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1.
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.  相似文献   

2.
A new method for determining the early history of the Earth-Moon system is described. Called the study of lunar paleotides, it describes a method for explaining features of the remnant lunar gravity field, and the generation of the lunar mascons. A method for the determination of Earth-Moon distances compared with the radiometric ages of the maria is developed. It is shown that the Moon underwent strong anomalous gravitational tidal forces, for a durationt<106yr, prior to the formation of the mascon surfaces. As these tidal forces had not been present at the time of the formation of the Moon, this shows that the Moon could not have been formed in orbit about the Earth.There are tides in the affairs of men which, taken at the flood, lead on to fortune... William Shakespeare 1564–1616  相似文献   

3.
Among the lunar laser range measurements obtained during the past six years at McDonald Observatory, those available cover the period August 1969-November 1974, being 1377 normal observations made on the three Apollo reflectors and that of Lunokhod II. The fit of these data led to a rms residual of 55 cm. In this study, a large number of parameters have been resolved, including the geocentric coordinates of the telescope, the selenocentric coordinates of each of the reflectors, as well as orbital elements of the Moon. In addition, the interest has been directed more specially towards the study of the rotational motion of the Moon and particularly the problem of its free librations. The performed resolutions give the evidence of the three modes of free oscillations. The determined amplitudes arise to 1.7 in longitude and 0.5 and 8.7 in latitude, with the respective periods of 2.9 years, 27.3 days and 75 years. In connection with these parameters, the fittings determined also the most of part of elements of lunar gravitational field: the moment of inertia parameters and, and a number of the third degree harmonics. These new results should now permit a research on the implications of these oscillations effects, concerning the impact history of the Moon and the properties of its internal structure. On the basis of the amplitudes determined here, one can already estimate an order of the magnitude for theQ dissipation coefficient comparable with that determined from seismic studies of the Moon.  相似文献   

4.
The equation for the two-particles cosmic-ray distribution function is derived by means of the Boltzmann kinetic equation averaging. This equation is valid for arbitrary ratio of regular and random parts of the magnetic field. For small energy particles the guiding-center approximation is used. On the basis of the derived equation the dependence between power spectra of cosmic-ray intensity and random magnetic field is obtained. If power spectra are degree functions for high energy particles ( 10 GeV nucleon–1), then the spectral exponent of magnetic field lies between and –2, where is the spectral exponent of cosmic-ray power spectra. The experimental data concerning moderate energy particles are in accordance with =, which demonstrates that the magnetic fluctuations are isotropic or cosmic-ray space gradient is small near the Earth orbit.  相似文献   

5.
The results of a simultaneous solution for the orbital elements of Moon and planets are given and their derivation is discussed. A modern Cowell integrator is used for orbit computations, and least-squares fits are made to some 40000 optical observations taken since 1913. The model includes relativistic terms, the leading zonal harmonics of Earth and Moon, the precession of the lunar equator, and the tidal couple between Earth and Moon. The tidal term in the Moon's mean longitude is found to be –19±4 per century squared. The solution also yields an extrapolation of the atomic time scale back to 1912.5. At that time, the difference between atomic and ephemeris time is about 6±2 s. Lunar declinations observed by the Washington transit circles, after receiving limb corrections and thus with respect to the center of Watts' reference sphere, are smaller than computed values by 0.33±0.01. It is found that solar oblateness cannot quite be determined with optical data covering about 50 yr, butJ 2 is unlikely to be much larger than 10–5. The advance of Mercury's perihelion is verified to within our resolution of 2 per century to match that predicted by Einstein.The solution presented here is believed to be the only simultaneous improvement of the orbits of Moon and planets. This simultaneity is found to be an essential feature in separating the Moon's mean motion, the lunar tidal deceleration, and the corrections to the Earth rotation rate. It is now possible to refer all astronomical events of the past 60 yr to a time with uniform rate, namely the atomic clock system. Considering the long baseline, this model should facilitate the prediction of fast variables, such as the lunar longitude, with considerably increased confidence. The planetary orbital elements compete with efforts of similar scope and accuracy at the Massachusetts Institute of Technology and the Jet Propulsion Laboratory.  相似文献   

