Consequences of a geosynchronous phase for the moon

Fission from the Earth's mantle explains why the density of the Moon is similar to that of the Earth's mantle.If following the fission origin of the Moon, the Earth-Moon distance increases progressively, the Moon can recollect chemicals evaporated by the Earth but not volatile enough to be lost as gases.In this way, the surface of the Moon can be enriched in refractory elements as most of the authors have proposed.At 3 Earth radii the long geosynchronous phase allows the formation of a solid crust which will record the Earth's magnetic field and the equilibrium hydrostatic from at that distance.When geosynchronism is broken the Moon will recede; its shape will no longer fit the hydrostatic form. The crust will either break or will exercise pressure on the lower layers. Meteor craters will allow lava to come to the surface. Such flows will be very large where the shape of the crust does not fit at all the geosynchronous form. Large lava flows will appear this way on the near side where the shape has changed the most. The new lava flows no longer record the magnetic field of the Earth because with the end of the synchronous position the field is alternative for the Moon; only the remanent field can influence the new lava.Three out of five samples dated at 3.6 b.y. suggest nevertheless that the field decreased slowly without becoming alternative. This means that the geosynchronous phase may have lasted longer and put the Moon on a more distant orbit, as Alfvén and Arrhenius suggested.The interpretation of lunar magnetism as influenced by the Earth cannot discard any interpretation or suggestion of its own lunar magnetic process. It is quite possible that both mechanisms have worked as some samples show.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 Accademic Nazionale del Lincei in Rome, Italy.     

Fission and geosynchronous release of the Moon

The problem of the origin of the Moon has led to various hypotheses: simultaneous accretion, fission, capture, etc. These theories were based primarily on global mechanical considerations. New geological data (Turcotteet al., 1974; Kahn and Pompea, 1978) have led to fresh approaches and new versions of these theories.As suggested by Wise (1969) and O'Keefe (1972), the initial Earth may have taken unstable forms when radial segregation sped up the rotation. The Moon may have been created as the small part of the pyroid of Poincaré.Fission theory was mainly discarded, in the past, on the basis of energy considerations. We are now arriving at the conclusion that these considerations are void if the fission was followed by a very long period of geostationary rotation of the Moon at a distance of about 3 Earth radius (i.e., out of the Roche limit). Indeed the large amount of energy of the initial system could have been released slowly and therefore evacuated by losses of material and radiation.The accretion of the Earth and the radial segregation of heavy chemicals toward the center has led to a differential rotation of the different layers with a faster rotation at the center. During the geostationary period the Moon was synchronous with respect to the surface layer. That Earth-Moon system has both a correct angular momentum and a large stability provided that the viscosity of intermediate layers was small enough, which is in concordance with its high temperature.Even with a very hot system, a superficial cold layer appears because of its low conductivity and the radiation equilibrium with outer space. This implies a slow loss of energy: the geosynchronous Moon receded extremely slowly.During the geostationary period lithophile elements were extracted with water by the radial segregation and were deposited in the area facing the Moon. One massive continent was formed, as suggested by Grjebine (1978).As the continent became thicker and sank into the mantle, convection currents appeared and speeded up the cooling of the Earth. The viscosity increased and the synchronization between the Moon and the surface of the Earth became more difficult to maintain. When synchronism was broken important lunar tides transferred energy and momentum from the Earth to the Moon which receded toward its present position and the modification of its equilibrium shape explains the formation of lunar maria in the near side.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.     

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.     

