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.     

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.     

On the thermal history of a moon of fission origin

Model calculations show that the thermal history of a Moon which originated by fission from the proto-Earth is the same as that for the Moon as it is currently understood. In particular, a fissioned Moon currently has a small percent of partial melt or at least near solidus temperatures below depths of 800 km in accord with the seismic data which show that the deep interior of the Moon has a very lowQ. The models have moderate (20–50%) degrees of partial melting in the upper mantle (depths < 300 or 200 km) in the period between 3 to 4 × 10⁹ years ago and, therefore, can account for the mare filling epoch. Finally the heat flow of the models is 18 ergs cm^–2 s^–1 which is close to the average of 19 ergs cm^–2 s^–1 derived from the Apollo heat flow experiments. These findings add further support for the fission origin of the Moon.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

Possible effect of subsurface inhomogeneities on the lunar microwave spectrum

Inhomogeneities beneath the lunar surface could alter the average microwave emission spectrum of the Moon in a fashion generally consistent with observations, even in the absence of an average heat flux or density gradients with depth. The lunar subsurface was modeled as an inhomogeneous lossy dielectric with three-dimensional refractive index fluctuations characterized by independent horizontal and vertical correlation lengths. The model suggests that attempts to infer the physical properties of the Moon from the lunar microwave spectrum could be significantly inaccurate if subsurface scattering were neglected.     

Interpretation of lunar heat flow data

Lunar heat flow observations at the Apollo 15 and 17 sites can be interpreted to imply bulk U concentrations for the Moon of 5 to 8 times those of normal chondrites and 2 to 4 times terrestrial values inferred from the Earth's heat flow and the assumption of thermal steady state between surface heat flow and heat production. A simple model of nearsurface structure that takes into account the large difference in (highly insulating) regolith thickness between mare and highland provinces is considered. This model predicts atypically high local values of heat flow near the margins of mare regions - possibly a factor of 10 or so higher than the global average. A test of the proposed model using multifrequency microwave techniques appears possible wherein heat flow traverse measurements are made across mare-highland contacts. The theoretical considerations discussed here urge caution in attributing global significance to point heat-flow measurements on the Moon.     

Using space manifold dynamics to deploy a small satellite constellation around the Moon

The possibility of communicating with the far side of the Moon is essential for keeping a continuous radio link with lunar orbiting spacecraft, as well as with manned or unmanned surface facilities in locations characterized by poor coverage from Earth. If the exploration and the exploitation of the Moon must be sustainable in the medium/long term, we need to develop the capability to realize and service such facilities at an affordable cost. Minimizing the spacecraft mass and the number of launches is a driving parameter to this end. The aim of this study is to show how Space Manifold Dynamics can be profitably applied in order to launch three small spacecraft onboard the same launch vehicle and send them to different orbits around the Moon with no significant difference in the Delta-V budgets. Internal manifold transfers are considered to minimize also the transfer time. The approach used is the following: we used the linearized solution of the equations of motion in the Circular Restricted Three Body Problem to determine a first–guess state vector associated with the Weak Stability Boundary regions, either around the collinear Lagrangian point L1 or around the Moon. The resulting vector is then used as initial state in a numerical backward-integration sequence that outputs a trajectory on a manifold. The dynamical model used in the numerical integration is four-body and non-circular, i.e. the perturbations of the Sun and the lunar orbital eccentricity are accounted for. The trajectory found in this way is used as the principal segment of the lunar transfer. After separation, with minor maneuvers each satellite is injected into different orbits that lead to ballistic capture around the Moon. Finally, one or more circularization maneuvers are needed in order to achieve the final circular orbits. The whole mission profile, from launch to insertion into the final lunar orbits, is modeled numerically with the commercial software STK.     

Lunar thermal history revisited

The internal temperatures, heat fluxes, and rates of evolution of volcanic liquids for lunar models with initial radioactivities and temperatures that decrease going downward in the Moon are calculated. These conditions lead to a volcanism concentrated very early in lunar history even when other heat sources, e.g. melting due to accretion, are excluded.     

