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.     

Dynamical History of the Earth–Moon System

Differential equations describing the tidal evolution of the earth's rotation and of the lunar orbital motion are presented in a simple close form. The equations differ in form for orbits fixed to the terrestrial equator and for orbits with the nodes precessing along the ecliptic due to solar perturbations. Analytical considerations show that if the contemporary lunar orbit were equatorial the evolution would develop from an unstable geosynchronous orbit of the period about 4.42 h (in the past) to a stable geosynchronous orbit of the period about 44.8 days (in the future). It is also demonstrated that at the contemporary epoch the orbital plane of the fictitious equatorial moon would be unstable in the Liapunov's sense, being asymptotically stable at early stages of the evolution. Evolution of the currently near-ecliptical lunar orbit and of the terrestrial rotation is traced backward in time by numerical integration of the evolutional equations. It is confirmed that about 1.8 billion years ago a critical phase of the evolution took place when the equatorial inclination of the moon reached small values and the moon was in a near vicinity of the earth. Before the critical epoch t _cr two types of the evolution are possible, which at present cannot be unambiguously distinguished with the help of the purely dynamical considerations. In the scenario that seems to be the most realistic from the physical point of view, the evolution also has started from a geosynchronous equatorial lunar orbit of the period 4.19 h. At t < t _cr the lunar orbit has been fixed to the precessing terrestrial equator by strong perturbations from the earth's flattening and by tidal effects; at the critical epoch the solar perturbations begin to dominate and transfer the moon to its contemporary near-ecliptical orbit which evolves now to the stable geosynchronous state. Probably this scenario is in favour of the Darwin's hypothesis about originating the moon by its separation from the earth. Too much short time scale of the evolution in this model might be enlarged if the dissipative Q factor had somewhat larger values in the past than in the present epoch. Values of the length of day and the length of month, estimated from paleontological data, are confronted with the results of the developed model.     

Identification of Meteorites,or What on Earth is a Meteorite?

Abstract. Examples of the problems encountered in the tracing, recovery and identification of meteorites from witnessed fireballs, indicate the failure of museum collections to be truly representative of the known increment from space and of our lack of knowledge of the varieties of material coming to earth from space. The history of the development of criteria for the recognition of meteorites is traced and some of the witnessed but rejected falls of history are listed. Objection is raised to the almost total dependence upon chemistry—particularly upon the presence of nickel—in meteoritic identification. Stress is laid upon the importance of fusion crust as an identifying characteristic of meteorites.     

The Distribution and Significance of Evaporitic Weathering Products on Antarctic Meteorites

Abstract— The distribution of white evaporitic deposits differs among different meteorite compositional groups and weathering categories of Antarctic meteorites. Evaporites occur with unusual frequency on carbonaceous chondrites, and are especially common in carbonaceous chondrites of weathering categories A and B. Among achondrites, weathering categories A and A/B show the most examples of evaporite weathering. Unlike carbonaceous chondrites and achondrites, most evaporite-bearing ordinary (H and L) chondrites are from rustier meteorites of weathering categories B and, to a lesser degree, B/C and C. LL chondrites are conspicuous by their complete lack of any evaporitic weathering product. Almost two-thirds of all evaporite-bearing meteorites belong to weathering categories A, A/B, and B. Where chemical data are available, surficial evaporite deposits are associated with elemental anomalies in meteorite interiors. Meteorites of weathering classes B, A/B, and even A may have experienced significant element redistribution and/or contamination as a result of terrestrial exposure. Evaporite formation during terrestrial weathering cannot be neglected in geochemical, cosmochemical, and mineralogical studies of Antarctic meteorites. A lower-case “e” should be added to the weathering classification of evaporite-bearing Antarctic meteorites, to inform meteorite scientists of the presence of evaporite deposits and their associated compositional effects.     

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

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

Lightcurves of 1999 Leonid Impact Flashes on the Moon

Optical flashes observed on the night side of the Moon during the 1999 Leonid meteor shower have attracted the interest of astronomers. These flashes are attributed to high-velocity impacts of Leonid meteoroids on the lunar surface. Here, we report five lunar flashes detected over a 5.8-h observation period centered at 11:25 UT on Nov. 18, 1999, in Japan. The flashes are characterized by an abrupt brightening. Three flashes exhibited afterglows that remained visible for at least 50 ms, which is longer than the duration predicted for radiation from an impact-generated plasma cloud. We show that thermal radiation from hot droplets ejected from the lunar surface during high-velocity impacts could be the cause of the afterglows.     

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.     

