A determination of the parameters of the level surface of lunar gravity

The spectral coefficients of the selenoid have been obtained by inverting the potential series for lunar gravity. The reference value of the lunar level surface has been determined on the base of the mean radius of lunar topography. This enables to evaluate the parameters of the tri-axial reference ellipsoid best fitted to the lunar level surface.     

New Trends in the Development of the Lunar Physical Libration Theory

A review of the modern state of the lunar libration theory is presented. A significant progress in the lunar investigation is achieved due to the simultaneous processing of results of the satellite Doppler tracing and of the lunar laser ranging. The data evidencing existence of a small iron core in the Moon are discussed. In this connection, the further development of the theory of rotation of the Moon presents the study of internal structure and dynamics of a lunar body. A model of a two-layer Moon can have a very advanced application to explain some observed phenomena and to be as a first approach in the modelling of internal processes determining the lunar rotation.     

Effects of the physical libration of the moon on lunar orbiters

Lunar physical libration, which is true oscillation of lunar equator in the space, alters the lunar gravitational field in the space coordinate system and affects the orbiting motion of lunar orbiters (hereafter called as lunar satellites) correspondingly. The effect is very similar to that of the precession and nutation on the earth satellites, and a similar treatment can be used. The variations in the gravitational force and in the orbit perturbation solution are clearly given in this paper together with numerical illustrations.     

自适应光学应用于月球激光测距中视场旋转对大气波前倾斜量提取的影响

自适应光学技术应用于月球激光测距试验中需要实时针对月面扩展源进行大气波前倾斜量的提取,望远镜在跟踪月亮的过程中存在月面本身相对望远镜的物方视场的旋转以及望远镜自身的运动所引起的像方视场的旋转,本文讨论了望远镜物方视场及像方视场旋转的规律以及其对大气波前倾斜量提取的影响。     

Primary and secondary magnetizations in lunar rocks - Implications for the ancient magnetic field of the Moon

The nature of the ancient magnetic field of the Moon, in which lunar rocks acquired their remanent magnetism, has emerged as an important potential source of evidence, if somewhat controversial, for a lunar core which at a period in the Moon's history was the source of the magnetic field. Many of the lunar rocks possess a stable, primary remanence (NRM) with characteristics consistent with and indicative of thermo-remanent magnetization, acquired when the rocks cooled in an ambient magnetic field. Also present are secondary components of magnetization, one type of which appears to have been acquired between collection on the Moon and reception in the laboratory and others which were apparently acquired on the Moon.An important question to be answered is whether meteorite impacts play any part in lunar magnetism, either in modifying pre-existing magnetizations or by imparting a shock remanent magnetism (SRM) in a transient magnetic field associated with the impact. With current knowledge, SRM, in either a global lunar magnetic field of a transient field, and TRM cannot be distinguished, and in the paper the secondary magnetization characteristic of lunar rocks are examined to investigate whether their nature favours the presence of a permanent lunar magnetic field or whether they are consistent with an origin as a transient field-generated SRM.Besides terrestrial processes of secondary magnetization, such as viscous, chemical and partial thermoremanent magnetization, possible processes peculiar to the Moon are discussed and their likely importance assessed in relation to lunar sample history. The nature of the secondary magnetizations appear to be best explained on the assumption that they are due to one or more of the processes that require an ambient lunar field, namely viscous, partial thermoremanent and shock magnetization. When associated with other types of evidence obtained from lunar magnetism studies, investigations of lunar sample remanent magnetism now favours the existence of an ancient lunar magnetic field.     

The Flux of Lunar Meteorites onto the Earth

Numerous new finds of lunar meteorites in Oman allow detailed constraints to be obtained on the intensity of the transfer of lunar matter to the Earth. Our estimates show that the annual flux of lunar meteorites in the mass interval from 10 to 1000 g to the entire Earth's surface should not be less than several tenths of a kilogram and is more likely equal to tens or even a few hundred kilograms, i.e., a few percent of the total meteorite flux. This corresponds to several hundred or few thousand falls of lunar meteorites on all of Earth per year. Even small impact events, which produce smaller than craters on the Moon smaller than 10 km in diameter, are capable of transferring lunar matter to the Earth. In this case, the Earth may capture between 10 to 100% of the mass of high-velocity crater ejecta leaving the Moon. Our estimates for the lunar flux imply rather optimistic prospects for the discovery of new lunar meteorites and, consequently, for the analyses of the lunar crust composition. However, the meteorite-driven flux of lunar matter did not play any significant role in the formation of the material composition of the Earth's crust, even during the stage of intense meteorite bombardment.     

Rotation of the moon and lunar coordinate systems

The need for precise definition of lunar reference systems is stressed and the principles on which systems of lunar coordinates could be based are established. Differences between coordinate systems defined by the dynamical properties of the lunar configuration and the rotational motion of the lunar globe about its centre of gravity are outlined, and rigorous mathematical formulae relating those systems have been developed. The principles of reduction of measurements are outlined and in the Appendix the absolute coordinates obtained for 700 lunar features are presented.Paper presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971.     

