New approaches to the Moon's isotopic crisis

Abstract

Recent comparisons of the isotopic compositions of the Earth and the Moon show that, unlike nearly every other body known in the Solar System, our satellite's isotopic ratios are nearly identical to the Earth's for nearly every isotopic system. The Moon's chemical make-up, however, differs from the Earth's in its low volatile content and perhaps in the elevated abundance of oxidized iron. This surprising situation is not readily explained by current impact models of the Moon's origin and offers a major clue to the Moon's formation, if we only could understand it properly. Current ideas to explain this similarity range from assuming an impactor with the same isotopic composition as the Earth to postulating a pure ice impactor that completely vaporized upon impact. Several recent proposals follow from the suggestion that the Earth–Moon system may have lost a great deal of angular momentum during early resonant interactions. The isotopic constraint may be the most stringent test yet for theories of the Moon's origin.

1. The giant impact hypothesis

The giant impact hypothesis of the Moon's origin arose in the aftermath of the successful Apollo missions to the Moon, which returned hundreds of kilograms of lunar surface material to the Earth and engendered a vigorous research programme in lunar science. The returned Apollo samples (supplemented by the Soviet Luna sample returns and lunar meteorite finds) did not fit any of the three classic models of lunar origin (fission, capture and co-accretion) and initiated a period of deep confusion about the Moon's origin lasting from about 1969 to 1984. During this time, a great many detailed facts about the Moon, its geology, geochemistry and chronology were gleaned from the lunar rocks, but no clear picture of its origin emerged.

It is now clear that the Moon is a differentiated body with a bulk chemical composition generally similar to that of the Earth's mantle, but compared with the Earth, the Moon is strongly depleted in volatiles such as Na, K, Rb and especially water. Until recently, bulk chemical estimates also suggested that the Moon is slightly enriched in refractory elements such as Al and Ca, although revisions of the Moon's crustal thickness have now made the Moon seem more similar to the Earth in these elements. In addition, the Moon's silicate rocks are believed to contain about twice as much iron oxide, FeO, as the Earth's mantle, although Warren [1] dissents from this difference, as listed in table 1. Table 1, after Khan et al. [2], compares several estimates of the major oxide abundances in the bulk silicate Moon with a similar estimate for the Earth's mantle. The slight enrichment of the Moon in Al and Ca reported in this table has now been largely or completely erased by the recent discoveries of NASA's GRAIL mission that reduced the average crustal thickness of the Moon to 35 km [9]. The volatile element depletions, however, remain as strong chemical differences between the Earth and Moon, in spite of more recent discoveries suggesting that the Moon's interior is not as depleted in water as initially supposed.

Table 1.

Bulk silicate composition of the Moon [2].

source	CaO	FeO	MgO	Al2O3	SiO2
Ringwood [3]	3.7	14.1	32.9	4.2	45.1
Taylor [4]	4.6	13.1	32.3	6.1	43.9
Wänke & Dreibus [5]	3.8	13.1	32.6	4.6	45.9
O'Neill [6]	3.3	12.4	35.1	3.9	44.6
Kushov & Kronrod I [7]	4.8	10.4	28.5	6.3	50.0
Kushov & Kronrod II [7]	4.3	11.7	29.6	5.9	48.5
Warren [1]	3.0	9.1	35.6	3.8	46.2
bulk silicate Earth; McDonough & Sun [8]	3.6	8.2	38.2	4.5	45.5

Geochemist Ted Ringwood [10,11] suggested that the chemical differences between the Earth and Moon could be explained if one supposed that the Moon formed out of Earth mantle material that was first vaporized and then re-condensed under conditions that permitted volatiles to escape. Ringwood did not, however, offer a plausible scenario under which this evaporation could occur [12] and his idea lay fallow for more than a decade.

