The precise positioning of lunar farside lander using a four-way lander-orbiter relay tracking mode

China is planning to land a spacecraft on the farside of the Moon, a premiere, by 2018. In essence, the traditional tracking modes, based on direct visibility, cannot operate for the lunar farside lander tracking, and therefore a relay satellite, visible at the same time by both the lander and the Earth, will be required, operating in the so-called four-way mode (Earth-relay satellite-lander-relay satellite-Earth). In this paper, we firstly give the mathematical formulation of the four-way relay tracking mode and of its partial derivatives with respect to the relevant parameters, implemented in our POD software WUDOGS (Wuhan University Deep-space Orbit determination and Gravity recovery System). In a second step, in simulation mode, we apply this relay mode to determining lander coordinates, which are absolutely needed for a sample return mission, or to add constraints on rotation models of the Moon. The results show that with Doppler measurements at a 0.1 mm/s error level, the positioning of the farside lander could be done at centimeters level (1-\(\delta\)) in the case of a circumlunar relay satellite; and at a 5 meters level (1-\(\delta\)) in the case of a Lagrange point (L2) Halo relay satellite.     

Crustal properties of Mercury by morphometric analysis of multi‐ring basins on the Moon and Mars

Abstract— We use satellite altitude free‐air and terrain gravity correlations to differentiate regional variations in crustal viscosity and transient cavity diameters of impact basins on the Moon and Mars that we combine with surface roughness for a rheological assessment of the crust of Mercury. For the Moon and Mars, we separate the free‐air anomalies into terrain‐correlated and terrain‐decorrelated components using the spectral properties of the free‐air and computed terrain gravity effects. Adjusting the terrain effects for the terrain‐correlated anomalies yields compensated terrain effects that we evaluate for crustal thickness variations of the impact basins. We interpret the terrain‐correlated anomalies for uncompensated elements of the crustal thickness variations that we find are strongly correlated with the distribution of basin rings from photogeologic analyses. Hence, we estimate the transient cavity diameter from the innermost diameter of the gravity‐inferred rings. Comparing these diameters with the related crustal thickness estimates clearly differentiates regional variations in the crustal rheologies. For the Moon, the analysis points to a farside crust that was significantly more rigid than the nearside crust during bombardment time. For Mars, the growth in transient cavity diameters with apparent crustal age also reflects increased viscosity due to crustal cooling. These results are also consistent with local estimates of surface roughness developed from the root‐mean‐squared topography over 64 times 64° patches centered on the basins. Hence for Mercury where gravity observations are lacking, rheological inferences on its crust may result from comparing photometric estimates of transient cavity diameter and local surface roughness with the lunar and martian estimates. These results for the Beethoven Basin, a typical multi‐ring impact feature of Mercury, suggest that the viscosity of the mercurian crust was relatively great during bombardment time. This enhanced rigidity, despite crustal temperatures that were probably much hotter than those of the Moon and Mars, may reflect an extremely dry crust for Mercury in its early development.     

The lunar‐wide effects of basin ejecta distribution on the early megaregolith

Abstract— The lunar surface is marked by at least 43 large and ancient impact basins, each of which ejected a large amount of material that modified the areas surrounding each basin. We present an analysis of the effects of basin formation on the entire lunar surface using a previously defined basin ejecta model. Our modeling includes several simplifying assumptions in order to quantify two aspects of basin formation across the entire lunar surface: 1) the cumulative amount of material distributed across the surface, and 2) the depth to which that basin material created a well‐mixed megaregolith. We find that the asymmetric distribution of large basins across the Moon creates a considerable nearside‐farside dichotomy in both the cumulative amount of basin ejecta and the depth of the megaregolith. Basins significantly modified a large portion of the nearside while the farside experienced relatively small degrees of basin modification following the formation of the large South Pole‐Aitken basin. The regions of the Moon with differing degrees of modification by basins correspond to regions thought to contain geochemical signatures remnant of early lunar crustal processes, indicating that the degree of basin modification of the surface directly influenced the distribution of the geochemical terranes observed today. Additionally, the modification of the lunar surface by basins suggests that the provenance of lunar highland samples currently in research collections is not representative of the entire lunar crust. Identifying locations on the lunar surface with unique modification histories will aid in selecting locations for future sample collection.     