Co-accretion of the Earth-Moon system after the giant impact: reduction of the total angular momentum by lunar impact ejecta

Though the Moon is considered to have been formed by the so-called giant impact, the mass of the Earth immediately after the impact is still controversial. If the Moon was formed during the Earth's accretion, a subsequent accretion of residual heliocentric planetesimals onto the protoearth and the protomoon must have occurred. In this co-accretion stage, a significant amount of lunar-impact-ejecta would be ejected to circumterrestrial orbits, since the mean impact velocity of the planetesimals with the protomoon is much larger than the escape velocity of the protomoon. Orbital calculations of test particles ejected from the protomoon, whose semimajor axis is smaller than that of the present Moon, reveal that most of the particles escaping from the protomoon also escape from the Hill sphere of the protoearth and reduce the planetocentric angular momentum of the primordial Earth-Moon system. Using the results of the ejecta simulations, we investigate the evolution of the mass ratio and the total angular momentum (Earth's spin angular momentum + Moon's orbital angular momentum) of the Earth-Moon system during the co-accretion. We find that the mass of the protomoon is almost constant or rather decreases and the total angular momentum decreases significantly, if the random velocity of planetesimals is as large as the escape velocity of the protoearth. On the other hand, if the random velocity is the half of the escape velocity of the protoearth, the mass ratio is kept to be almost as large as the present value and the decrease of the total angular momentum is not so significant. Comparing with the results of giant impact simulations, we find that the mass of the protoearth immediately after the Moon-forming impact was 0.7-0.8 times the present value if the impactor-to-target mass ratio was 3:7, whereas the giant impact occurred almost in the end of the Earth's accretion if the impactor-to-target mass ratio was 1:9.     

Indigenous abundances of siderophile elements in the lunar highlands: Implications for the origin of the moon

Substantial indigenous abundances of siderophile elements have been found to be present in the lunar highlands. The abundances of 13 siderophile elements in the parental magma of the highlands crust were estimated by using a simple model whereby the Apollo 16 highlands were regarded as being a mixture of three components (i.e. cumulus plagioclase + intercumulus magma that was parentel to the highlands crust + meteoritic contamination by ordinary chondrites). The parental magma of the highlands was found to possess abundances of siderophile elements that were generally similar to the abundances of the unequivocally indigenous siderophile elements in primitive, low-Ti mare basalts. This striking similarity implies that these estimated abundances in the parental highlands magma are truly indigenous, and also supports the basic validity of our simple model.It is shown that metal/silicate fractionation within the Moon cannot have been the cause of the siderophile element abundances in the parental highlands magma and primitive, low-Ti mare basalts. The relative abundances of the indigenous siderophile elements in highland and mare samples seem, instead, to be the result of complex processes which operatedprior to the Moon's accretion.The abundances of the relatively involatile, siderophile elements in the parental highlands magma are strikingly similar to the abundances observed in terrestrial oceanic tholeiites. Furthermore, the abundances of the relatively volatile, siderophile elements in the parental highlands magma are also systematically related to the corresponding abundances in terrestrial oceanic tholeiites. In fact, the parental magma of the lunar highlands can be essentially regarded as having been a volatile-depleted, terrestrial oceanic tholeiite.The complex, siderophile element fractionations in the Earth's upper mantle are thought to be the result of core segregation. However, it is well-known that the siderophile element abundances do not correspond to expectations based solely upon equilibration of metal/silicate at low-pressures, as evidenced by the over-abundances of Au, Re, Ni, Co and Cu. Ringwood (1977a) has suggested that the siderophile element abundances in the Earth's upper mantle are the product of equilibration at very high-pressures between the mantle and a segregating core that contained substantial quantities of an element with a low atomic weight, such as oxygen. Comparable processes cannot have operated within the Moon due to its small internal pressures and the very small size of its possible core. Therefore, the fact that the Moon exhibits a systematic resemblance to the Earth's upper mantle is highly significant.The origin of the Moon is discussed in the context of these results. The possibility that depletion of siderophile elements occurred in an earlier generation of differentiated planetesimals similar to those which formed the basaltic achondrites, stony-irons, and irons is examined but can be dismissed on several grounds. It seems that the uniquely terrestrial siderophile signature within the Moon can be explained only if the Moon was derived from the Earth's mantle subsequent to core-formation.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