Our modern understanding of the Moon's origin grew out of dynamical studies of planetary accretion that, over the decades from the 1950s to the 1980s, focused on the likelihood of increasingly large impacts during the end stages of planetary growth. Urey [13] had posited growth from cosmic dust falling directly onto growing planets, resulting in very cold internal temperatures (indeed, he believed that the Moon was an undifferentiated body right up until Apollo 11 brought back the first samples of igneous rocks). Safronov [14] and Kaula [15] envisioned multi-kilometre planetesimal impacts that somewhat alleviated the lack of initial heating of the Earth and Moon, but not until the work of Wetherill [16] and Greenberg et al. [17] was it appreciated that the final stages of planetary accretion must have occurred through giant, planetary-scale impacts.

The radical idea that the Moon might have been born during a planetary size impact late in Earth's accretion history was first vetted at a conference in 1974, at which Hartmann & Davis [18], reasoning by an appeal to the hierarchical growth scenario, suggested that a very large impact might have injected a cloud of dust and debris from the Earth into orbit and thus formed the Moon. At the same conference, Cameron & Ward [19], reasoning from the large ‘excess’ angular momentum of the Earth–Moon system compared with the other planets in our Solar System, went much further and argued that the impactor would have to be as big as Mars to inject the necessary angular momentum and at the same time actually orbit material by non-gravitational accelerations of expanding vapour. These apparently outrageous suggestions were not taken seriously by most of the lunar science community until a conference on the origin of the Moon in 1984 pointed up the difficulties of the classic origins.

The possibility of a giant impact then received support from numerical simulations [20,21], which showed that a very large impact (and only a planetary-scale impact) could eject a moon-mass of material into orbit around the Earth and give it the observed angular momentum of the Earth–Moon system. Cameron & Ward [19] had argued that the debris could be injected into orbit by pressure gradients in a cloud of expanding vapour and that the ejected debris' orbits would subsequently be circularized by particle–particle collisions in the dense disc. Stevenson [22] supported this idea and further proposed that gravitational torques from the massive and highly distorted Earth–projectile system would also be effective, a mechanism supported by subsequent numerical simulations. Melosh & Sonett [23] argued that the process of impact jetting during an oblique collision could produce sufficient amounts of high-temperature vapour and that this vapour would be an approximately equal mixture of target and projectile material. Because jetting only incorporates material from near the surface of the impacting objects, they emphasized that metallic iron would be excluded from the orbiting debris provided that both projectile and target bodies had already formed cores. Following previous workers [18,19], Melosh and Sonett also emphasized the fundamental link between the geochemical evidence for volatile depletion and the essential role of vaporization in injecting material into orbit. Stevenson [24] examined the dynamics of a two-phase melt and vapour disc orbiting the Earth and again found that such a disc could plausibly form a satellite closely resembling our Moon.

The first numerical simulations of the moon-forming impact were performed in the aftermath of the 1984 Kona conference. The model of Benz et al. [20] employed the smooth particle hydrodynamic (SPH) method, which has subsequently become the method of choice for these complex simulations that must incorporate self-gravity, thermodynamics and hydrodynamics. Kipp & Melosh [21] used an Eulerian hydrodynamic simulation, a method that has only recently become capable of fully addressing these complexities [25].

Subsequent numerical simulations by Canup & Asphaug [26] strongly supported the giant impact scenario and demonstrated a wide class of conditions under which a planetary-scale impact could produce a large moon with the angular momentum of our current Earth–Moon system. These simulations readily explain the presence of a moon in orbit around the Earth, the depletion of volatiles in its material and the lack or strong depletion of metallic iron in the Moon. Small compositional differences between the Earth and Moon (such as the Moon's putative high iron oxide content) could be explained by differences between the proto-Earth and the projectile (now often called ‘Theia’) [27].

All of the initial numerical simulations of the Moon's origin were constrained by the then-perceived need to nearly match the angular momentum of the Earth–Moon system [28]. The other major constraint was that the final mass in an orbiting proto-lunar disc must be at least equal to, or perhaps twice as large as, the current Moon's mass to account for viscous dissipation in the disc and consequent de-orbiting of some material as the disc spreads. All of these simulations agreed in finding that a Mars-mass impactor striking obliquely at a velocity not much larger than the Earth's escape velocity best satisfies these two constraints.

