Collisionless encounters and the origin of the lunar inclination

Past extent of lunar permanently shadowed areas

As the Moon migrated away from Earth, it experienced a major spin axis reorientation. Permanently shadowed regions (PSRs), which are thought to have trapped ices and are a main focus of lunar exploration, appeared and grew after this (Cassini state) transition and are often younger than their host craters. Here, we calculate the lunar spin axis orientation and the extent of PSRs based on recent advances for the time evolution of the Earth-Moon distance. The solar declination reached twice its current value 2.1 billion years (Ga) ago, when the PSR area was about half as large. The PSR area becomes negligible beyond 3.4 Ga ago. The site of an artificial impact in Cabeus Crater, where various volatiles have been detected, became continuously shadowed only about 0.9 Ga ago, and hence, cold-trapping has continued into this relatively recent time period. Overall estimates for the amount of cold-trapped ices have to be revised downward.

Why the day is 24 hours long: The history of Earth's atmospheric thermal tide, composition, and mean temperature

The Sun drives a semidiurnal (12-hour) thermal tide in Earth's atmosphere. Zahnle and Walker suggested that an atmospheric oscillation with period P_res ≈ 10.5 hours resonated with the Solar driving ≈600 million years ago (Ma), when the length of day (lod) was ≈21 hours. They argued that the enhanced torque balanced the Lunar tidal torque, fixing the lod. We explore this hypothesis using two different global circulation models (GCMs), finding P_res = 11.4 and 11.5 hours today, in excellent agreement with a recent measurement. We quantify the relation between P_res, mean surface temperature [Formula: see text], composition, and Solar luminosity. We use geologic data, a dynamical model, and a Monte Carlo sampler to find possible histories for the Earth-Moon system. In the most likely model, the lod was fixed at ≈19.5 hours between 2200 and 600 Ma ago, with sustained high [Formula: see text] and an increase in the angular momentum L_EM of the Earth-Moon system of ≈5%.

Vertical angular momentum constraint on lunar formation and orbital history

There are various scenarios for the formation of the Moon and subsequent dynamical evolution of the Earth–Moon system, all of which are subject to a constraint that has not previously been fully exploited. Using this constraint, we demonstrate that the recently proposed high-obliquity scenario is not consistent with the present Earth–Moon system. This constraint will have to be taken into account in all future investigations of the formation and evolution of the Moon.

The Moon likely formed in a giant impact that left behind a fast-rotating Earth, but the details are still uncertain. Here, we examine the implications of a constraint that has not been fully exploited: The component of the Earth–Moon system’s angular momentum that is perpendicular to the Earth’s orbital plane is nearly conserved in Earth–Moon history, except for possible intervals when the lunar orbit is in resonance with the Earth’s motion about the Sun. This condition sharply constrains the postimpact Earth orientation and the subsequent lunar orbital history. In particular, the scenario involving an initial high-obliquity Earth cannot produce the present Earth–Moon system. A low-obliquity postimpact Earth followed by the evection limit cycle in orbital evolution remains a possible pathway for producing the present angular momentum and observed lunar composition.

Hydrogen isotopic evidence for early oxidation of silicate Earth

The Moon-forming giant impact extensively melts and partially vaporizes the silicate Earth and delivers a substantial mass of metal to Earth's core. The subsequent evolution of the magma ocean and overlying atmosphere has been described by theoretical models but observable constraints on this epoch have proved elusive. Here, we report thermodynamic and climate calculations of the primordial atmosphere during the magma ocean and water ocean epochs respectively and forge new links with observations to gain insight into the behavior of volatiles on the Hadean Earth. As accretion wanes, Earth's magma ocean crystallizes, outgassing the bulk of its volatiles into the primordial atmosphere. The redox state of the magma ocean controls both the chemical composition of the outgassed volatiles and the hydrogen isotopic composition of water oceans that remain after hydrogen escape from the primordial atmosphere. The climate modeling indicates that multi-bar H₂-rich atmospheres generate sufficient greenhouse warming and rapid kinetics resulting in ocean-atmosphere H₂O-H₂ isotopic equilibration. Whereas water condenses and is mostly retained, molecular hydrogen does not condense and can escape, allowing large quantities (~10² bars) of hydrogen - if present - to be lost from the Earth in this epoch. Because the escaping inventory of H can be comparable to the hydrogen inventory in primordial water oceans, equilibrium deuterium enrichment can be large with a magnitude that depends on the initial atmospheric H₂ inventory. Under equilibrium partitioning, the water molecule concentrates deuterium and, to the extent that hydrogen in other forms (e.g., H₂) are significant species in the outgassed atmosphere, pronounced D/H enrichments (~1.5-2x) in the oceans are expected from equilibrium partitioning in this epoch. By contrast, the common view that terrestrial water has a carbonaceous chondritic source requires the oceans to preserve the isotopic composition of that source, undergoing minimal D-enrichment via equilibration with H₂ followed by hydrodynamic escape. Such minimal enrichment places upper limits on the amount of primordial atmospheric H₂ in contact with Hadean water oceans and implies oxidizing conditions (logfO₂>IW+1, H₂/H₂O<0.3) for outgassing from the magma ocean. Preservation of an approximate carbonaceous chondrite D/H signature in the oceans thus provides evidence that the observed oxidation of silicate Earth occurred before crystallization of the final magma ocean, yielding a new constraint on the timing of this critical event in Earth history. The seawater-carbonaceous chondrite "match" in D/H (to ~10-20%) further constrains the prior existence of an atmospheric H₂ inventory - of any origin - on post-giant-impact Earth to <20 bars, and suggests that the terrestrial mantle supplied the oxidant for the chemical resorption of metals during terrestrial late accretion.

