A model of lunar evolution

There have been many models describing the evolution of our sister planet. As information from the intensive exploration by the Apollo program has accumulated, more constraints on these models have emerged. We specifically consider a hypothesis in which there is a present day asthenosphere, a heat flow between 24 and 32 ergs cm⁻² s⁻¹ and a crust which developed early in the Moon's history by melting of the outer 100 to 200 km. We have also introduced a constraint which keeps the deep interior below the Curie point of iron for the first 1 to 1.5 b.y. so that it is able to carry the memory of an early field which magnetized the cold interior. The magnetized mare basalts and breccias cooled in this field from above the Curie point of iron (≈800°C.) and acquired a thermoremanent magnetization. While fully recognizing that some of these constraints are subject to other interpretations, it is nevertheless instructive to consider the thermal history that follows from such a model. First, the initial temperature must be high enough to cause melting in the outer 100–200 km, while the interior temperature must be cool enough to be below the Curie point of iron. Second, the crust in this model cools off so rapidly that the mare basalts could not be developed as late as indicated in lunar history. Rather we propose that the mare basalts result from local remelting associated with giant impacts. Third, the Moon's deep interior must have warmed up enough to erase the memory of the ancient magnetic field from the deep interior and to develop the asthenosphere which has been detected seismically. Fourth, if this asthenosphere is real, the viscosity of the Moon as a function of temperature must be high enough to have prevented convective cooling until the temperature increased to a value near the solidus temperature. At this temperature, the Moon would then likely cool by convection in the solid state. It is, therefore, a consequence of this model that solid body convection tool place late in lunar history. This may well have contributed to the lunar center of figure and center of mass offset, to the low order terms in its gravity field and to, its disequilibrium moment of inertia differences.     

A lunar soil evolution model

Comminution, agglutination, and replenishment processes in a lunar soil are modeled by a system of time dependent, linear differential equations. In the model a soil is subdivided into coarse particle, fine particle, and agglutinate fractions. The relative mass abundance of each component in a mature soil is found to be proportional to rates for the reworking processes. Evolution of the grain size distribution from a fresh ejecta blanket to a mature soil is described quantitatively in terms of the changing proportions of the three soil constituents. If size data is available for an immature soil and a mature soil of the same system, rates for the various processes can be calculated under certain simplifying assumptions.     

Large-scale evolution of the lunar surface

The first part of the paper describes the relationship between the erosional stage of craters and the crater areal density. It is shown that class-2 and -3 craters are progressively more abundant as the crater areal density increases, while craters of class 4 and 5 are more abundant with decreasing crater areal densities. A geological model is proposed, in which the class of a newly foormed crater is 1. As time progresses, erosional agents will increase the class of the crater to class 2, then 3, and, in some cases, to 4. The length of time between classification steps is not known in terms of years, but is equivalent to the time necessary for the crater density to increase by 2 to 8 craters per unit area for creaters larger than 10 km, and by 10 to 20 for craters larger than 3.5 km. Craters of class 5 and some of class 4 are not formed by the same erosional agents, but are catastrophic, caused either by a mare-producing impact or by flooding of mare material.The second part of the paper presents a method for relatively dating large lunar areas. The method uses the model previously developed. A relative time sequence is constructed using the density of craters of classes 1, 2, and 3 and the percentage of these which is of class 1. As an example, 18 large areas are defined on the lunar near side and are put in temporal order. Mare Serenitatis appears to have the youngest terrain, and an area southwest of the Rupes Altai appears to have the oldest.In the final part of the paper a geological model is developed in order to explain age differences in the terrae. The model calls for rejuvenation of lunar terrains, caused by the seismic waves and ballistic sedimentation resulting from large impacts. The area surrounding Mare Orientale is cited as an example of a terrain so affected. A similar effect on the terrae of the near side could explain the apparent age relationships measured.     

On the evolution of the lunar orbit

It is generally accepted that the Earth-Moon separation is at present increasing due to tidal dissipation. Values for the corresponding lunar deceleration and the related slowing of the Earth's rotation are obtained from astronomical observations and by studies of ancient eclipses. Extrapolation of these values leads to a close approach of the Earth and Moon 1–3 b.y. BP. However, justification for such an extrapolation is required. It has been hypothesized that periodicities in the Precambrian stromatolites can be used to determine the number of solar days in a lunar month prior to 500 m.y. BP. These data combined with dynamic constraints on the number of solar days in a lunar month indicate a close approach of the Earth and Moon at 2.85 ± 0.25 b.y. BP. It is suggested that the mare volcanism on the Moon and high-temperature Archean volcanism on the Earth prior to this date were caused by tidal heating. It is also suggested that the strong tidal heating during a close approach could have contributed to the formation of the first living organisms.     