Given these constraints, all of these previous simulations found that the projectile, while contributing about 10% to the mass of the Earth (roughly equal to the ratio of the mass of Mars to the mass of the Earth), contributed between 70 and 90% to the mass of the Moon-forming disc (summarized by Canup et al. [25]). These highly unequal contributions of the projectile material to the Earth and Moon were not initially regarded as a serious problem: indeed, this was seen as a way to explain the larger iron abundance in the bulk Moon. Mcfarlane [27], on geochemical grounds, even argued that the Earth could not have contributed more than about 50% of the mass of the Moon. However, we now recognize this asymmetric mass contribution as a looming problem; a problem brought on by high-precision measurements of isotopes in the Earth and Moon.

2. Isotopic similarity of the Earth and Moon

There were signs of an isotopic problem with the then-understood giant impact hypothesis as early as 2001. Three-isotope (¹⁶O, ¹⁷O and ¹⁸O) oxygen measurements on the SNC (Shergottie, Nakhlite and Chassigny Martian) meteorites indicated a significant offset between the Martian and terrestrial mass-fractionation lines [29]. Older oxygen isotopic measurements with large error bars could accommodate this small difference between Earth isotopes and Mars (assuming that the modern planet Mars is a proxy for the Moon-forming impactor Theia), but these new measurements indicated that, lacking some homogenization mechanism, Mars itself could not have been the impactor. This can, of course, be reconciled if the actual impactor is isotopically nearly identical to the Earth (as the enstatite meteorites nearly are), but as error bars shrank, the O-isotopic similarity between the Earth and Moon came to seem anomalous. A very small difference in the Δ¹⁷O ratio between the Earth and lunar rocks of about 12±3 ppm has recently been reported [30] (as well as a larger difference from enstatite chondrites), but that still leaves the Earth–Moon system as more similar in O isotopes than any other two bodies in the Solar System. The Earth–Moon similarity contrasts sharply with the O-isotope trends of most meteorites, which are substantially different from the Earth–Moon system and from each other. Nor is there any apparent trend with distance from the Sun, for while Mars' O-isotopes lie above the Earth–Moon mass-fractionation line, the still more distant Vesta's O-isotopes (represented by the HED meteorite clan) lie well below that line.

Adding to the eerie similarity between oxygen isotopes of the Earth and Moon, many other isotopic systems show a near identity of the two bodies. In 1995, Humayun & Clayton [31,32] showed that ³⁹K and ⁴¹K are nearly identical in the Earth and Moon, although this similarity is not unique to the Earth–Moon system, because this identity is found in nearly all Solar System bodies and is surprisingly independent of K depletion in the rocks. In 1998, Lugmair & Shukolyukov [33] extended the similarity between the Earth and Moon to the ⁵³Mn–⁵³Cr system. In 2007, this similarity was further extended to ²⁸Si, ²⁹Si, ³⁰Si [34] and more tellingly to the radiogenic ¹⁸²W, ¹⁸⁴W system [35], although that study did report a slight excess of ¹⁸²W/¹⁸⁴W that was not statistically significant. The similarity in the W system indicates that the impactor and proto-Earth must have had a nearly identical history of iron–silicate differentiation, a situation that is hard to envision in the context of current models for terrestrial planet formation. Finally, in 2012, Zhang et al. [36] showed that the highly refractory element Ti also shows near identity of ⁴⁷Ti and ⁵⁰Ti between the Earth and Moon. The difference between the abundance of these two isotopes in the Earth and Moon is only about 1/150 of the difference between the Earth and carbonaceous chondrites, again underlining the eerie similarity between the Earth and Moon.