Heterogeneous delivery of silicate and metal to the Earth by large planetesimals

After the Moon's formation, Earth experienced a protracted bombardment by leftover planetesimals. The mass delivered during this stage of late accretion has been estimated to be approximately 0.5% of Earth's present mass, based on highly siderophile element concentrations in the Earth's mantle and the assumption that all highly siderophile elements delivered by impacts were retained in the mantle. However, late accretion may have involved mostly large (≥ 1,500 km in diameter)-and therefore differentiated-projectiles in which highly siderophile elements were sequestered primarily in metallic cores. Here we present smoothed-particle hydrodynamics impact simulations that show that substantial portions of a large planetesimal's core may descend to the Earth's core or escape accretion entirely. Both outcomes reduce the delivery of highly siderophile elements to the Earth's mantle and imply a late accretion mass that may be two to five times greater than previously thought. Further, we demonstrate that projectile material can be concentrated within localized domains of Earth's mantle, producing both positive and negative ¹⁸²W isotopic anomalies of the order of 10 to 100 ppm. In this scenario, some isotopic anomalies observed in terrestrial rocks can be explained as products of collisions after Moon formation.

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

In the giant-impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however, the current lunar orbital inclination of five degrees requires a subsequent dynamical process that is still unclear. In addition, the giant-impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the lunar inclination in the past must have been very large, defying theoretical explanations. We present a 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 modelling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the Earth-Moon system. Our tidal evolution model supports recent high-angular-momentum, giant-impact scenarios to explain the Moon's isotopic composition and provides a new pathway to reach Earth's climatically favourable low obliquity.

Asteroid bombardment and the core of Theia as possible sources for the Earth's late veneer component

The silicate Earth contains Pt-group elements in roughly chondritic relative ratios, but with absolute concentrations <1% chondrite. This veneer implies addition of chondrite-like material with 0.3-0.7% mass of the Earth's mantle or an equivalent planet-wide thickness of 5-20 km. The veneer thickness, 200-300 m, within the lunar crust and mantle is much less. One hypothesis is that the terrestrial veneer arrived after the moon-forming impact within a few large asteroids that happened to miss the smaller Moon. Alternatively, most of terrestrial veneer came from the core of the moon-forming impactor, Theia. The Moon then likely contains iron from Theia's core. Mass balances lend plausibility. The lunar core mass is ~1.6 × 10²¹ kg and the excess FeO component in the lunar mantle is 1.3-3.5 × 10²¹ kg as Fe, totaling 3-5 × 10²¹ kg or a few percent of Theia's core. This mass is comparable to the excess Fe of 2.3-10 × 10²¹ kg in the Earth's mantle inferred from the veneer component. Chemically in this hypothesis, Fe metal from Theia's core entered the Moon-forming disk. H₂O and Fe₂O₃ in the disk oxidized part of the Fe, leaving the lunar mantle near a Fe-FeO buffer. The remaining iron metal condensed, gathered Pt-group elements eventually into the lunar core. The silicate Moon is strongly depleted in Pt-group elements. In contrast, the Earth's mantle contained excess oxidants, H₂O and Fe₂O₃, which quantitatively oxidized the admixed Fe from Theia's core, retaining Pt-group elements. In this hypothesis, asteroid impacts were relatively benign with ~1 terrestrial event that left only thermophile survivors.