Thermal evolution of the moon

The thermal history and current state of the lunar interior are investigated using constraints imposed by recent geological and physical data. Theoretical temperature models are computed taking into account different initial conditions, heat sources, differentiation and simulated convection. To account for the early formation of the lunar highlands, the time duration of magmatism and presentday temperatures estimated from lunar electrical conductivity profiles, it is necessary to restrict initial temperatures and abundances of radioactivie elements. Successful models require that the outer half of the Moon initially heated to melting temperatures, probably due to rapid accretion. Differentiation of radioactive heat sources toward the lunar surface occurred during the first 1.6 billion years. Temperatures in the outer 500 km are currently low, while the deep interior (radius less than 700 to 1000 km) is warmer than 1000°C, and is of primordial material. In some models there is a partially melted core. The calculated surface heat flux is between 25 and 30 erg/cm² s.Presently at the Research Triangle Institute, Research Triangle, North Carolina 27709, U.S.A.     

Thermal history and evolution of the moon

Possible models for the thermal evolution of the Moon are constrained by a wide assortment of lunar data. In this work, theoretical lunar temperature models are computed taking into account different initial conditions to represent possible accretion models and various abundances of heat sources to correspond to different compositions. Differentiation and convection are simulated in the numerical computational scheme.Models of the thermal evolution of the Moon that fit the chronology of igneous activity on the lunar surface, the stress history of the lunar lithosphere implied by the presence of mascons, and the surface concentrations of radioactive elements, involve extensive differentiation early in lunar history. This differentiation may be the result of rapid accretion and large-scale melting or of primary chemical layering during accretion. Differences in present-day temperatures for these two possibilities are significant only in the inner 1000 km of the Moon and are not resolvable with presently available data.If the Apollo 15 heat flow is a representative value, the average uranium concentration in the moon is 65±15 ppb. This is consistent with achondritic bulk composition (between howardites and eucrites) for the Moon.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

The evolution of the moon: A finite element approach

Thermal convection has considerable influence on the thermal evolution of terrestrial planets. Previous numerical models of planetary convection have solved the system of partial differential equations by finite difference methods, or have approximated it by parametrized methods. We have evaluated the applicability of a finite element solution of these equations. Our model analyses the thermal history of a self-gravitating spherical planetary body; it includes the effects of viscous dissipation, internal melting, adiabatic gradient, core formation, variable viscosity, decay of radioactive nucleides, and a depth dependent initial temperature profile. Reflecting current interest, physical parameters corresponding to the Moon were selected for the model.Although no initial basalt ocean is assumed for the Moon, partial melting is observed very early in its history; this is presumably related to the formation of the basalt maria. The convection pattern appears to be dominated by an L-2 mode. The present-day lithospheric thickness in the model is 600 km, with core-mantle temperatures close to 1600 K. Surface heat flux is 25.3 mW m^–2, higher than the steady state-value by about 16%.The finite element method is clearly applicable to the problem of planetary evolution, but much faster solution algorithms will be necessary if a sufficient number of models are to be examined by this method.Notation coefficient of thermal expansion - _ij Kronecker delta - absolute or dynamic viscosity - perturbation in temperature - thermal diffusivity - kinematic viscosity - density - stress tensor - B.P. before present - c specific heat at constant pressure or volume (Boussinesq approximation) - d depth of convection - E ^* activation energy for creep - g gravity - Ga billions of years - H(t) heat generation per unit mass per unit time at timet - k Boltzmann's constant - K mean thermal conductivity - Ma millions of years - p pressure - q heat flux - q _ss steady-state heat flux - Ra Rayleigh number - S volumetric heat sources, includes radioactivity and viscous dissipation - t time - T temperature - u verocity vector - V ^* activation volume for creep     

The formation of the moon

Supporting evidence for the fission hypothesis for the origin of the Moon is offered. The maximum allowable amount of free iron now present in the Moon would not suffice to extract the siderophiles from the lunar silicates with the observed efficiency. Hence extraction must have been done with a larger amount of iron, as in the mantle of the Earth, of which the Moon was once a part, according to the fission hypothesis. The fission hypothesis gives a good resolution of the tektite paradox. Tektites are chemically much like products of the mantle of the Earth; but no physically possible way has been found to explain their production from the Earth itself. Perhaps they are a product of late, deep-seated lunar volcanism. If so, the Moon must have inside it some material with a strong resemblance to the Earth's mantle. Two dynamical objections to fission are shown to be surmountable under certain apparently plausible conditions.     