Stability and evolution of primeval lunar satellite orbits

There are several independent sources of evidence which suggest that the multiring basins of the lunar surface were created by the impact of natural satellites of the Moon, early in solar system history. If this hypothesis is correct the orbits of these primeval satellites would need to be stable for significant periods, to account for the known age differences of these basins. The stability of these primeval satellite orbits is considered. We find constraints on the satellite masses and initial orbits for long-term and short-term orbit stability. Dissipation due to lunar tidal friction may contribute significantly to the stability of close orbits.     

On the chronology of lunar origin and evolution

An origin of the Moon by a Giant Impact is presently the most widely accepted theory of lunar origin. It is consistent with the major lunar observations: its exceptionally large size relative to the host planet, the high angular momentum of the Earth–Moon system, the extreme depletion of volatile elements, and the delayed accretion, quickly followed by the formation of a global crust and mantle.According to this theory, an impact on Earth of a Mars-sized body set the initial conditions for the formation and evolution of the Moon. The impact produced a protolunar cloud. Fast accretion of the Moon from the dense cloud ensured an effective transformation of gravitational energy into heat and widespread melting. A “Magma Ocean” of global dimensions formed, and upon cooling, an anorthositic crust and a mafic mantle were created by gravitational separation.Several 100 million years after lunar accretion, long-lived isotopes of K, U and Th had produced enough additional heat for inducing partial melting in the mantle; lava extruded into large basins and solidified as titanium-rich mare basalt. This delayed era of extrusive rock formation began about 3.9 Ga ago and may have lasted nearly 3 Ga.A relative crater count timescale was established and calibrated by radiometric dating (i.e., dating by use of radioactive decay) of rocks returned from six Apollo landing regions and three Luna landing spots. Fairly well calibrated are the periods ≈4 Ga to ≈3 Ga BP (before present) and ≈0.8 Ga BP to the present. Crater counting and orbital chemistry (derived from remote sensing in spectral domains ranging from γ- and x-rays to the infrared) have identified mare basalt surfaces in the Oceanus Procellarum that appear to be nearly as young as 1 Ga. Samples returned from this area are needed for narrowing the gap of 2 Ga in the calibrated timescale. The lunar timescale is not only used for reconstructing lunar evolution, but it serves also as a standard for chronologies of the terrestrial planets, including Mars and possibly early Earth.The Moon holds a historic record of Galactic cosmic-ray intensity, solar wind composition and fluxes and composition of solids of any size in the region of the terrestrial planets. Some of this record has been deciphered. Secular mixing of the Sun was constrained by determining ³He/⁴He of solar wind helium stored in lunar fines and ancient breccias. For checking the presumed constancy of the impact rate over the past ≈3.1 Ga, samples of the youngest mare basalts would be needed for determining their radiometric ages.Radiometric dating and stratigraphy has revealed that many of the large basins on the near side of the Moon were created by impacts about 4.1 to 3.8 Ga ago. The apparent clustering of ages called “Late Heavy Bombardment (LHB)” is thought to result from migration of planets several 100 million years after their accretion.The bombardment, unexpectedly late in solar system history, must have had a devastating effect on the atmosphere, hydrosphere and habitability on Earth during and following this epoch, but direct traces of this bombardment have been eradicated on our planet by plate tectonics. Indirect evidence about the course of bombardment during this epoch on Earth must therefore come from the lunar record, especially from additional data on the terminal phase of the LHB. For this purpose, documented samples are required for measuring precise radiometric ages of the Orientale Basin and the Nectaris and/or Fecunditatis Basins in order to compare these ages with the time of the earliest traces of life on Earth.A crater count chronology is presently being built up for planet Mars and its surface features. The chronology is based on the established lunar chronology whereby differences between the impact rates for Moon and Mars are derived from local fluxes and impact energies of projectiles. Direct calibration of the Martian chronology will have to come from radiometric ages and cosmic-ray exposure ages measured in samples returned from the planet.     

