Fission and geosynchronous release of the Moon

The problem of the origin of the Moon has led to various hypotheses: simultaneous accretion, fission, capture, etc. These theories were based primarily on global mechanical considerations. New geological data (Turcotteet al., 1974; Kahn and Pompea, 1978) have led to fresh approaches and new versions of these theories.As suggested by Wise (1969) and O'Keefe (1972), the initial Earth may have taken unstable forms when radial segregation sped up the rotation. The Moon may have been created as the small part of the pyroid of Poincaré.Fission theory was mainly discarded, in the past, on the basis of energy considerations. We are now arriving at the conclusion that these considerations are void if the fission was followed by a very long period of geostationary rotation of the Moon at a distance of about 3 Earth radius (i.e., out of the Roche limit). Indeed the large amount of energy of the initial system could have been released slowly and therefore evacuated by losses of material and radiation.The accretion of the Earth and the radial segregation of heavy chemicals toward the center has led to a differential rotation of the different layers with a faster rotation at the center. During the geostationary period the Moon was synchronous with respect to the surface layer. That Earth-Moon system has both a correct angular momentum and a large stability provided that the viscosity of intermediate layers was small enough, which is in concordance with its high temperature.Even with a very hot system, a superficial cold layer appears because of its low conductivity and the radiation equilibrium with outer space. This implies a slow loss of energy: the geosynchronous Moon receded extremely slowly.During the geostationary period lithophile elements were extracted with water by the radial segregation and were deposited in the area facing the Moon. One massive continent was formed, as suggested by Grjebine (1978).As the continent became thicker and sank into the mantle, convection currents appeared and speeded up the cooling of the Earth. The viscosity increased and the synchronization between the Moon and the surface of the Earth became more difficult to maintain. When synchronism was broken important lunar tides transferred energy and momentum from the Earth to the Moon which receded toward its present position and the modification of its equilibrium shape explains the formation of lunar maria in the near side.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

The origin of the Moon and the single-impact hypothesis,II

This is the second paper devoted to the numerical study of planetary collisions as a possible scenario for forming the Moon. We present a series of nine simulations of a collision between the protoearth and an impactor of various sizes. The mass ratio between the protoearth and the impactor ranged from 0.1 to 0.25. We were able to model both planets with iron cores, having modified our smoothed particle hydrodynamics code to allow the inclusion of up to 10 different material types. Two different relative velocities at infinity for the impactor were considered: ν_∞ = 0 km/sec and ν_∞ = 10 km/sec. We show that for a low-velocity collision and an impactor in the mass range 6.5 × 10²⁶ ≤ M_impactor ≤ 8.2 × 10²⁶ g, more than a lunar mass of iron-poor material is thrown into orbit. For an impactor with a mass within this range, the ejected mass that goes into orbit is for the most part divided comparably into material orbiting inside the Roche limit and into material orbiting outside the Roche limit. This material is either spread out in the form of a disk, or, for a relatively narrow range of masses toward the lower end of the range, clumped into an object of about lunar mass beyond the Roche limit. For impactors more massive than about 8.2 × 10²⁶ g we found that there is too little mass thrown into orbit. For very small mass impactors well over a lunar mass is placed in orbit, but a large amount of it is iron. In the high-velocity range we did not find a possible mass range for the impactor that would lead to the formation of an iron-poor disk massive enough to form the Moon.     

The origin of the Moon: Theories involving joint formation with the Earth

A planet the size of the Earth or the Moon is much like a blast furnace; it produces slag-like rock floating on a mass of liquid metal. In the Earth, the mantle and crust are the slag, and the core is the liquid iron.In the Moon, there is clear chemical evidence that liquid iron was separated from the mass, but the Moon has no detectable iron core. This points to some kind of joint origin, which put the metallic iron in the Earth's core. For instance, the Moon might have been a detached part of the rocky matter of the Earth, as suggested by G. H. Darwin in the 1880's. But is is also clear, as Ringwood has pointed out, the there has been an enormous loss of volatiles from both Earth and Moon, but especially from the Moon. It may be that the Moon formed from a sediment-ring of small bodies detached somehow from the outer parts of the Earth, as Öpik has suggested.If tektites come from the Moon, then Darwin's suggestion is probably right; if they come from the Earth, then the Öpik-Ringwood sediment ring may be the origin.Paper presented at the AAAS Symposium on the Early History of the Earth and Moon in Philadelphia on 28 December 1971.     

A new variant of the large-impact hypothesis for the origin of the Moon

The hypothesis is advanced that after collision of a Mars-sized impact with the Earth, collisions between debris particles themselves are able to place enough material into Earth orbit, to form the Moon. Collision probability estimates show that the collision frequency is high enough to place about one lunar mass into Earth orbit, if the average semimajor axis is of order of the Earth's Roche limit of 18 500 km.     

Implications of recent numerical calculations for the fission theory of the origin of the Moon

Recent numerical simulations of fission instabilities in rotating fluid masses give results which are consistent with some requirements of the fission hypothesis for the origin of the moon.     