Some isotopes do show differences between the Earth and Moon. For example, Paniello et al. [37] find an enrichment of heavy isotopes of Zn in lunar rocks which they attribute to the depletion of the volatile element Zn in a hot proto-lunar disc. Furthermore, some small isotopic differences may be expected between the Earth and Moon if, as is widely believed, the Earth received a ‘late veneer’ of chondritic material that supplied its inventory of highly siderophile elements, while the Moon escaped such an addition [38]. This late veneer could comprise between 0.1% and perhaps as much as 0.8% of the mass of the bulk silicate Earth and could plausibly explain the small differences in Δ¹⁷O recently detected between Earth and Moon rocks [30], as well as affecting other isotopic systems. Small, post-impact, differences in isotopic ratios such as ¹⁸²W/¹⁸⁴W occur on the Earth itself [39,40], so at some high level of precision we should expect isotopic divergences between the Earth and Moon that are more indicative of post-formation events than of their original heritage.

The obvious conclusion of all these isotopic similarities is that the Moon is almost entirely derived from the Earth's mantle. But what are we to make of the likely difference in FeO abundance between the Earth and Moon, and the volatile depletions of the Moon? We have the peculiar circumstance that the Earth and Moon, while apparently nearly identical in most isotope ratios, are substantially different in their bulk chemistry. Furthermore, if the Moon is entirely derived from the Earth's mantle, and if the giant impact models can only place about 30% of Earth mantle material into the orbiting debris disc, then where does that leave the giant impact hypothesis? At first sight, this would rule out the giant impact scenario. However, none of the other older models of the Moon's origin can accommodate these facts either. Evidently, the recent high-precision isotopic determinations in lunar rocks have created a crisis for both the giant impact origin, and every other origin scenario.

3. Proposed solutions to the puzzle

(a). The Earth and impactor had identical isotopic compositions

An easy and general solution would be to assume that the impactor was simply identical to the Earth in isotopic composition. Volatiles would be lost from the hot, partially vaporized orbiting disc by evaporation into space and the isotopic similarity becomes a non-problem. This solution presently seems implausible, given the wide range of oxygen isotopic compositions of the meteorites, but in fact we do not know the isotopic composition of bodies inside the orbit of Earth. It would be very revealing to discover that Venus or Mercury lie on the same mass-fractionation line as the Earth and Moon. Unfortunately, until a meteorite from either of these bodies is identified [41], or samples are returned, this possibility remains speculative. Possibly the impactor was a close relative of the Earth [42] that accreted in a location similar to that of the Earth. All scenarios of this type have difficulty, however, in explaining the similarity of the W isotopes, that imply a history of accretion and differentiation that is very similar to that of the Earth.

(b). Are the existing numerical simulations adequate?

Nearly all of the current simulations use the SPH method, a meshless Lagrangian numerical technique that, for a long period of time, seemed to be the only way to handle the extreme distortions of an impact while including the shifting forces of massive, self-gravitating masses of material. None of the simulations so far published are truly converged in the sense that an increase in resolution gives precisely the same results of lower resolution computations. However, Canup et al. [25] have shown that SPH and a conventional Eulerian hydrocode (CTH with adaptive mesh refinement) give nearly identical results and that resolution is not a major issue.

Adequate equations of state are a continuing issue. Hydrocodes cannot properly represent the outcomes of collisions without an adequate model for the response of candidate geologic materials to impact shock and pressure release cycling. Recent improvements in the ANEOS analytical equation of state package have incorporated molecular species [43], but observations of SiO₂ and other silicates at planetary shock conditions [44–46] now indicate that such models overestimate the shock pressure for vaporization by about a factor of 2, so that much improvement, as well as expansion of existing equations of state to more realistic materials, is urgently needed.

The importance of an adequate equation of state was clearly demonstrated by Wada et al. [47], who argued that, if the orbiting lunar disc is entirely vapour, it is quickly perturbed by strong internal shocks and loses much of its mass onto the Earth within hours. A stable, Moon-forming disc requires the presence of a condensed liquid or solid phase to prevent the formation of these instabilities. This subject has not, to date, received the attention from the Moon-origin community that it deserves, and more work of this kind is needed to properly understand the long-term stability requirements of the Moon-forming disc. In particular, the results of Wada et al. are somewhat at odds with the standard model of viscous disc evolution [48], which predicts that a small fraction of the disc's mass should spread outwards as angular momentum is exchanged within the disc.