The evolution of the lunar Nectaris multiring basin

Nectaris is an 820-km-diameter, multiring impact basin located on the near side of the Moon. The transient cavity is estimated to have been less than 90 km in depth and materials were excavated from a depth of less than 30 km. About 2 km thickness of impact melt is believed to line the cavity center. The impact event probably took place at about 3.98 ± 0.03 × 10⁹ years ago. Nectaris ejecta forms a substantial proportion of the surface materials at the Apollo 16 site. Inter-ring plains deposits were deposited after the formation of the Nectaris basin. The most persuasive origin for the smooth plains is one of extrusives overlain by a thin veneer of ejecta. Basaltic fragments within Apollo 16 samples are believed to have been largely derived from Nectaris. A titanium-rich Apollo 16 mare basalt fragment has an age of 3.79 ± 0.05 × 10⁹ years but, although some relatively titanium-enriched basalts occur in southern Nectaris, titanium-rich basalts are nowhere seen at the surface of the mare. The earliest recognized eruptives appear to be low-titanium (perhaps VLT) basalts found as pyroclastic materials on Daguerre and in the Gaudibert region. The majority of the surface basalts are of intermediate composition (possibly similar to Apollo 12 basalts) and have an age of approximately 3.6 × 10⁹ years. The basalt fill is estimated to have a minimum thickness of 3 km. Flood-style eruptions appear to have been the main form of extrusion. Mare ridges exhibit a strong north-south preferential alignment and appear to postdate basalt emplacement. The lack of basin-related graben in Nectaris is consistent with a thick lithosphere. The basin ring structure is best preserved in the southwest and least preserved in the northeast. This is believed to result from horizontal variations in the crust and lithosphere thicknesses and from the influence of the preexisting Fecunditatis and Tranquillitatis basins; the ring structure is best preserved where the lithosphere was thickest. Floor-fractured craters within Nectaris are intimately associated with the basalt fill both in terms of age and location. Theophilus ejecta, small craters, and Tycho rays, combined with subsidence and mare ridge development, were the only modifying influences on Nectaris since the termination of basalt eruptions.     

Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

The evolution of the lunar orbit revisited. I

After recalling the contribution of Halley, J. Kepler, and G. Darwin to our understanding of the secular acceleration of the Moon, we establish a set of differential equations for the variation of the semi-major axis, and the inclination of the Moon on the maximum area plane. These equations are obtained without expanding the disturbing function, due to the tidal bulge, in term of the elliptic elements. The equations thus obtained are simple enough to allow us a qualitative discussion of the solution, followed by a numerical integration.The results obtained show the Moon was in the distant past in a retrograde orbit, approaching the Earth, its inclination increasing towards 90°; once after a closer approach to the Earth, the Moon receeded and it will finally reach an equilibrium point, the orbital and the equatorial planes being blended.The solution of the equations appears as a fascicle of curves, becoming extremely dense as we come nearer to the present. Owing to the high sensitivity of the solution to the initial conditions, a weak disturbance added to our modeled forces may lead to a past situation very different from the conclusion drawn by Goldreich (1966) and MacDonald (1964); the minimal approach distance could be greater than 10 Earth's radii.     

Electromagnetic evidence concerning the lunar interior and its evolution

This paper reviews the evidence for magnetization of the Moon found from discovery of remanence in lunar samples, direct measurements of fields on the surface of the Moon, and direct and indirect determination of fields from lunar orbit. It is shown that the evidence implies that the fields are not only local but that regional properties are found though there is still no direct evidence for a global dipole moment. Limits on the detectibility of a global dipole are given and it is shown that the strength of magnetization for reasonable thermal gradients places possible dipole moments just below the threshold of detectibility of current experiments. The hypothesis of plate magnetics is reviewed. Current ideas regarding the source of the background magnetic field presumed responsible for the magnetization are critically considered. These are the dynamo hypothesis and primordial magnetization. Consequences of both are discussed and finally the constraints placed upon the thermal evolution of the Moon are considered.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

The evolution of the lunar orbit revisited,II

We present here a model for the tidal evolution of an isolated two-body system. Equations are derived, including the dissipation in the planet as in the satellite, in a frequency dependent lag model. The set of differential equations obtained is still valid for large eccentricity, as well as for all inclinations. The reference plane chosen enables us to study the evolution for both the orbital plane and the equatorial plane.The results obtained show the Moon, after having approached the Earth with small variations for the inclination and the eccentricity, exhibits strong increase for the two parameters in the vicinity of the closest approach. In every case the eccentricity tends towards the value 1, whereas the variations of the in clinations are dependent on the magnitude of the dissipation in the satellite.Some qualitative results are also investigated for the final behaviour of satellites such as Triton and the Galilean satellites.     