Effect of a giant impact on the thermal evolution of the moon

The effects of a giant impact on the thermal evolution of the Moon are investigated. It is found that an impact similar to that of Imbrium creates lateral temperature variations of more than 200 deg within the upper 200 km of the Moon. Starting with a common lithosphere of 70 km thickness, the lithosphere beneath the basin grows to 200 km in thickness within 0.5 b.y. after the impact, while that beneath the highlands reaches to only 100 km in thickness during this period. The model presented for the thermal evolution of the Moon is compatible with (1) the existence of mascons for more than 3 b.y., (2) the late magmatization and subsequent volcanic activities during 4 to 3 b.y. ago and (3) the negative gravity rings around the large mascons.     

Electrical conductivity,internal temperatures and thermal evolution of the moon

The electrical conductivity of olivine and pyroxene is a strong function of the fugacity of oxygen in the atmosphere with which the mineral is in equilibrium. Lunar temperature profiles calculated from data on the electrical conductivity of these two minerals at oxygen fugacities similar to those which exist in the Moon indicate considerably higher temperatures for the lunar interior than obtained from conductivity data collected under normal atmospheric conditions. These high interior temperatures, the extensive differentiation associated with the formation of the lunar maria, and the radioactive element content of the Moon indicate that the Moon accreted at temperatures between 600 and 1000°C. Gravitational heating during accretion would lead to melting of at least the outer 200 km of the Moon and would produce conditions favourable to separation of a metal-sulfide melt sufficient to form a core of 200–300 km radius. Such a core would reach the center of the Moon within a few million years after accretion. This core could produce the remanent magnetization observed in the surface rocks. Dynamo action would cease with the cessation of convective motion within the core as the temperature of the surrounding mantle increased due to radioactive heating. With the radioactivity assumed in the present model and the high accretion temperature, this event would require less than 2 b.y., but more than 1.6 b.y.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

The thermal history of the moon

A simple analysis shows that the normal assumption of an outward heat flow, together with the normally assumed surface layer of low thermal conductivity, would give rise to microwave emission effects and to local variations in surface temperature which are not in fact observed. It is concluded that either the surface layer must be much thinner than is at present postulated, or that the outward flow of heat must be much smaller than is supposed.     

The ultraviolet reflectivity of the moon

The ultraviolet flux from the entire lunar disk has been measured in a series of rocket flights from Woomera at several wavelength bands in the range 2400-2900 Å and also at the wavelength of the hydrogen Lα line (1216 Å). Comparison of these measurements with other observations shows that between the visible and middle ultraviolet part of the spectrum, the lunar albedo decreases sharply towards shorter wavelengths falling to (0.7 ± 0.1) percent at 2400 Å which is a factor of ten less than the visible albedo. The measured albedo at 1216 Å is (0.3 ± 0.1) percent indicating that the decline in reflectivity with decreasing wavelength is less rapid at far ultraviolet wavelengths than is the decline between visible and middle ultraviolet.     

The earliest maps of the moon

The aim of the present paper is to give a brief account of the history of lunar mapping in the pre-telescopic era, and that immediately following the discovery of the telescope. It is pointed out that the first (and also last) extant map of the Moon based on naked-eye observations was prepared some time before 1603 by William Gilbert - discoverer of the terrestrial magnetism - though it was published only posthumously in 1651. Moreover, the recently unearthed drawings of the Moon by Thomas Harriott in England based on telescope observations between 1609 and 1610 are in no way inferior (if not otherwise) than those published by Galileo Galilei at the same time. As G. C. La Galla's drawings of the Moon published in Venice in 1612 are in reality identical with those of Galileo, the third independent contribution to lunar mapping was made by P. Christoph Scheiner in Germany between 1611 and 1613; preceding those by C. Malapert (1916) or Gassendi and Mellan more than twenty years later.     