On the origin of ancient lunar magnetic fields

The maximum value of possible lunar dynamo-field in our epoch is estimated in the scheme of precession dynamo model. In the light of our notions on the evolution of the Earth-Moon system this scheme may account for the size and character of ancient lunar fields that resulted in magnetization of surface lunar rocks, as well as for the absence of lunar dipole field of paleomagnetic origin in our epoch.     

On the accuracy of lunar ephemerides using the data provided by the future Russian lunar laser ranging system

The potential effect of the future Russian lunar laser ranging system (LLRS) on the accuracy of lunar ephemerides is discussed. In addition to the LLRS in Altai, several other observatories suitable for the LLRS installation are considered. The variation of accuracy of lunar ephemerides in the process of commissioning of new LLRS stations is estimated by mathematical modeling. It is demonstrated that the error in the determination of certain lunar ephemeris parameters may be reduced by up to 16% after seven years of operation of the Altai LLRS with a nearly optimal observational program.     

Long-term degradation of optical devices on the Moon

Forty years ago, Apollo astronauts placed the first of several retroreflector arrays on the lunar surface. Their continued usefulness for laser ranging might suggest that the lunar environment does not damage optical devices. However, new laser ranging data reveal that the efficiency of the three Apollo reflector arrays is now diminished by a factor of 10 at all lunar phases and by an additional factor of 10 when the lunar phase is near full Moon. These deficits did not exist in the earliest years of lunar ranging, indicating that the lunar environment damages optical equipment on the timescale of decades. Dust or abrasion on the front faces of the corner-cube prisms may be responsible, reducing their reflectivity and degrading their thermal performance when exposed to face-on sunlight at full Moon. These mechanisms can be tested using laboratory simulations and must be understood before designing equipment destined for the Moon.     

Precession of the lunar core

Goldreich (Goldreich, P. [1967]. J. Geophys. Res. 72, 3135) showed that a lunar core of low viscosity would not precess with the mantle. We show that this is also the case for much of lunar history. But when the Moon was close to the Earth, the Moon’s core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (Dwyer, C.A., Stevenson, D.J. [2005]. An Early Nutation-Driven Lunar Dynamo. AGU Fall Meeting Abstracts GP42A-06) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core. So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0-29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.     

A geological interpretation of the lunar surface

This interpretation of lunar surface features is based on the differentiation of siliceous and basaltic substances similar to those of the earth. Our hypothesis is that lunar maria are composed of basaltic matter similar to that of terrestrial ocean basins, and that the lunar continents (bright regions) are composed of siliceous blocks.     

Lunar modulation on the occurrence frequency of the afternoon counter-electrojet events at Trivandrum

Distribution, over the lunar age, of the frequency of occurrence of the afternoon counter-electrojet events at Trivandrum during the period 1959–1978 is examined in each of the calendar months. A strong lunar modulation on the occurrence frequency is seen in January; this may be related to the global enhancement of the lunar tide during January. The modulation is also prominent in April, although 62% of the events in that month occur irrespective of the lunar age. The occurrence frequency at Trivandrum appears to be least influenced by the Moon in the northern summer months.     

Coordinates of the centre of the figure of lunar marginal zone

On the basis of large-scale star-calibrated lunar photographs the rectangular selenoequatorial coordinates of the centre of the figure of lunar marginal zone have been obtained with reference to its mass centre, the position of which has been computed by the ephemerides j = 2 and LURE-2. A new definition method of lunar mass centre coordinates by photographic observation in system j = 2 and LURE-2 is proposed.     

Solar-wind interactions with the moon: Nature and composition of nitrogen compounds

The lunar atmosphere and magnetic field are very tenuous. The solar wind, therefore, interacts directly with the lunar surface material and the dominant nature of interaction is essentially complete absorption of solar-wind particles by the surface material resulting in no upstream bowshock, but a cavity downstream. The solar-wind nitrogen ion species induce and undergo a complex set of reactions with the elements of lunar material and the solar-wind-derived trapped elements. The nitrogen concentration indigeneous to the lunar surface material is practically nil. Therefore any nitrogen and nitrogen compounds found in the lunar surface material are due to the solar-wind implantation of nitrogen ions. The flux of the solar-wind nitrogen ion species is about 6×10³ cm^–2 s^–1. Since there is no evidence for accumulation of nitrogen species in the lunar surface material, the outflux of nitrogen species from the lunar material to the atmosphere is the same as the solar-wind nitrogen ion flux. The species of the outflux are primarily NO and NH₃, and their respective concentrations in the near surface lunar atmosphere are found by calculation to be 327 and 295 cm^–3. The calculated concentration of NH₃ seems to be consistent with the sunrise concentration results of the mass spectrometer implanted on the lunar surface. This is not the case for the concentration of NO. According to the presently calculated concentration value of NO, the mass spectrometer should have detected NO at sunrise, but no report was made for its detection. There is also discrepancy about the concentration of N₂ which is explained in this paper. The concentrations of nitrogen species in the lunar material at the time of sample collection on the Moon remained about the same when the samples were analyzed on the Earth. However, no specific experiment was planned to detect the nitrogen species in the lunar material samples.     