(c). Material equilibration between the orbiting disc and proto-Earth

In the face of this isotopic crisis, Pahlevan & Stevenson [49] made the ingenious suggestion that the orbiting disc and the hot, post-impact Earth can efficiently exchange material through a cloud of vapour surrounding both the hot molten disc and the Earth. Focusing on the oxygen isotopes, they argued that the vapour pressure of O-containing silicate species was high enough to permit significant exchange and that the disc would remain hot long enough to permit equilibration of O-isotopes.

Unfortunately, there are several problems with this proposal. A geochemical objection is that, while O-species might be volatile enough for substantial exchange between the Earth and proto-Moon, the similarity of Ti isotopes [36] requires much higher temperatures for equilibration because the vapour pressure of TiO species is very low at the temperature of ca 3000 K proposed by Pahlevan and Stevenson. The low volatility of TiO species would require substantially longer equilibration times (more than a year [36], as opposed to one week for forsterite vapour [49]) than envisioned in the original Pahlevan and Stevenson proposal. It is possible that exchange of minor refractory species such as TiO might take place through fine dust in the solid state, but this idea needs to be developed quantitatively. A second, physics-based, objection is that the isotopic equilibration requires an unlikely exchange process that permits large amounts of material to cycle between the hot, post-impact Earth and the orbiting disc without substantially altering its angular momentum.

This latter objection is based on the fact that the post-impact Earth must have been spinning with a period substantially longer than the orbital period of the ejected proto-lunar disc. If all of the angular momentum of the present Earth–Moon system is concentrated back into the Earth, its rotational period would have been approximately 4 h (this estimate is approximate because it assumes that the moment of inertia of the rapidly rotating Earth is equal to that of the present Earth—in fact, a highly oblate rapidly rotating planet would have a higher moment of inertia and thus a longer period, so this is a conservative estimate). However, for the Earth to match the rotation rate of an orbiting disc, its rotational period must be close to 1.5 h. So if the angular momentum of the disc were to equilibrate with the Earth, the disc could not maintain its orbital velocity and the bulk of its mass would collapse back onto the Earth, leaving too little material in orbit to form our Moon.

It is easy to estimate how much mass must be exchanged between the Earth and an orbiting proto-lunar disc to equilibrate isotopes to any given degree. I follow the model of Pahlevan & Stevenson [49], but unlike them I write the equations in terms of the amount of mass exchanged m_exch to illustrate this process. Figure 1 shows a schematic of the model: we consider two isotope reservoirs, the proto-Earth and the orbiting disc, in which the concentration of isotopic species A, which is a function of mass exchanged A(m_exch), in the proto-Earth of mass M is A_earth while in the orbiting disc of mass m the concentration is A_moon. The total amount of isotope A is conserved, so we impose the constraint MA_earth+mA_moon=constant. If we let the completely equilibrated concentration (which can be approached but never actually attained) be A_equil, it is easy to show that, as a function of mass exchanged, the concentration in each reservoir is given by

1.1

and

1.2

where

1.3

from which it is easy to deduce the fractional decrease in concentration

1.4

Thus, to reduce an initial difference in the concentration of isotope A between the proto-Earth and the orbiting disc to 1% of its initial concentration, a mass nearly equal to 4.6 times the mass of the disc itself must be exchanged (because M≫m for the Earth and Moon, m_* is nearly equal to m itself), as illustrated in figure 2.

Figure 1.

Isotopic equilibration by exchange of a parcel of mass dm between an orbiting disc of mass m and the post-impact proto-Earth of mass M. The isotopic concentrations of species A in the disc is A_moon and in the Earth is A_earth.

Figure 2.

The approach of isotope concentrations in the orbiting disc and the proto-Earth as a function of the amount of mass exchanged. The initial difference is reduced to 1% of the original after a total of about five times the mass of the disc has cycled between the disc and the proto-Earth. For the purposes of illustration, the initial concentration of isotope A is arbitrarily set to 5 units in the orbiting disc and 2 in the proto-Earth. The Earth/disc mass ratio is 1/80. However, the amount of mass exchange for a 1% decline in the difference between the isotopic abundance in the proto-Earth and disc is independent of the actual values of the initial abundances. (Online version in colour.)