On the petrology and early development of the crust of a moon of fission origin

It is proposed that the primitive suite of upland rocks formed as a result of the cumulation of plagioclase which crystallized in disequilibrium from a convecting magma containing previously crystallized and co-crystallizing olivine and pyroxene. As the plagioclase was removed from this magma by flotation, it carried with it melt and mafic crystals in varying, but predictable proportions. This model successfully accounts for the major petrological characteristics of the upland suite of rocks, in particular, the reversed An vs Mg' trend, the quartz normative anorthosites and the olivine to pyroxene ratio variations vs plagioclase content of the rocks.It is shown that the crystallization sequence for the Moon is one where the pyroxenes of the peridotite upper mantle and crust were formed as a result of the reaction olivine + quartz (melt) pyroxene. This reaction occurred at depth (100–300 km) in the moon after the dunite lower mantle had formed, but while olivine was still crystallizing at the surface. As a result of this reaction, the crystallization of the last 20% of the Moon took place mainly along the olivine-plagioclase cotectic and not at the olivine-pyroxene-plagioclase peritectic as previously proposed. This crystallization sequence leads directly to an explanation of the fact that olivine rich rocks make up a significant fraction of the crust, despite the presence of a pyroxene dominated upper mantle directly below the crust. Also the reaction olivine + quartz (melt) pyroxene is exothermic and as such provided heat energy at the bottom of the magma system needed to set it into strong convective motion. As a result, the magma was kept stirred and the olivine and pyroxene in the cooling magma were kept in equilibrium with the melt, thus finally producing the relatively uniform peridotite of the upper mantle.A refined model for the distribution of U, Th and K in the crust of a pyroline moon is presented. It is demonstrated that the KREEP layer, which formed at the crust-upper mantle interface at the end of the crystallization of the Moon, was quickly destroyed by impact excavation and the upwards migration of the low melting KREEP materials. As a result of these processes the KREEP layer no longer exists in the Moon and all of its components are mixed in the crust. As a result, the crust contains about 80% of the heat producing U, Th and K of the Moon. The predicted values of the concentrations of U, Th and K in the crust based on this model are almost exactly those found for the average upland crust by the orbiting-ray experiment. This result not only strongly supports the models proposed in this paper but also supports the suggestion that the mean heat flow of the moon is 13–14 ergs/cm²/sec, i.e. that predicted for a Moon of fission origin in an earlier paper.The results and models presented in this paper further support the hypothesis that the Moon is a gravitationally differentiated body which originated by fission from a protoearth.Contribution No. 127, Institut für Geophysik, Kiel.     

An empirically derived lunar gravity field

The heat-flow experiment is one of the Apollo Lunar Surface Experiment Package (ALSEP) instruments that was emplaced on the lunar surface on Apollo 15. This experiment is designed to make temperature and thermal property measurements in the lunar subsurface so as to determine the rate of heat loss from the lunar interior through the surface. About 45 days (1 1/2 lunations) of data has been analyzed in a preliminary way. This analysis indicates that the vertical heat flow through the regolith at one probe site is 3.3 × 10^–6 W/cm² (±15%). This value is approximately one-half the Earth's average heat flow. Further analysis of data over several lunations is required to demonstrate that this value is representative of the heat flow at the Hadley Rille site. The mean subsurface temperature at a depth of 1 m is approximately 252.4K at one probe site and 250.7K at the other. These temperatures are approximately 35K above the mean surface temperature and indicate that conductivity in the surficial layer of the Moon is highly temperature dependent. Between 1 and 1.5m, the rate of temperature increase as a function of depth is 1.75K/m (±2%) at the probe 1 site. In situ measurements indicate that the thermal conductivity of the regolith increases with depth. Thermal-conductivity values between 1.4 × 10^–4 and 2.5 × 10^–4 W/cm K were determined; these values are a factor of 7 to 10 greater than the values of the surface conductivity. If the observed heat flow at Hadley Base is representative of the moonwide rate of heat loss (an assumption which is not fully justified at this time), it would imply that overall radioactive heat production in the Moon is greater than in classes of meteorites that have formed the basis of Earth and Moon bulk composition models in the past.Lamont-Doherty Geological Observatory Contribution Number 1800.     

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.     

Main braking phase for a soft moon landing as a form of trajectory correction

Rationale is given for the braking profile of a spacecraft making a soft landing on the Moon’s surface, including the following four phases: main braking, free fall, repeated braking, and descent at a constant speed. Due to the large altitude differential over the braking path in near-polar regions of the Moon, main braking is proposed as a type of trajectory correction impulse using no altimeter. The boundary problem solution and statistical calculations are used to give the potential energy costs and characteristics of the dispersion characteristics for this phase and choose an optimal thrust-to-weight ratio for the phase.     