Evidence for isostasy in the lunar mascon Maria

The pronounced positive gravity anomalies in the lunar circular maria imply lack of isostatic compensation of the lunar mascons. This lack of isostasy is hard to reconcile with the rheological properties of the lunar crust. Analysis of the negative ring anomalies that appear to surround the major positive gravity peaks indicates that associated with each mascon is a mass deficit of approximately the same size. In view of the lunar rheology these mass deficits most probably represent compensating mass deficits beneath the lunar mascon maria. Consequently, most lunar mascons appear to be near isostatic equilibrium, and the observed gravity anomalies may be essentially the superposition of positive gravity peaks due to the basaltic mare fill, and less pronounced, broader gravity lows due to the compensating mass deficits at depth.     

Physical and mechanical properties of the lunar soil (a review)

We review the data on the physical and mechanical properties of the lunar soil that were acquired in the direct investigations on the lunar surface carried out in the manned and automatic missions and in the laboratory examination of the lunar samples returned to the Earth. In justice to the American manned program Apollo, we show that a large volume of the data on the properties of the lunar soil was also obtained in the Soviet automatic program Lunokhod and with the automatic space stations Luna-16, -20, and -24 that returned the lunar soil samples to the Earth. We consider all of the main physical and mechanical properties of the lunar soil, such as the granulometric composition, density and porosity, cohesion and adhesion, angle of internal friction, shear strength of loose soil, deformation characteristics (the deformation modulus and Poisson ratio), compressibility, and the bearing capacity, and show the change of some properties versus the depth. In most cases, the analytical dependence of the main parameters is presented, which is required in developing reliable engineering models of the lunar soil. The main physical and mechanical properties are listed in the summarizing table, and the currently available models and simulants of the lunar soil are reviewed.     

Effects of initial velocity on the sinking of ilmenite-bearing cumulates in the early lunar mantle:Insight from the theory of Rayleigh-Taylor instability

The early lunar mantle overturn,associated with the sinking of the dense ilmenite-bearing cumulate(IBC)crystallized at the shallow lunar mantle,provides satisfactory explanations for the origination of high-Ti basalt,the abnormally strong magnetic field between~3.9 and~3.6 Ga and the low-viscosity zone in the deep lunar mantle,but still poses a debate regarding the initial state of IBC in the early lunar mantle.If the sinking of IBC initiated before the end of lunar magma ocean crystallization,the solidified IBC can acquire a greater thickness and a higher initial velocity at the IBC-mantle boundary.The variation of initial velocity can affect the strain rate of IBC and,correspondingly,the dislocation creep components at the shallow lunar mantle.In this work,we analyze the effects of initial velocity on the dynamics of early lunar mantle by using the theory of Rayleigh-Taylor instability.To couple the effects of diffusion creep and dislocation creep for all major minerals in the lunar mantle,we exploit an improved Minimized Power Geometric(IMPG)model and isostress mixing model to characterize the upper limit and lower limit for the viscosity of the lunar mantle comprising four major minerals,i.e.olivine,orthopyroxene,clinopyroxene and ilmenite.The modeling results suggest that a high initial velocity,in any case,can shorten the onset time,tending to promote the early lunar mantle overturn even in a rheologically-strong lunar mantle.The effect of initial velocity on the overturn wavelength shows a strong dependence on the rheological mixing model.For the isostress mixing model,the increase of initial velocity tends to elongate the overturn wavelength.For the IMPG mixing model,the overturn wavelength is insensitive to the variation of initial velocity.As the actual lunar mantle rheology sandwiches between the rheologies predicted by isostress mixing model and IMPG model,it can be anticipated that the increase of initial velocity tends to elongate the overturn wavelength.In consideration of the importance of the initial velocity on the dynamics of early lunar mantle,future investigations should focus on the dynamics of the solid IBC in the solidifying lunar magma ocean.     

Lunar cratering asymmetries with high lunar orbital obliquity and inclination of the Moon

Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history. Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination. Here, we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude. With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon, we then have derived general formulas of the cratering rate spatial variation based on the crater scaling law. Our formulas with addition of lunar obliquity and inclination can reproduce the lunar cratering rate asymmetry at the current Earth-Moon distance and predict the apex/ant-apex ratio and the pole/equator ratio of this lunar cratering rate to be 1.36 and 0.87, respectively. The apex/ant-apex ratio is decreasing as the obliquity and inclination increasing. Combining with the evolution of lunar obliquity and inclination, our model shows that the apex/ant-apex ratio does not monotonically decrease with Earth-Moon distance and hence the influences of obliquity and inclination are not negligible on evolution of apex/ant-apex ratio. This model is generalizable to other planets and moons, especially for different spin-orbit resonances.     

Quasi-periodic solutions of the spatial lunar three-body problem

In this paper, we consider the spatial lunar three-body problem in which one body is far away from the other two. By applying a well-adapted version of KAM theorem to Lidov–Ziglin’s global study of the quadrupolar approximation of the spatial lunar three-body problem, we establish the existence of several families of quasi-periodic orbits in the spatial lunar three-body problem.