6.
Based on a large body of observational data on radio emission from the Moon, we study the dependence of lunar radio temperature variations on illumination conditions. The data were obtained with the RATAN-600 radio telescope with a high sensitivity and resolution, which has not yet been used to construct radio images of the Moon. The harmonic parameters (amplitudes and phase angles) were determined both for the average Moon and for regions with temperature anomalies revealed by the RATAN-600 observations. These parameters allow the physical properties of the lunar soil to be investigated. The distribution of the loss-angle tangent (tan ), one of the characteristics of the lunar material, over the Moon was determined. The loss-angle tangent is related to the content of ilmenite, a rock containing oxygen, iron, and titanium, in the lunar soil. Studies of the ilmenite distribution on the Moon are particularly important in view of the prospects for building a habitable lunar base that needs oxygen. It is relatively easy and cheap to extract oxygen, iron, and titanium from ilmenite.  相似文献   

7.
A comparison of the lunar frontside gravity field with topography indicates that low-density ( 2.9 g cm–3) types of rock form a surface layer or crust of variable thickness: 40-60 km beneath terrae; 20-40 km beneath non-mascon maria; 0-20 km beneath mascon maria. The observed offset between lunar centers of mass and figure is consistent with farside crustal thicknesses of 40-50 km, similar to frontside terra thicknesses.The Moon is asymmetric in crustal thickness, and also in the distribution of maria and gamma radioactivity. Early bombardment of the Moon by planetesimals, in both heliocentric and geocentric orbits, is examined as a possible cause of the asymmetries. The presence of a massive companion (Earth) causes a spin-orbit coupled Moon to be bombarded non-uniformly. The most pronounced local concentration of impacts would have occurred on the west limb of the Moon, when it orbited close to the Earth, if low-eccentricity heliocentric planetesimals were still abundant in the solar system at that time.A very intense bombardment of this type could have redistributed crustal material on the Moon, thinning the west limb crust appreciably. This would have caused a change in position of the principal axes of inertia, and a reorientation of the spin-orbit coupled Moon such that the thinnest portion of its crust turned toward one of the poles. Erupting lavas would have preferentially flooded such a thin-crusted, low-lying area. This would have caused another readjustment of principal moments, and a reorientation of the Moon such that the mare areas tipped toward the equator. The north-south and nearside-farside asymmetries of mare distribution on the present Moon can be understood in terms of such a history.Paper dedicated to Prof. Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.  相似文献   

8.
Paleocratering of the Moon: Review of post-Apollo data   总被引：1，自引：0，他引：1  
As a result of the dating of lunar samples, we are in a position to utilize the lunar surface as a recorder of environmental conditions in the Earth-Moon neighborhood in the past. Plots of crater density vs rock age at different lunar landing sites can be used to date unexplored lunar provinces. These plots also demonstrate evolution in the population of planetesimals that struck the Moon. Prior to 4.1 aeons ago, the cratering rate on the Moon was at least 103 times the present rate, and the rate declined with a half-life less than 8×107 yr. During the interval from 4.1 to 3.2 aeons ago, the number of planetesimals showed an exponential decay with a half-life about 3×108 yr, corresponding to sweep-up of particles from solar orbits somewhat similar to those of Apollo asteroids. A more nearly constant cratering rate applied in the last three aeons. These data indicate that the Moon displays at least the final stages of an ancient accretion process; they also set certain conditions on possible capture processes relating to the Moon's origin. Pre-Apollo expectations that the Moon would provide a Rosetta Stone for interpreting solar system history and planet formation thus appear justified.Paper given at Philadelphia meeting of American Association for Advancement of Science, December, 1971.  相似文献   

9.
Observations of the lunar luminescence are reported for a dozen of specific Moon features using the line-depth method with a high resolution spectroscopic technique. The data indicate a variation of the Moon proper emission as a function of the phase angle which is interpreted as a proof of the thermoluminescent origin of this emission.  相似文献   