Bombardment as a cause of the lunar asymmetry

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.     

Specifics of the orbital evolution of the CORONAS-F satellite at the final stage of its flight

We report the results of our analysis of the variations in the orbit of the CORONAS-F satellite (August 31, 2001–December 6, 2005) during the low-orbit flight stage. We show that extreme solar events and the accompanying phenomena in the near-Earth space and in Earth’s upper atmosphere during the 2004–2005 period (the declining phase of 23rd solar-activity cycle) significantly affected the duration of the “low-orbit” flight stage of the CORONAS-F satellite.     

On the deviation of the lunar center of mass to the East. Two possible mechanisms based on evolution of the orbit and rounding off the shape of the Moon

From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed.     

The origin of selected lunar geochemical anomalies: Implications for early volcanism and the formation of light plains

The Apollo orbital geochemistry, photogeologic, and other remote sensing data sets were used to identify and characterize geochemical anomalies on the eastern limb and farside of the Moon and to investigate the processes responsible for their formation. The anomalies are located in the following regions: (1) Balmer basin, (2) terrain northeast of Mare Smythii, (3) near Langemak crater, (4) Pasteur crater, (5) terrain northwest of Milne basin, (6) northeast of Mendeleev basin, (7) north and northeast of Korolev basin, (8) terrain north of Taruntius crater, and (9) terrain north of Orientale basin. The anomalies are commonly associated with Imbrian- or Nectarian-aged light plains units which exhibit dark-haloed impact craters. The results of recent spectral reflectance studies of dark-haloed impact craters plus consideration of the surface chemistry of the anomalies strongly indicate that those geochemical anomalies associated with light plains deposits which display dark-haloed impact craters result from the presence of basaltic units that are either covered by varying thickness of highland debris or have a surface contaminated with significant amounts of highlands material. The burial or contamination of ancient volcanic surfaces by varying amounts of highland material appears to have been an important (though not the dominant) process in the formation of lunar light plains. Basaltic volcanism on the eastern limb and farside of the Moon was more extensive in both space and time than has been accepted.     

Lunar Dust: Properties and Investigation Techniques

Physical conditions in the near-surface layer of the Moon are overviewed. This medium is formed in the course of the permanent micrometeoroid bombardment of the lunar regolith and due to the exposure of the regolith to solar radiation and high-energy charged particles of solar and galactic origin. During a considerable part of a lunar day (more than 20%), the Moon is passing through the Earth’s magnetosphere, where the conditions strongly differ from those in the interplanetary space. The external effects on the lunar regolith form the plasma-dusty medium above the lunar surface, the so-called lunar exosphere, whose characteristic altitude may reach several tens of kilometers. Observations of the near-surface dusty exosphere were carried out with the TV cameras onboard the landers Surveyor 5, 6, and 7 (1967–1968) and with the astrophotometer of Lunokhod-2 (1973). Their results showed that the near-surface layer glows above the sunlit surface of the Moon. This was interpreted as the scattering of solar light by dust particles. Direct detection of particles on the lunar surface was made by the Lunar Ejects and Meteorite (LEAM) instrument deployed by the Apollo 17 astronauts. Recently, the investigations of dust particles were performed by the Lunar Atmosphere and Dust Environment Explorer (LADEE) instrument at an altitude of several tens of kilometers. These observations urged forward the development of theoretical models for the lunar exosphere formation, and these models are being continuously improved. However, to date, many issues related to the dynamics of dust and the near-surface electric fields remain unresolved. Further investigations of the lunar exosphere are planned to be performed onboard the Russian landers Luna-Glob and Luna-Resurs.     