On the accelerations of the Moon and Sun,the constant of gravitation,and the origin of mountains

In a previous paper Lyttleton (1976) has shown that the apparent secular accelerations of the Sun and Moon, as given by de Sitter, can be largely explained if the Earth is contracting at the rate required by the phase-change hypothesis for the nature of the core. More reliable values for these accelerations have since become available which warrant a redetermination of the various effects concerned on the basis of constantG, and this is first carried out in the present paper. The lunar tidal couple, which is the same whetherG is changing or not, is found to be (4.74±0.38)×10²³ cgs, about three-quarters that yielded by the de Sitter values, while within the theory the Moon would take correspondingly longer to reach close proximity to the Earth at about 1.5×10⁹ years ago.The more accurate values of the accelerations enable examination to be made of the effects that a decreasingG would have, and it is shown that a valueG/G=–3×10^–11 yr^–1 can be weakly satisfied compared with the close agreement found on the basis of constantG, while a value as large numerically asG/G=–6×10^–11 yr^–1 seems to be definitely ruled out. On the iron-core model, an intrinsic positive component of acceleration of the angular velocity cannot be reconciled at all with the secular accelerations even for constantG, and far less so ifG is decreasing at a rate suggested by any recent cosmological theory.ItG=0, the amount of contraction available for mountain-building would correspond to a reduction of surface area of about 49×10⁶ km² and a volume to be redistributed of 160×10⁹ km³ if the time of collapse were 2.5×10⁹ years ago. For earlier times, the values are only slightly reduced. IfG/G=–3×10^–11 yr^–1, the corresponding values are 44×10⁶ km² and 138×10⁹ km³ for collapse at –2.5×10⁹ yr, and not importantly smaller at 38×10⁶ km² and 122×10⁹ km³ for collapse at –4.5×10⁹ yr. Any of these values would suffice to account in order of magnitude for all the eras of mountain-building. An intense brief period of mountain-building on an immense scale would result from the Ramsey-collapse at whatever time past it may have occurred.     

Formation of an iron-poor Moon by partial capture,or: Yet another exotic theory of lunar origin

It is shown how it is possible to explain the low abundance of iron and siderophiles in the Moon in a natural way. This is done by an extension of Öpik's mechanism, whereby one or more planetoids pass through Earth's Roche zone, are broken up, and have part of their material captured. Assuming the planetoids are differentiated, the iron core can easily escape capture. This process does not involve any dissipation mechanisms and goes a long way toward explaining the peculiar bulk composition of the Moon. The picture is consistent with that of Urey, in which the early solar system contained more (and smaller) planets than it does today. In the second part of the paper, dynamical considerations are applied for two models, and it is shown that capture from one (or a few) planetoids is quite feasible, whereas a large number of contributors is highly unlikely.     

Nuclear Planetology:Especially Concerning the Moon and Mars

To approach basic scientific questions on the origin and evolution of planetary bodies such as planets, their satellites and asteroids, one needs data on their chemical composition. The measurements of gamma-rays, X-rays and neutrons emitted from their surface materials provide information on abundances of major elements and naturally radioactive gamma-ray emitters. Neutron spectroscopy can provide sensitive maps of hydrogen-and carbon-containing compounds, even if buried, and can uniquely identify layers of carbon-dioxide frost. Nuclear spectroscopy, as a means of compositional analysis, has been applied via orbital and lander spacecraft to extrater-restrial planetary bodies:the Moon, Venus, Mars, Mercury and asteroids. The knowledge of their chemical abundances, especially concerning the Moon and Mars, has greatly increased in recent years. This paper describes the principle of nuclear spectroscopy, nuclear planetary instruments carried on planetary missions so far, and the nature of observational results and findings of the Moon and Mars, recently obtained by nuclear spectroscopy.     

Bessel and librations of the Moon

On the occasion of the twohundredth anniversary of F. W. Bessel's birth, his method of heliometric observations for the determination of the Moon's physical libration constants and of the reduction of these observations is presented.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sterwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

Moon: Origin and evolution of multi-ring basins

This paper summarizes current data and new observations on lunar basin systems. Parts 1–4 review earlier literature and give new crater-counts used to reconstruct basin histories. Among the results are: basin rings are defined by faults, hills, craters, and/or wrinkle ridges; all of these are inter-related; 2 plays a special role in the ratios of ring diameters; flooding occurred in many basins prior to the formation of the familiar front-side maria; 3 km is a typical depth of lava flooding in basins. Parts 5–11 interpret these results in terms of origin and evolution of basins. Polar concentrations of basins and old, large craters are found (Figures 28 and 29). Basins originated by impacts of very early planetesimals left over from or created during formation of the Moon (6). Concentric fractures were produced by the impacts. Concentric rings developed along fractures during subsequent sagging of the basin into partially melted substrata, along the lines of theory and experiments by Lance and Onat (1962) (Figures 36 and 37). There is marginal empirical evidence that some rings formed significantly after their basins (8). The structure of specific rings depended on the nature of volcanic products extruded. Wrinkle ridges, peak-rings, rings of craters, concentric graben, and central peaks are all consequences of basin-forming evolutionary processes (9, Figure 41), Flooding by lava was a final stage in basin evolution. Lava extruded from concentric ring-faults, wrinkle ridges, and crater and basin rims (10). Mascons are directly correlated with the amount of mare lava, but not correlated with basin age or morphology (11). Section 12 summarizes the results and compares them to those of other authors.     

