the lunar inclination include a sequence of luni-solar resonances 1 , resonant interaction with the protolunar disk 2 , and encounters with large planetesimals following lunar formation 3 . However, past studies of lunar tidal history 6,11,12 ignored the obliquity tides within the Moon, despite the Moon having very large "forced" obliquity when it was between 30 and 40 Earth radii (R E ) due to the lunar spin axis undergoing the Cassini state transition 18,19 .…”

Collisionless encounters and the origin of the lunar inclination

“…The change in angular momentum corresponding to modern inclination excitation of ~5 degrees is likely a few tens of percent or less. Hence, the standard giant impact scenario 4 followed by little subsequent dynamical modification is compatible with the dynamical state of the modern system, while a high angular momentum impact scenario 3,5 would require another dynamical mechanism such as the evection resonance 3,12,16 to be reconciled with the modern EM system. Each suite of simulations is composed of two subsets: one with late accretion delivered via 1 body (greater excitation), the other 4 (lesser excitation).…”

“…Previous work on this problem has sought to identify mechanisms such as a gravitational resonance between the newly formed Moon and the Sun 12 or the remnant proto-lunar disk 13 that can excite the lunar inclination to a level consistent with its current value.…”

“…After the giant impact and at most ~10 3 years 14,15 , the Moon has accreted, interacted with 13 and caused the collapse of the remnant proto-lunar disk onto the Earth 6 , passed the evection resonance with the Sun 3,12,16 , and begun a steady outward tidal evolution. On a timescale (~10 6 -10 7 years) rapid relative to that characterizing depletion of planetesimals in the final post-Moon formation stage of planetary accretion 17 (called "late accretion"), the lunar orbit expands through the action of tides to an EM separation of ~20-40 R E .…”