Near-Earth object velocity distributions and consequences for the Chicxulub impactor

An Öpik-based geometric algorithm is used to compute impact probabilities and velocity distributions for various near-Earth object (NEO) populations. The resulting crater size distributions for the Earth and Moon are calculated by combining these distributions with assumed NEO size distributions and a selection of crater scaling laws. This crater probability distribution indicates that the largest craters on both the Earth and the Moon are dominated by comets. However, from a calculation of the fractional probabilities of iridium deposition, and the velocity distributions at impact of each NEO population, the only realistic possibilities for the Chicxulub impactor are a short-period comet (possibly inactive) or a near-Earth asteroid. For these classes of object, sufficiently large impacts have mean intervals of 100 and 300 Myr respectively, slightly favouring the cometary hypothesis.     

The Leonard Award Address Presented 1998 July 27, Dublin,Ireland: On the difficulties of making Earth-like planets

Abstract— Here I discuss the series of events that led to the formation and evolution of our planet to examine why the Earth is unique in the solar system. A multitude of factors are involved: These begin with the initial size and angular momentum of the fragment that separated from a molecular cloud; such random factors are crucial in determining whether a planetary system or a double star develops from the resulting nebula. Another requirement is that there must be an adequate concentration of heavy elements to provide the 2% “rock” and “ice” components of the original nebula. An essential step in forming rocky planets in the inner nebula is the loss of gas and depletion of volatile elements, due to early solar activity that is linked to the mass of the central star. The lifetime of the gaseous nebula controls the formation of gas giants. In our system, fine timing was needed to form the gas giant, Jupiter, before the gas in the nebula was depleted. Although Uranus and Neptune eventually formed cores large enough to capture gas, they missed out and ended as ice giants. The early formation of Jupiter is responsible for the existence of the asteroid belt (and our supply of meteorites) and the small size of Mars, whereas the gas giant now acts as a gravitational shield for the terrestrial planets. The Earth and the other inner planets accreted long after the giant planets, from volatile-depleted planetesimals that were probably already differentiated into metallic cores and silicate mantles in a gas-free, inner nebula. The accumulation of the Earth from such planetesimals was essentially a stochastic process, accounting for the differences among the four rocky inner planets—including the startling contrast between those two apparent twins, Earth and Venus. Impact history and accretion of a few more or less planetesimals were apparently crucial. The origin of the Moon by a single massive impact with a body larger than Mars accounts for the obliquity (and its stability) and spin of the Earth, in addition to explaining the angular momentum, orbital characteristics, and unique composition of the Moon. Plate tectonics (unique among the terrestrial planets) led to the development of the continental crust on the Earth, an essential platform for the evolution of Homo sapiens. Random major impacts have punctuated the geological record, accentuating the directionless course of evolution. Thus a massive asteroidal impact terminated the Cretaceous Period, resulted in the extinction of at least 70% of species living at that time, and led to the rise of mammals. This sequence of events that resulted in the formation and evolution of our planet were thus unique within our system. The individual nature of the eight planets is repeated among the 60-odd satellites—no two appear identical. This survey of our solar system raises the question whether the random sequence of events that led to the formation of the Earth are likely to be repeated in detail elsewhere. Preliminary evidence from the “new planets” is not reassuring. The discovery of other planetary systems has removed the previous belief that they would consist of a central star surrounded by an inner zone of rocky planets and an outer zone of giant planets beyond a few astronomical units (AU). Jupiter-sized bodies in close orbits around other stars probably formed in a similar manner to our giant planets at several astronomical units from their parent star and, subsequently, migrated inwards becoming stranded in close but stable orbits as “hot Jupiters”, when the nebula gas was depleted. Such events would prevent the formation of terrestrial-type planets in such systems.     

Are Phobos and Deimos the result of a giant impact?