10.
Johann Heinrich Lambert, a Swiss-German scholar, was counted among the most famous men of his time. Being an autodidact and without formal university studies, he won access to the modern sciences, in particular to philosophy, mathematics, astronomy and physics; and indeed he was most successful in all these fields. In the area of mathematics, for example, he made contributions to the theory of irrational numbers (continued fractions), to the problem of parallel lines and non-Euclidian geometry, to trigonometry (group-theoretical formulation of Nepper's rule), the foundations of the perspective, he gave a proof for the irrationality of e and and moreover some remarkable indications for their transcendency, to mention only a few. In the field of astronomy, he made contributions not only to the foundations of photometry but also to the orbital determination of planets and comets, which culminated in Lambert's Theorem. This, as well as his Cosmologische Briefe (with which he made a contribution to the structure of the world parallel to the Kantian view) is the subject matter of the following report. Even in philosophy Lambert kept pace with Kant (Criterium veritatis, 1761 when he said: Wir wissen, dass Gestalt und Grösse vom Orte umabhängige Bestimmungen sind.).
Zusammenfassung Johann Heinrich Lambert, ein deutsch-schweizer Wissenschaftler, gehörte zu den berühmtesten Männern seiner Zeit. Er hat als Autodidakt ohne Studium an einer Hochschule sich den Zugang zu den modernen Wissenschaften, insbesondere zue Philosophie, zur Mathematik, zu Astronomie und Physik geschaffen und auf diesen Gebieten Fortschrittliches geleistet. Auf dem Gebiete der Mathematik z.B. waren es seine Beiträge zur Theorie der Irrationalzahlen (Kettenbrüche), zum Problem der Parallellinien und der nichteuklidischen Geometrie, zur Trigonometrie (gruppentheoretischer Ansatz für die Neppersche Regel), die Begründung der Perspektive, Beweis der Irrationalität von e und mit Ansätzen zum Nachweis ihrer Transzendenz, um nur einiges herauszuheben. Auf dem Gebiete der Astronomie waren es neben seinen Grundlagen für die Photometrie seine Beiträge zur Bahnbestimmung von Planeten und Kometen, die er mit dem nach ihm benannten Lambertschen Theorem krönte. Darüber und über seine Cosmologischen Briefe, mit denen er einen Beitrag zur Struktur der welt parallel zu der von Kant gegeben hat, wird im folgenden ausführlich gehandelt. Auch in der Philosophie war er im Gleichschritt mit Kant (Criterium veritatis 1761 mit dem Ausspruch: Wir wissen, daß Gestalt und Größe vom Orte unabhängige Bestimmungen sind.).

Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.  相似文献   

11.
New satellite measurements of the lunar-surface radiation temperature are used to construct the spatial angular function of thermal radiation of the Moon in the infrared (10.5–12.5 m) spectral range. The basic material for investigations is the scanned cosmic spectrozonal images of the lunar surface transmitted by the first Russian geostationary artificial meteorological satellite GOMS. The formulas for calculating the angular parameters are given, and the photometric function of thermal radiation of the Moon is plotted as a function of the incidence angle, the reflection angle, and the azimuthal angle between the planes of the incident and reflected rays.  相似文献   

12.
Lunar physical librations and laser ranging   总被引：1，自引：0，他引：1  
The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured, in addition to and, by laser ranging to the Moon. Combining the laser ranging determinations of = 630.6 ± 0.5 × 10–6 and = 226.4 ± 3.0 × 10–6 with lunar orbiter measurements ofC 20 andC 22 givesC/MR 2=0.395 -0.010 +0.006 . Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.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.  相似文献   

13.
On the Dynamics of Weak Stability Boundary Lunar Transfers   总被引：1，自引：1，他引：0  
Recent studies demonstrate that lunar and solar gravitational assists can offer a good reduction of total variation of velocity Vneeded in lunar transfer trajectories. In particular the spacecraft, crossing regions of unstable equilibrium in the Earth—Moon—Sun system, can be guided by the Sun towards the lunar orbit with the energy needed to be captured ballistically by the Moon. The dynamics of these transfers, called weak stability boundary (WSB) transfers, will be studied here in some detail. The crucial Earth—Moon—Sun configurations allowing such transfers will be defined. The Sun's gravitational effect and lunar gravitational capture will be analyzed in terms of variations of the Jacobi constants in the Earth—Sun and Earth—Moon systems. Many examples will be presented, supporting the understanding of the dynamical mechanism of WSB transfers and analytical formulas will be obtained in the case of quasi ballistic captures.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

14.
The acceleration of the mean lunar longitude has a small effect on the periods of most terms in a Fourier expansion of the longitude. There are several planetary perturbation terms that have small amplitudes, but whose periods are close to the resonant period of the lunar libration in longitude. Some of these terms are moving toward resonance, some are moving away from resonance, and the periods of those terms that do not include the Delaunay variables in their arguments are not moving. Because of its acceleration of longitude, the Moon is receding from the Earth, so the magnitude of the restoring torque that the Earth exerts on the rotating Moon is gradually attenuating; thus resonance itself is moving, but at a much slower rate than the periods of the accelerating planetary perturbations. There are five planetary perturbation terms from the ELP-2000 Ephemeris (with amplitudes of 0.00001 or greater) that have passed through resonance in the past two million years. One of them is of special interest because it appears to be the excitation source of a supposed free libration in longitude that has been detected by the lunar laser ranging experiment. The amplitude of the term is only 0.00021 but it could be the source of the 1 amplitude free libration term if the viscoelastic properties of the Moon are similar to those of the Earth.  相似文献   