The sunlit lunar atmosphere: A comprehensive study by CHACE on the Moon Impact Probe of Chandrayaan-1

The altitudinal/latitudinal profile of the lunar atmospheric composition on the sunlit side was unraveled for the first time by the Chandra’s Altitudinal Composition Explorer (CHACE) on the Moon Impact Probe, a standalone micro-satellite that impacted at the lunar south pole, as a part of the first Indian mission to Moon, Chandrayaan-1. Systematic measurements were carried out during the descent phase of the impactor with an altitude resolution of ∼250 m and a latitudinal resolution of ∼0.1°. The overall pressure on the dayside and the neutral composition in the mass range 1-100 amu have been measured by identifying 44 and 18 amu as the dominant constituents. Significant amounts of heavier (>50 amu) species also have been detected, the details of which are presented and discussed.     

On Choosing a Rational Flight Trajectory to the Moon

The algorithm for choosing a trajectory of spacecraft flight to the Moon is discussed. The characteristic velocity values needed for correcting the flight trajectory and a braking maneuver are estimated using the Monte Carlo method. The profile of insertion and flight to a near-circular polar orbit with an altitude of ~100 km of an artificial lunar satellite (ALS) is given. The case of two corrections applied during the flight and braking phases is considered. The flight to an ALS orbit is modeled in the geocentric geoequatorial nonrotating coordinate system with the influence of perturbations from the Earth, the Sun, and the Moon factored in. The characteristic correction costs corresponding to corrections performed at different time points are examined. Insertion phase errors, the errors of performing the needed corrections, and the errors of determining the flight trajectory parameters are taken into account.     

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.     

Young thrust-fault scarps in the highlands: evidence for an initially totally molten moon

Thermoelastic stress calculations show that if only the outer few hundred kilometers of the Moon was initially molten and if it had a cool interior, i.e., the magma ocean model of the Moon, the highlands should not have any young, compressional tectonic features. In contrast, if the Moon was initially totally molten, the highlands should have 10-km- scale, ?0.5- to 1 × 10⁹-year-old thrust faults. Observations using the Apollo panoramic imagery show that young thrust faults do exist in the highlands. Extrapolation of the data suggests that some 2000 thrust-fault scarps, whose average length is 9 km, are in the highlands. The fault scarps generally occur in series or complexes of four or five scarps. The average length of these complexes is 50 km; the largest observed complex is 120 km long. Extrapolation of the data suggests that there are about 400 such complexes. The ages of the scarps range from 60±30 to 680±250 my, with a possible bias of up to plus a factor of 2 or minus a factor of 4. These scarps are by far the youngest endogenic features on the Moon. The selenographical, size, age, morphological, and azimuth frequency distributions of the scarps can be explained by the effects of the kilobar-level thermoelastic stresses, the 100-bar-level tidal and rotational stresses, and influence by preexisting structures. These results show that the Moon has recently entered an epoch of late stage, global tectonism and favor the concept that the Moon was initially totally molten.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

A theory for the interpretation of lunar surface magnetometer data

The solution to the problem of the motion of the Moon relative to spatial irregularities in the interplanetary magnetic field is found. The lunar electrical conductivity is modeled by a two-layer conductivity profile. For the interaction of the Moon with the corotating sector structure of the interplanetary magnetic field it is found that the magnetic field in the lunar shell is the superposition of an oscillatory uniform field, an oscillatory dipole field and anoscillatory field that is toroidal about the axis of the motional electric field. With various lunar conductivity models and the theory of this paper, lunar surface magnetometer data can be quantitatively interpreted to yield information on the conductivity and consequently the temperature of the lunar core.Presently visiting the Max-Planck-Institut für Physik und Astrophysik, München, Germany.     

Generation of a secular system in the analytical theory for the motion of the moon

In order to generate an analytical theory of the motion of the Moon by considering planetary perturbations, a procedure of general planetary theory (GPT) is used. In this case, the Moon is considered as an addition planet to the eight principal planets. Therefore, according to the GPT procedure, the theory of the Moon’s orbital motion can be presented in the form of series with respect to the evolution of eccentric and oblique variables with quasi-periodic coefficients, which are the functions of mean longitudes for principal planets and the Moon. The relationship between evolution variables and the time is determined by a trigonometric solution for the independent secular system that describes the secular motion of a perigee and the Moon node by considering secular planetary inequalities. Principal planetary coordinates required for generating the theory of the motion of the Moon includes only Keplerian terms, the intermediate orbit, and the linear theory with respect to eccentricities and inclinations in the first order relative to the masses. All analytical calculations are performed by means of the specialized echeloned Poisson Series Processor EPSP.     

Unipolar induction in the moon and a lunar limb shock mechanism

The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,E _o, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 10³ mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.On leave from NASA Ames Research Center