Doubly averaged effect of the Moon and Sun on a high altitude Earth satellite orbit

Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI _ab, whereI _b=180°–I _a andI _a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A _lk coefficient defined in Equation (11) - B _lk coefficient defined in Equation (24) - C _km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H _k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J ₂ coefficient of second harmonic of Earth's gravitational potential (1082.637×10^–6 R _E ² ) - K _k, L_k, M_k expressions in Section 4 - expressions in Section 4 - p=a(1–e ²) semi-latus rectum - P _l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R _E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R _E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T _e period of long periodic oscillations ine for |I|<I _a - T _s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - ₁,₂₃ unit vectors in thex, y, z coordinate directions - _r , _s , _w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×10⁵ km s^–2) - gravitational constant times mass of Moon (or Sun) - _m gravitational constant times mass of Moon (/81.301) - _s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - _m radius of lunar ring (60.2665R _E) - _s radius of solar ring (23455R _E) - true anomaly - argument of perigee - ₀ initial value of - _i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.     

三轴椭圆星系形态与初始弥散速度分布

本文对具有初始几何形状及维里系数相同,但初始速度弥散度分布不同的三轴椭球进行了数值模拟。四个模型的最后质点分布及等密度轮廓的图象表明,三轴椭球的塌缩是与初始弥散速度的分布密切相关的。而不同的初始弥散速度分布可能与原星系在薄饼中不同的碎裂时刻有关。     

Magnetization of celestial bodies with special application to the primeval Earth and Moon

The magnetic fields of celestial bodies are usually supposed to be due to a ‘hydromagnetic dynamo’. This term refers to a number of rather speculative processes which are supposed to take place in the liquid core of a celestial body. In this paper we shall follow another approach which is more closely connected with hydromagnetic processes well-known from the laboratory, and hence basically less speculative. The paper should be regarded as part of a general program to connect cosmical phenomena with phenomena studied in the laboratory. As has been demonstrated by laboratory experiments, a poloidal magnetic field may be increased by the transfer of energy from a toroidal magnetic field through kink instability of the current system. This mechanism can be applied to the fluid core of a celestial body. Any differential rotation will produce a toroidal field from an existing poloidal field, and the kink instability will feed toroidal energy back to the poloidal field, and hence amplify it. In the Earth-Moon system the tidal braking of the Earth's mantle acts to produce a differential angular velocity between core and mantle. The braking will be transferred to the core by hydromagnetic forces which at the same time give rise to a strong magnetic field. The strength of the field will be determined by the rate of tidal braking. It is suggested that the magnetization of lunar rocks from the period ?4 to ?3 Gyears derives from the Earth's magnetic field. As the interior of the Moon immediately after accretion probably was too cool to be melted, the Moon could not produce a magnetic field by hydromagnetic effects in its core. The observed lunar magnetization could be produced by such an amplified Earth field even if the Moon never came closer than 10 or 20 Earth's radii. This hypothesis might be checked by magnetic measurements on the Earth during the same period.     

Impacts and tectonism in Earth and Moon history of the past 3800 million years

The Moon's surface, unlike the Earth's, displays a comparatively clear record of its past bombardment history for the last 3800 Myr, the time since active lunar tectonism under the massive pre-mare bombardment ended. From Baldwin's tabulation of estimated ages for a representative sample of large lunar craters younger than 3800 Ma, six major cratering episodes can be discerned. These six bombardment episodes, which must have affected the Earth too, appear to match in time the six major episodes of orogenic tectonism on Earth, despite typical resolution errors of ±100 Myr and the great uncertainties of the two chronologies. Since more highly resolved events during the Cenozoic and Mesozoic Eras suggest the same correlation, it is possible that large impacts have influenced plate tectonics and other aspects of geologic history, perhaps by triggering flood basalt eruptions.     

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

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

On the Classification of Meteorites

The classification of meteorites as a whole is briefly presented and discussed; in particular, it is pointed out that the intermediate or transitional group, now universally known as the siderolites (symbol, So), consists of 2 main subdivisions, namely the “irony stones,” hereinafter termed sideraerolites (Sa), and the “stony irons” or so-called lithosiderites (Li).     

彗木碰撞时刻及位置的确定

Shoemaker－Levy9号童星于1994年7月与木星碰撞己成为事实．本文依据众多碰撞时刻的观测报道，并结合碰撞预报，对其进行了系统研究．分析了用不同观测技术和观测手段所给出的碰撞时刻的报道，强调了碰撞物理过程的重要性．最后，按照统一的物理模式初步确定了各个碎核的碰撞时刻．并归算出木星南纬碰撞带区的自转速度约为9h55min-周，说明它没有受到营核连续撞击的影响．本文还将各管核撞击点在水面上的位置与预报做了比较．