Paleocratering of the Moon: Review of post-Apollo data

As a result of the dating of lunar samples, we are in a position to utilize the lunar surface as a recorder of environmental conditions in the Earth-Moon neighborhood in the past. Plots of crater density vs rock age at different lunar landing sites can be used to date unexplored lunar provinces. These plots also demonstrate evolution in the population of planetesimals that struck the Moon. Prior to 4.1 aeons ago, the cratering rate on the Moon was at least 10³ times the present rate, and the rate declined with a half-life less than 8×10⁷ yr. During the interval from 4.1 to 3.2 aeons ago, the number of planetesimals showed an exponential decay with a half-life about 3×10⁸ yr, corresponding to sweep-up of particles from solar orbits somewhat similar to those of Apollo asteroids. A more nearly constant cratering rate applied in the last three aeons. These data indicate that the Moon displays at least the final stages of an ancient accretion process; they also set certain conditions on possible capture processes relating to the Moon's origin. Pre-Apollo expectations that the Moon would provide a Rosetta Stone for interpreting solar system history and planet formation thus appear justified.Paper given at Philadelphia meeting of American Association for Advancement of Science, December, 1971.     

An intrinsic volatility scale relevant to the Earth and Moon and the status of water in the Moon

The notion of a dry Moon has recently been challenged by the discovery of high water contents in lunar apatites and in melt inclusions within olivine crystals from two pyroclastic glasses. The highest and most compelling water contents were found in pyroclastic glasses that are not very common on the lunar surface. To obtain more representative constraints on the volatile content of the lunar interior, we measured the Zn content, a moderately volatile element, of mineral and rock fragments in lunar soils collected during Apollo missions. We here confirm that the Moon is significantly more depleted in Zn than the Earth. Combining Zn with existing K and Rb data on similar rocks allows us to anchor a new volatility scale based on the bond energy of nonsiderophile elements in their condensed phases. Extrapolating the volatility curve to H shows that the bulk of the lunar interior must be dry (≤1 ppm). This contrasts with the water content of the mantle sources of pyroclastic glasses, inferred to contain up to approximately 40 ppm water based on H₂O/Ce ratios. These observations are best reconciled if the pyroclastic glasses derive from localized water‐rich heterogeneities in a dominantly dry lunar interior. We argue that, although late addition of 0.015% of a chondritic veneer to the Moon seems required to explain the abundance of platinum group elements (Day et al. 2007), the volatile content of the added material was clearly heterogeneous.     

Micrometeoroids: the Flux on the Moon and a Source of Volatiles

Solar System Research - One of the probable sources of water and other volatiles, forming ice deposits in the shadowed polar regions of the Moon, is cosmic matter delivered by comets and asteroids,...     

Internal structure of the Moon and moonquakes

I discuss the relation between the internal structure of the Moon and the radial distribution of the moonquake foci. I believe that the important factor conditioning the radial distribution is the fact that the rigidity of the lunar material decreases with increasing depth. Using a two-layer model, solutions of the elasticity equations are found for the cases of a uniform surface load and of a uniform radial body force. The results show that when the inner sphere is less rigid than the outer shell, the maximum sheer stress is located near the boundary of the two components, thus explainning why the moonquakes are mostly deep quakes. The results also suggest that a liquid core exists in the Moon.     

Stresses in the Moon

It is argued that a reliable theory of the stress history of the Moon should take into account several factors; and that direct observations of the Moon's surface can throw much light on this subject.     

Stress history of the Moon

The character of the lunar surface indicates that surface faulting has not been an important mechanism for the build-up of the lunar surface. If the radioactive content of the Moon is of the same order as that of chondritic meteorites, then the absence of major surface faults can be explained in a number of ways. A near-surface concentration of radioactivity will provide an equality of heat production and surface heat flow necessary for the maintenance of a constant lunar radius. Alternatively, the radioactivity could be deeply buried, with the radius still remaining constant over the past 2,000,000,000 years. Heat transported by mechanisms other than radiation and thermal conduction will also tend to keep the radius of the Moon at a constant value.

Even though the radius of the Moon remains constant, there is a major build-up of strain energy throughout the Moon. The rate is such that, on the average, something on the order of 10²⁴–10²⁵ ergs of distortional energy should be released per year throughout the Moon, provided the radioactivity is uniformly distributed. A near-surface concentration of the radioactivity might decrease this rate of energy release but certainly by no more than an order of magnitude. Under all circumstances it would appear that a Moon of chondritic composition would have strong Scismic activity.     

Cometary impact and the magnetization of the Moon

Collisions of comets with planetary bodies are capable of impressing patterns of magnetization onto them that match those observed for the Moon and possibly for Mercury. The ambient solar wind magnetic field is briefly but strongly enhanced as the large partially ionized cometary atmosphere is compressed against the planetary surface. Just at the time of peak field enhancement, the solid part of the comet collides with the surface and the compressed fields are permanently imprinted by shock magnetization.