Most processes that cycle material from one location to another also exchange momentum and hence angular momentum in rotating flows. Indeed, viscosity (a measure of momentum exchange) is generally linked to diffusion (a measure of material exchange) through the Einstein–Smoluchowski relation, which is a special case of the more general fluctuation–dissipation theorem. Although the Einstein–Smoluchkowsi relation strictly applies to molecular processes in kinetic theory, turbulent diffusion is frequently (although not invariably) well represented by similar statistical models via the eddy diffusion approximation [50]. It is difficult to envision a process that could exchange as much as five times the disc mass without also exchanging enough angular momentum to bring the disc down. Stone & Balbus [51] argue that material convection in Keplerian discs transports angular momentum inward, not outward as required for the evolution of an accretion disc. In this case, the disc might not collapse due to viscous dissipation, but the inner portions would then rise to higher altitude as their angular momentum increases, cutting off exchange of material between the proto-Earth and disc, which would again thwart the Pahlevan–Stevenson exchange mechanism. The Stone and Balbus analysis implicitly assumes a homogeneous fluid and it is unclear whether it applies to a two-phase disc that includes both a gas phase and a liquid that may differentially rotate and thus develop pressure waves, shocks and other azimuthal instabilities not included in their analysis. The analysis by Thompson & Stevenson [52] suggests that angular momentum exchange in a two-phase disc is dominated by gravitational instabilities rather than convective transfer, which would cause such a disc to spread faster than one dominated by convective exchange of angular momentum alone. Pahlevan & Stevenson [49] argue that the necessary isotopic exchange can, indeed, occur on the time scale for evolution of the proto-lunar disc, but the fact that the Earth and disc must exchange a mass comparable to, or greater than, the mass of the disc itself while the disc remains in orbit seems incredible and requires a more rigorous demonstration.

(d). Fast, ice-rich impactors

A novel proposal suggested that a way out of the isotopic impasse might be through an ice-rich impactor, perhaps an intruder from the outer Solar System, striking at high speed [53] (also T. Bowling and B. Johnson 2011, personal communication). Reufer et al. [54] explored a suite of collisions involving fast, less grazing impacts that included icy impactors, but found that at most 73% of the Moon-forming disc could be derived from the Earth. These computations imposed the usual constraint on matching the total angular momentum of the Earth–Moon system, but in the light of the next section this might need to be re-visited.

(e). Is the angular momentum constraint valid?

A fresh, new approach to the Moon-origin problem was initiated by Ćuk & Stewart [55] in a paper that has shaken the ground beneath all previous approaches. They argued that much of the initial angular momentum of the Earth–Moon system could have been drained away through solar tidal torque as the Moon went through a resonance, known as the evection resonance [56], between the Moon's perigee precession period and the year. This resonance forces the Moon into a highly eccentric orbit that is subject to solar tidal torques. Although the efficacy of this resonance is currently in dispute (J. Wisdom 2013, personal communication), if there is some mechanism that removes the angular momentum constraint then there may be new ways in which a giant impact can loft a larger fraction of the Earth's mantle into orbit.

This new freedom from the angular momentum constraint was exploited by Ćuk & Stewart themselves [55], who demonstrated that a fast impact with a fast-spinning Earth could, under the right conditions, loft a disc consisting primarily of Earth mantle material. The most successful simulations require a retrograde impact (that is, the Earth's spin on the struck hemisphere is in the opposite direction to the flight of the impactor). Canup [57] also exploited the lifting of the angular momentum constraint, suggesting that the similarity of the Earth's and Moon's isotopes could be explained if the impactor was nearly the same size as the proto-Earth and thus the final Earth- and Moon-forming disc received nearly equal contributions from both bodies.