Despite many efforts an adequate theory describing the origin of Phobos and Deimos has not been realized. In recent years a number of separate observations suggest the possibility that the martian satellites may have been the result of giant impact. Similar to the Earth–Moon system, Mars has too much angular momentum. A planetesimal with 0.02 Mars masses must have collided with that planet early in its history in order for Mars to spin at its current rate (Dones, L., Tremaine, S. [1993]. Science 259, 350–354). Although subject to considerable error, current crater-scaling laws and an analysis of the largest known impact basins on the martian surface suggest that this planetesimal could have formed either the proposed 10,600 by 8500-km-diameter Borealis basin, the 4970-km-diameter Elysium basin, the 4500-km-diameter Daedalia basin or, alternatively, some other basin that is no longer identifiable. It is also probable that this object impacted Mars at a velocity great enough to vaporize rock (>7 km/s), which is necessary to place large amounts of material into orbit. If material vaporized from the collision with the Mars-spinning planetesimal were placed into orbit, an accretion disk would have resulted. It is possible that as material condensed and dissipated beyond the Roche limit forming small, low-mass satellites due to gravity instabilities within the disk. Once the accretion disk dissipated, tidal forces and libration would have pulled these satellites back down toward the martian surface. In this scenario, Phobos and Deimos would have been among the first two satellites to form, and Deimos the only satellite formed—and preserved—beyond synchronous rotation. The low mass of Phobos and Deimos is explained by the possibility that they are composed of loosely aggregated material from the accretion disk, which also implies that they do not contain any volatile elements. Their orbital eccentricity and inclination, which are the most difficult parameters to explain easily with the various capture scenarios, are the natural result of accretion from a circum-planetary disk.     

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.     

Design optimization and background modeling of the HEX experiment on Chandrayaan-I

Spacecraft and their subsystem components are subject to a very hazardous radiation environment in both near-Earth and deep space orbits. Knowledge of the effects of this high energy particle and electromagnetic radiation is essential in designing sensors, electronic circuits and living habitats for humans in near Earth orbit, en route to and on the Moon and Mars. This paper discusses the use of Monte Carlo simulations to optimize system design, radiation source modeling, and determination of background in sensors due to galactic cosmic rays and radiation from the Moon. The results demonstrate the use of Monte Carlo particle transport toolkits to predict secondary production, determine dose rates in space and design required shielding geometry.     

On the chronology of lunar origin and evolution

An origin of the Moon by a Giant Impact is presently the most widely accepted theory of lunar origin. It is consistent with the major lunar observations: its exceptionally large size relative to the host planet, the high angular momentum of the Earth–Moon system, the extreme depletion of volatile elements, and the delayed accretion, quickly followed by the formation of a global crust and mantle.According to this theory, an impact on Earth of a Mars-sized body set the initial conditions for the formation and evolution of the Moon. The impact produced a protolunar cloud. Fast accretion of the Moon from the dense cloud ensured an effective transformation of gravitational energy into heat and widespread melting. A “Magma Ocean” of global dimensions formed, and upon cooling, an anorthositic crust and a mafic mantle were created by gravitational separation.Several 100 million years after lunar accretion, long-lived isotopes of K, U and Th had produced enough additional heat for inducing partial melting in the mantle; lava extruded into large basins and solidified as titanium-rich mare basalt. This delayed era of extrusive rock formation began about 3.9 Ga ago and may have lasted nearly 3 Ga.A relative crater count timescale was established and calibrated by radiometric dating (i.e., dating by use of radioactive decay) of rocks returned from six Apollo landing regions and three Luna landing spots. Fairly well calibrated are the periods ≈4 Ga to ≈3 Ga BP (before present) and ≈0.8 Ga BP to the present. Crater counting and orbital chemistry (derived from remote sensing in spectral domains ranging from γ- and x-rays to the infrared) have identified mare basalt surfaces in the Oceanus Procellarum that appear to be nearly as young as 1 Ga. Samples returned from this area are needed for narrowing the gap of 2 Ga in the calibrated timescale. The lunar timescale is not only used for reconstructing lunar evolution, but it serves also as a standard for chronologies of the terrestrial planets, including Mars and possibly early Earth.The Moon holds a historic record of Galactic cosmic-ray intensity, solar wind composition and fluxes and composition of solids of any size in the region of the terrestrial planets. Some of this record has been deciphered. Secular mixing of the Sun was constrained by determining ³He/⁴He of solar wind helium stored in lunar fines and ancient breccias. For checking the presumed constancy of the impact rate over the past ≈3.1 Ga, samples of the youngest mare basalts would be needed for determining their radiometric ages.Radiometric dating and stratigraphy has revealed that many of the large basins on the near side of the Moon were created by impacts about 4.1 to 3.8 Ga ago. The apparent clustering of ages called “Late Heavy Bombardment (LHB)” is thought to result from migration of planets several 100 million years after their accretion.The bombardment, unexpectedly late in solar system history, must have had a devastating effect on the atmosphere, hydrosphere and habitability on Earth during and following this epoch, but direct traces of this bombardment have been eradicated on our planet by plate tectonics. Indirect evidence about the course of bombardment during this epoch on Earth must therefore come from the lunar record, especially from additional data on the terminal phase of the LHB. For this purpose, documented samples are required for measuring precise radiometric ages of the Orientale Basin and the Nectaris and/or Fecunditatis Basins in order to compare these ages with the time of the earliest traces of life on Earth.A crater count chronology is presently being built up for planet Mars and its surface features. The chronology is based on the established lunar chronology whereby differences between the impact rates for Moon and Mars are derived from local fluxes and impact energies of projectiles. Direct calibration of the Martian chronology will have to come from radiometric ages and cosmic-ray exposure ages measured in samples returned from the planet.     