15.
It is known that the observed secular accelerations of the Sun and Moon are not consistent with the tidal interactions of the Earth with the Sun and Moon. Following Dicke, the hypothesis of variable constant of gravity is adopted and expressions for the accelerations are derived. It is shown that if the theoretical ratio of the acceleration is equated the observed one, a unique value for —/G can be calculated. Adopting the accelerations obtained by Fotheringham, Newton, Muller and Stephenson, and Stephenson, it is found that — /G ranges from 1.4 × 10–11 to 3.3 × 10–11 yr–1. This estimate is consistent with the one based upon the comparison of the lunar accelerations measured with respect to atomic and ephemis times.  相似文献   

16.
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.  相似文献   

17.
The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.  相似文献   

18.
Seismic refraction data, obtained at the Apollo 14 and 16 sites, when combined with other lunar seismic data, allow a compressional wave velocity profile of the lunar near-surface and crust to be derived. The regolith, although variable in thickness over the lunar surface, possesses surprisingly similar seismic properties. Underlying the regolith at both the Apollo 14 Fra Mauro site and the Apollo 16 Descartes site is low-velocity brecciated material or impact derived debris. Key features of the lunar seismic velocity profile are: (i) velocity increases from 100–300 m s–1 in the upper 100 m to 4 km s–1 at 5 km depth, (ii) a more gradual increase from 4 km s–1 to 6 km s–1 at 25 km depth, (iii) a discontinuity at a depth of 25 km and (iv) a constant value of 7 km s–1 at depths from 25 km to about 60 km. The exact details of the velocity variation in the upper 5 to 10 km of the Moon cannot yet be resolved but self-compression of rock powders cannot duplicate the observed magnitude of the velocity change and the steep velocity-depth gradient. Other textural or compositional changes must be important in the upper 5 km of the Moon. The only serious candidates for the lower lunar crust are anorthositic or gabbroic rocks.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.  相似文献   

19.
The currently known astronomical, chemical and magnetic data are not uniquely indicative of an extensively and globally molten Moon. We argue here for an accretional layering in the Moon, but at temperatures below solidus. The excess mass in the near side of the Moon compatible with a 2 km displacement in the center of mass relative to the centre of figure and the moment of inertia data is considered to be due to Fe-FeS liquid formation and inhomogeneous segregation. These Fe-FeS bodies, termed fescons, are shown to be capable of accounting for the presently available magnetization data, by acting as small regenerative dynamos with a time-stability less than that of the terrestrial equivalent. The chemical characteristics of the highly differentiated materials (KREEP, granite etc.) are considered to be due to small scale localized melting caused by collisional events, from sources in which accessory phases play a significant role. Mare basalts are considered to be melts in the overlying material produced at a later time by40K radioactivity in the fescons. Some consequences of the present hypothesis are suggested.We conclude that these and other characteristics of the lunar materials are reconcilable with a cold Moon such as discussed by Urey over the past two decades.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.  相似文献   

20.
Y. C. Whang 《Solar physics》1970,14(2):489-502
This paper presents a continued study of the two-dimensional guiding-center model of the solar wind interaction with the Moon. The characteristics theory and the computational method are discussed. The magnetic permeability of plasma is (1 + /2)–1 in the solar wind flow upstream of the Moon, and it changes to 1 in the void region of the lunar wake. The gradual change of the magnetic permeability in the penumbral region from the interplanetary condition to the void condition is explained as the source of field perturbations in the lunar wake. Perturbations of the magnetic field propagate as magnetoacoustic waves in a frame of reference moving with the plasma flow. Computer solutions were obtained to show that (i) the two principal perturbations of the magnetic field in the lunar wake (the umbral increase and the penumbral decrease) are confined to a region bounded by a Mach cone tangent to the lunar body, and (ii) the penumbral increases occur outside the lunar Mach cone. Computer solutions are also used to identify the source of field perturbations and to simulate the solar wind-moon interaction under varying interplanetary conditions.  相似文献   

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