The thermal and radiation exposure history of lunar meteorites

Abstract— We have measured the natural and induced thermoluminescence (TL) of seven lunar meteorites in order to examine their crystallization, irradiation, and recent thermal histories. Lunar meteorites have induced TL properties similar to Apollo samples of the same provenance (highland or mare), indicating similar crystallization and metamorphic histories. MacAlpine Hills 88104/5 has experienced the greatest degree of impact/regolith processing among the highland-dominated meteorites. The basaltic breccia QUE 94281 is dominated by mare component but may also contain a significant highland component. For the mare-dominated meteorites, EET 87521 may have a significant highland impact-melt component, while Asuka 881757 and Y-793169 have been heavily shocked. The thermal history of Y-793169 included slow cooling, either during impact processing or during its initial crystallization. Our natural TL data indicate that most lunar meteorites have apparently been irradiated in space a few thousand years, with most <15,000 a. Elephant Moraine 87521 has the lowest irradiation exposure time, being <1,000 a. Either the natural TL of ALHA81005, Asuka 881757 and Y-82192 was only partially reset by lunar ejection or these meteorites were in small perihelia orbits (≤0.7 AU).     

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating Moon in the field of the Earth is expanded in terms of parameters orienting the spin angular momentum relative to the pricipal axes of the Moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love numberk ₂. The principal periodic terms in the longitude of a point on the Moon due to variations of the tide caused by the Earth are shown to have amplitudes between 3.9 × 10^–3 and 1.6 × 10^–2 with a period of an anomalistic month, 3.0 × 10^–4 and 1.2 × 10^–3 with a period of one-half an anomalistic month and 2.4 × 10^–4 and 9.6 × 10^–4 with a period of one-half of a nodical month. The extremes in the amplitudes correspond to rigidities of 8 × 10¹¹ cgs and 2 × 10¹¹ cgs, respectively, the former rigidity being comparable to that of the Earth. Only the largest amplitude given above is comparable to that detectable by the projected precision of the laser ranging to the lunar retrorereflectors, and this amplitude corresponds to an improbably low rigidity for the Moon. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given, where it is shown that elasticity can alter the period of the free wobble of 75.3 yr by only 3 × 10^–4 to 10^–3 of this period. Also, the effect of elasticity on the period of free libration is completely negligible by many orders of magnitude. If the Moon's rigidity is close to that of the Earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the Moon can be determined from variations in the rotation.Currently on leave from the Dept. of Physics, University of California, Santa, Barbara, California.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

On the effects of lunar tides in the Tianjin latitude observations

In this paper we have analysed the effect of the lunar tide on the latitude observations of 25260 star-pairs with the zenith telescope, ZTL-180 of Tianjin Latitude Station during 1960–1966. For the M₂ wave, we found an amplitude of 0.0108 and hence a value of 1 + k − 1 = 1.34. When the effect of the ocean tide is subtracted, the value of 1 + k − 1 is reduced to 1.315. This is in very good agreement with the value 1.31, deduced by geophysicists for the Asia region.     

The early thermal evolution of Mars

Hf‐W isotopic systematics of Martian meteorites have provided evidence for the early accretion and rapid core formation of Mars. We present the results of numerical simulations performed to study the early thermal evolution and planetary scale differentiation of Mars. The simulations are confined to the initial 50 Myr (Ma) of the formation of solar system. The accretion energy produced during the growth of Mars and the decay energy due to the short‐lived radio‐nuclides ²⁶Al, ⁶⁰Fe, and the long‐lived nuclides, ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th are incorporated as the heat sources for the thermal evolution of Mars. During the core‐mantle differentiation of Mars, the molten metallic blobs were numerically moved using Stoke's law toward the center with descent velocity that depends on the local acceleration due to gravity. Apart from the accretion and the radioactive heat energies, the gravitational energy produced during the differentiation of Mars and the associated heat transfer is also parametrically incorporated in the present work to make an assessment of its contribution to the early thermal evolution of Mars. We conclude that the accretion energy alone cannot produce widespread melting and differentiation of Mars even with an efficient consumption of the accretion energy. This makes ²⁶Al the prime source for the heating and planetary scale differentiation of Mars. We demonstrate a rapid accretion and core‐mantle differentiation of Mars within the initial ~1.5 Myr. This is consistent with the chronological records of Martian meteorites.     