Exosphere generation of the Moon investigated through a high-energy neutral detector

Observation of the lunar exosphere is a tool for remote sensing of the surface properties. The sources of this exosphere are related to the interactions of the lunar surface with the solar radiation, with the solar wind or Earth??s magnetospheric plasma, and with the interplanetary dust and meteorites. In fact, the exospheric particles are continuously created and subsequently lost in the interplanetary space, photo-ionized or re-adsorbed by the surface. Eventually, the estimation of the surface composition is not possible without the knowledge of the active release mechanisms. The relative weight of the different release processes of the various atoms, ions and molecules from the surface is still an open debate. Investigation of the Moon??s release processes and interaction with the near-Earth environment is of crucial importance for both determining the relative process release contribution and understanding the surface evolution of other airless bodies, like Mercury and the giant planets?? moons. In this work, an attempt to analyze the processes that take place on the surface of these small airless bodies, as a result of their exposure to the space environment, has been realized by means of the MonteCarlo Environment Simulation Tool (EST), applied to the Moon. The model results show that the different release processes can be identified by analysing the exospheric energy distribution. Finally, the instrument concept of the ??Analizzatore Lunare di ENA?? (ALENA), part of the MAGIA payload and specifically designed for detecting the high-energy particles released from the lunar surface is presented.     

Disharmony of the spheres: Recent trends in planetary surface nomenclature

Inadvisable departures from tradition in naming newly mapped features on Mars, Mercury, and the Moon have been implemented and proposed since 1970. Functional need for place names also has become confused with cartographic convenience. Much of the resulting new nomenclature is neither unique, efficient, nor imaginative. The longstanding classical orientation in Solar System geography needs to be firmly reasserted. The Mädler scheme for designating smaller craters on the Moon should be retained and extended to the farside. Names of surface features on other bodies might best reflect the traditional connotations of planet and satellite names: for example, most crates on Mars would be named for mythical heroes and military personalities in ancient history, craters on Mercury might commemorate explorers or commercial luminaries, and features on Venus would bear the names of famous women.     

On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

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.     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.     

Numerical Simulation of the Orbital Evolution of Near-Earth Asteroids Close to Mean Motion Resonances

The dynamics of near-Earth asteroids near mean motion resonances with the Earth or other planets is considered. The probability domains of the motion of some near-Earth asteroids close to low-order resonances are presented. The investigations have been carried out by means of a numerical integration of differential equations, taking into account the perturbations from the major planets and the Moon. For each investigated object an ensemble of 100 test particles with orbital elements nearby those of the nominal orbit has been constructed and its evolution has been retraced over the time interval (–3000, +3000 years). The initial set of orbits has been generated on the basis of probable variations of the initial orbital elements obtained from the least square analysis of observations.This revised version was published online in October 2005 with corrections to the Cover Date.