The moon after Apollo

The Apollo missions have gradually increased our knowledge of the Moon's chemistry, age, and mode of formation of its surface features and materials Apollo 11 and 12 landings proved that mare materials are volcanic rocks that were derived from deep-seated basaltic melts about 3.7 and 3.2 billion years ago, respectively. Later missions provided additional information on lunar mare basalts as well as the older, anorthositic, highland rocks. Data on the chemical make-up of returned samples were extended to larger areas of the Moon by orbiting geochemical experiments. These have also mapped inhomogeneities in lunar surface chemistry, including radioactive anomalies on both the near and far sides.Lunar samples and photographs indicate that the moon is a well-preserved museum of ancient impact scars. The crust of the Moon, which was formed about 4.6 billion years ago, was subjected to intensive metamorphism by large impacts. Although bombardment continues to the present day, the rate and size of impacting bodies were much greater in the first 0.7 billion years of the Moon's history. The last of the large, circular, multiringed basins occurred about 3.9 billion years ago. These basins, many of which show positive gravity anomalies (mascons), were flooded by volcanic basalts during a period of at least 600 million years. In addition to filling the circular basins, more so on the near side than on the far side, the basalts also covered lowlands and circum-basin troughs.Profiles of the outer lunar skin were constructed from the mapping camera system, including the laser altimeter, and the radar sounder data. Materials of the crust, according to the lunar seismic data, extend to the depth of about 65 km on the near side, probably more on the far side. The mantle which underlies the crust probably extends to about 1100 km depth. It is also probable that a molten or partially molten zone or core underlies the mantle, where interactions between both may cause the deep-seated moonquakes.The three basic theories of lunar origin—capture, fission, and binary accretion—are still competing for first place. The last seems to be the most popular of the three at this time; it requires the least number of assumptions in placing the Moon in Earth orbit, and simply accounts for the chemical differences between the two bodies. Although the question of origin has not yet been resolved, we are beginning to see the value of interdisciplinary synthesis of Apollo scientific returns. During the next few years we should begin to reap the fruits of attempts at this synthesis. Then, we may be fortunate enough to take another look at the Moon from the proposed Lunar Polar Orbit (LPO) mission in about 1979.     

The chemical composition and structure of the moon

Three types of igneous rocks, all ultimately related to basaltic liquids, appear to be common on the lunar surface. They are: (1) iron-rich mare basalts, (2) U-, REE-, and Al-rich basalts (KREEP), and (3) plagioclase-rich or anorthositic rocks. All three rock types are depleted in elements more volatile than sodium and in the siderophile elements when relative element abundances are compared with those of carbonaceous chondrites. The chemistry and age relationships of these rocks suggest that they are derived from a feldspathic, refractory element-rich interior that becomes more pyroxenitic; that is, iron/magnesium-rich; with depth.It is suggested that the deeper parts of the lunar interior tend toward chondritic element abundances. The radial variation in mineralogy and bulk chemical composition inferred from the surface chemistry is probably a primitive feature of the Moon that reflects the accretion of refractory elementenriched materials late in the formation of the body.     

The moon as the origin of the Earth's continents

Paleontological data and celestial mechanics suggest that the Moon may have stayed in a geosynchronous corotation around the Earth as a geostationary satellite. Excess energy may have slowly been released as heat, transferred as movement around the Sund or lost with matter ejected into space.The radial segregation process which was responsible for the formation of the Earth's iron core also brought water and lithophile elements dissolved in the water towards the surface. These elements were deposited in the area facing the Moon for several reasons, and a single continent was formed. Its level continuously matched the sea level, so the continent was formed under shallow water. When the geosynchronous corotation of the Moon became impossible, the tides become important, the Moon receded and the Earth slowed down and became more and more spherical; the variation of its oblateness from about 8% to 0.3% was incompatible with the shape of the continent, that broke into pieces.Almost all the data were have on the Earth's age, the composition of the continents, sea water and the atmosphere fit this approach as does lunar data.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.     