On the effects of higher convection modes on the thermal evolution of small planetary bodies

The effects of higher modes of convection on the thermal evolution of a small planetary body is investigated. Three sets of models are designed to specify an initially cold and differentiated, an initially hot and differentiated, and an initially cold and undifferentiated Moon-type body. The strong temperature dependence of viscosity enhances the thickening of lithosphere so that a lithosphere of about 400 km thickness is developed within the first billion years of the evolution of a Moon-type body. The thermally isolating effect of such a lithosphere hampers the heat flux out of the body and increases the temperature of the interior, causing the solid-state convection to occur with high velocity so that even the lower modes of convection can maintain an adiabatic temperature gradient there. It is demonstrated that the effect of solid-state convection on the thermal evolution of the models may be adequately determined by a combination of convection modes up to the third or the fourth order harmonic. The inclusion of higher modes does not affect the results significantly.     

Distribution, ,movement,and evolution of the volatile elements in the lunar regolith

The abundances and distributions of carbon, nitrogen, and sulfur in lunar soils are reviewed. Carbon and nitrogen have a predominantly extra-lunar origin in lunar soils and breccias, while sulfur is mostly indigeneous to the Moon. The lunar processes which effect the movement, distribution, and evolution of carbon, nitrogen, and sulfur, along with the volatile alkali elements sodium, potassium, and rubidium during regolith processes are discussed. Possible mechanisms which may result in the addition to or loss from the Moon of these volatile elements are considered.     

The moon's thermal state and an interpretation of the lunar electrical conductivity distribution

Heat convection, being a more general theory than conduction theory, compels one to give reasons for using the latter theory as the basis of thermal evolution studies. Such reasons are supplied by considerations of material rheology.The specific case of the thermal regime of the Moon is first considered as a steady state problem. It is demonstrated that no plausible creep resistance of lunar material and heat generation is compatible with a purely conductive theory of lunar thermal evolution. The most plausible, steady state models give convective cores extending to within 200–300 km of the surface. The radial temperature gradients in such cores is virtually confined to a thermal boundary layer but averages to about a tenth of degree/km. The (steady) central temperature for the most plausible lunar rheologies lie between 600–1000°C. Such models are compatible with the first interpretations of lunar magnetometry. The case for considering the lunar thermal state as such a quasi-static state is discussed.It is also predicted that in very local zones the viscous dissipation of the general circulation produces much higher temperatures. Chemical differentiation and seismicity would have their origin in such low viscosity zones.     

Gas interaction effects on lunar bonded particles and their implications

Some of the bonded particles of lunar soil samples separated upon exposure to reactive gases such as oxygen, water vapor, their mixtures, acids and bases. The bondings between particles susceptible to gas-disruption seemed to be generally weak and appeared to have taken place via highly radiation-damaged layers at the particle surfaces. These amorphous layers with an average thickness of about 0.05µm were produced by the solar wind exposure of about 2000 years. Therefore, the solar wind was responsible for the formation of these weak bondings and also probably responsible for disruption of these bondings. Apollo 11 and 12 landed in the equatorial region and about 1500 km apart. Thus, the solar wind effects on materials at these sites should have been about the same and the proportion of bonded particles separated by reactive gas exposure should also have been about the same; but the number of separations observed was about 2.7 (average) times greater in the Apollo 11 soil sample than in the Apollo 12 soil sample. This finding suggests that the number of weakly bonded particles and probably the solar-wind damaged amorphous layer particles at these sites was about in the same proportion. It is, therefore, considered that materials from certain depth (practically not exposed to the solar wind) of another site were transported and mixed during recent years (considerably less than 2000 years) with the original materials of the Apollo 12 site. This is consistent with the conclusions made by other investigators.