4. Have we now found the answer?

Both Ćuk & Stewart [55] and Canup [57] have thus demonstrated that, with the freedom allowed by loosening the angular momentum constraint, it is possible to form a Moon by impact that closely resembles the Earth in its isotopic ratios. Both scenarios pass through a hot disc phase from which volatile elements can presumably be lost. Neither readily explains the Moon's excess of FeO, although nor do any other models seem capable of explaining that one remaining difference.

So, is the giant impact scenario again on a secure footing? It may seem so, and yet I am personally very uneasy about these (and all other!) explanations. The root of my unease boils down to a somewhat subjective feeling about the ‘naturalness’ of an explanation. By ‘natural’, I mean that the major features of the outcome (in this case, a moon that is a near isotopic twin of its primary) should be an almost inevitable result of the formation process. However, both of the currently successful scenarios by Ćuk & Stewart [55] and Canup [57] require a narrow range of initial conditions. A bit more mass to the projectile, a slightly different impact angle or velocity, and the isotopic similarity disappears. Both those papers contain extensive tables of many, many simulations that, while producing a moon, do not produce one that is isotopically as close to its primary as is our Moon.

The strongest constraint on the isotopic similarity of our Moon and the Earth is still that from the oxygen isotopes. The recently reported difference of 12±3 ppm in Δ¹⁷O [30] shrinks the error bars still more and further contracts the range of acceptable impact models.

How special a set of initial conditions should we find acceptable? Unfortunately, we have only one Moon, and so one can always argue that we are simply very, very ‘lucky’ to have one whose isotopic ratios are so similar to the Earth. But the history of science teaches us that an appeal to very special circumstances is generally a poor bet (the Earth is not the centre of the Universe, our Sun is not the only star with planets, etc.). When do we reject a scenario when it becomes ‘too’ improbable? Unfortunately, the annals of science also tell us that the answer to this question is ‘never’: there is always someone advocating a special but highly improbable solution to nearly every question. Nevertheless, good science suggests that we should not rest on one (or two!) possible but unlikely solution(s), but continue to seek for one whose probability of occurrence is much higher. Strange coincidences do (and must!) occur, but they are rare by nature.

The first round of the giant impact scenario had that air of ‘naturalness’. Given that planetary-scale collisions dominate the late stages of accretion, nearly every such impact launched material into orbit and produced a moon. Not all such moons were like our Moon: most had less mass, but nevertheless it remains true that nearly every giant impact produces some sort of moon orbiting the final planet (such a moon may crash at a later stage due to unfavourable tidal interactions, as probably occurred on Venus). But we now find that the canonical giant impact scenario does not produce a moon with nearly the same isotopic ratios as its primary. That can happen, but it requires a rather special set of circumstances. Most such moons receive much more material from the impactor than from the impactee. Does this tell us that the canonical scenario is wrong or are we missing something?

Of the face of it, these results might suggest a return to some version of George Darwin's fission model of lunar origin [58], in which the Moon spun off the equator of a fast-spinning Earth. But this scenario leaves unexplained the presence of at least a small core and the depletion of volatile species in the Moon, facts that the canonical impact model treats well. And then there is the enhancement of FeO in the Moon. Can some merger of the canonical giant impact and Darwin's fission model lead to a moon like our Moon, perhaps through the lifting of the angular momentum constraint? If something like Darwin's theory receives new life, the non-zero inclination of the Moon to the Earth's equator would seem to be a problem, although some progress has already been made on this topic [59].

5. What is needed?

Explaining the origin of the Moon with all the present facts in hand currently seems impossible. We could hope to find some process that adds large amounts of energy and momentum to the Earth's mantle, without leaving a trace of its own material. But how could this be? A projectile composed of 100% ice (unlikely)? A solid iron projectile that then vanishes from the Moon-forming disc (slightly less unlikely)? A projectile that is identical in composition to the Earth (unlikely according to current accretion models)? Or something we have not yet thought of?

Our spectacular, large Moon is one of the principal features of our planet. However, in spite of all the progress we have made since the first Apollo landing on 20 July 1969, the very existence of our Moon still conceals mysteries that await solution.

Funding statement

My research was supported by NASA's Lunar Science Institute at the Southwest Research Institute under grant no. NNA09DB32A.