Magnetism of the moon

The Malkus theory of a precessionally driven magnetoturbulence in a liquid core is applied to the Moon. It is shown that a lunar magnetic field requires the presence of a non-metallic core at at least 2500K or of an iron core at at least 2000K. Within the limits of our present knowledge these requirements may have been satisfied in the past. A new mechanism is proposed which is based on tidal effects in the outer solid and liquid shells whose existence is suggested by measurements of lunar radioactivity. This mechanism could account for the generation of local rather than poloidal fields at low latitudes in agreement with observation.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Viscosity of the moon

Using data from the present gravitational potential and surface topography of the Moon, it is possible to determine a lower limit of about 5 b.y. for the relaxation time of the mascons. Assuming that the Moon has behaved as a Maxwellian viscoelastic body since the formation of the mascons, this relaxation time indicates a value of about 10²⁷ poise for the viscosity of the lunar interior. Such a high viscosity implies that there has been no convection current inside the upper 800 km of the Moon since the formation of the mascons. Lunar Science Institute Contribution No. 99. The research in this paper was done while the author was a Visiting Scientist at the Lunar Science Institute, which is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration.     

The origin of the moon and the single-impact hypothesis I

Recently the single-impact hypothesis for forming the Moon has gained some favorable attention. We present in this paper a series of three-dimensional numerical simulations of an impact between the protoearth and an object about 0.1 of its mass. For computational convenience both objects were assumed to be composed of granite. We studied the effects on the outcome of the collision of varying the impact parameter, the initial internal energy, and the relative velocity. The results show that if the impact parameter is large enough so that the center of the impactor approximately grazes the limb of the protoearth, the impactor is not completely destroyed; part of it forms a clump in a large elliptical orbit about the Earth. This clump does not collide with the Earth, since the effects, first, of vapor pressure gradients during the impact, and later, of angular momentum transfer due to the rotation of the deformed Earth, have modified the ballistic trajectory. However, since the orbit of the clump comes close to the Earth (within the Roche limit) the clump will be destroyed and spread out to form a disk around the Earth. The amount of angular momentum in the Earth-Moon system thus obtained tends to fall short of the observed amount; this deficiency would be eliminated if the mass of the impactor were somewhat greater than the one assumed here. The scenario for making the Moon from a single-impact event is supported by these simulations.     

The residual permanent magnetic dipole moment of the moon

The residual dipole moment of the outer spherical shell of the Moon, magnetized in the field of an internal dipole is calculated for the case when the permeability of the shell differs from unity. It is shown that, using an average value of surface magnetization from returned lunar crystalline rock samples and a global figure for the lunar permeability of 1.012, that a residual moment of the order of 10¹⁵ to 10¹⁶ Am² is expected. This value is some two or three orders of magnitude lower than the moment for a shell magnetized in an external uniform field and is of the same order as the upper limit of the residual moment detected by Russellet al. (1974). At present the magnetic data and the thermal state of the Moon are not known with sufficient accuracy to distinguish between a crust magnetized in an internal dipole field of constant polarity and a crust magnetized in the dipole field of a self-reversing core dynamo. Refined measurements of the relevant parameters together with the theory presented in this paper could enable these two possibilities to be distinguished.     

Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the Moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the Moon is presented. The model assumes that the Moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting Moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outershell, about 400 km thick, was partially or completely molten just after the accretion of the Moon and that the Moon should have been formed in a period shorter than 1000 yr. If the Moon formed at a position nearer to the Earth than its present one, the Moon might have been formed in a period of less than one year.On leave from Geophysical Institute, University of Tokyo.Contribution No. 2104, Division of Geological and Planetary Sciences, California Institute of Technology.     

Topocentric aberration of the moon

Aberrational displacement of the observed topocentric positions of the Moon differ from the aberrational effect in its apparent ephemeris geocentric coordinates. The differential aberrational corrections due to the mutual positions of the observer and the Moon, may account to 0 _. ^″ 3. The reduction method of astrometric observations of the Moon, which takes into account this effect, is proposed.     

Pre-capture orbits of the moon

If the mass of the Earth was not considerably larger than at present, the pre-capture orbit of the Moon was in the range 0.9–1.1 A.U. Capture occurred within several 10⁸ years after formation of the Moon.