The evolution of the lunar orbit revisited. I

After recalling the contribution of Halley, J. Kepler, and G. Darwin to our understanding of the secular acceleration of the Moon, we establish a set of differential equations for the variation of the semi-major axis, and the inclination of the Moon on the maximum area plane. These equations are obtained without expanding the disturbing function, due to the tidal bulge, in term of the elliptic elements. The equations thus obtained are simple enough to allow us a qualitative discussion of the solution, followed by a numerical integration.The results obtained show the Moon was in the distant past in a retrograde orbit, approaching the Earth, its inclination increasing towards 90°; once after a closer approach to the Earth, the Moon receeded and it will finally reach an equilibrium point, the orbital and the equatorial planes being blended.The solution of the equations appears as a fascicle of curves, becoming extremely dense as we come nearer to the present. Owing to the high sensitivity of the solution to the initial conditions, a weak disturbance added to our modeled forces may lead to a past situation very different from the conclusion drawn by Goldreich (1966) and MacDonald (1964); the minimal approach distance could be greater than 10 Earth's radii.     

Comments on ‘the origin of the Earth—Moon system’

The main points are presented of a new hypothesis of the origin of the Earth—Moon system, developed on the basis of Savi's (1961) theory of the origin of rotation of celestial bodies. The cooling off and contraction due to gravitational attraction on vast particle systems, with the pushing out of electrons from atom shells result in a continually increasing density. Depending on the amount of mass, this pushing out can lead to the expulsion of electrons and the creation of a magnetic field by which a rotational motion is brought about. These conditions are satisfied for the Earth's mass and all larger masses. If the Earth and the Moon formed a unique body, the protoplanet, then once rotational motion had begun, the primeval spherical body must have taken the shape of a large Jacobi ellipsoid. New condensation followed, however no longer solely around the centre of the protoplanet, but also along the edge of the ellipsoid, the process leading to the creation of the dual Earth—Moon system.     

Accretion process of the moon

Recent geochemical and geophysical data suggest that the initial temperature of the Moon was strongly peaked toward the lunar surface. To explain such an initial temperature distribution, a simple model of accretion process of the Moon is presented. The model assumes that the Moon was formed from the accumulation of the solid particles or gases in the isolated, closed cloud. Two equations are derived to calculate the accretion rate and surface temperature of the accreting Moon. Numerical calculations are made for a wide range of the parameters particle concentration and particle velocity in the cloud. A limited set of the parameters gives the initial temperature profiles as required by geochemical and geophysical data. These models of the proto-moon cloud indicate that the lunar outershell, about 400 km thick, was partially or completely molten just after the accretion of the Moon and that the Moon should have been formed in a period shorter than 1000 yr. If the Moon formed at a position nearer to the Earth than its present one, the Moon might have been formed in a period of less than one year.On leave from Geophysical Institute, University of Tokyo.Contribution No. 2104, Division of Geological and Planetary Sciences, California Institute of Technology.     

Earth X-ray albedo for cosmic X-ray background radiation in the 1–1000 keV band

We present calculations of the reflection of the cosmic X-ray background (CXB) by the Earth's atmosphere in the 1–1000 keV energy range. The calculations include Compton scattering and X-ray fluorescent emission and are based on a realistic chemical composition of the atmosphere. Such calculations are relevant for CXB studies using the Earth as an obscuring screen (as was recently done by INTEGRAL ). The Earth's reflectivity is further compared with that of the Sun and the Moon – the two other objects in the Solar system subtending a large solid angle on the sky, as needed for CXB studies.     

Hard X-ray emission of the Earth's atmosphere: Monte Carlo simulations

We perform Monte Carlo simulations of cosmic ray-induced hard X-ray radiation from the Earth's atmosphere. We find that the shape of the spectrum emergent from the atmosphere in the energy range 25–300 keV is mainly determined by Compton scatterings and photoabsorption, and is almost insensitive to the incident cosmic ray spectrum. We provide a fitting formula for the hard X-ray surface brightness of the atmosphere as would be measured by a satellite-borne instrument, as a function of energy, solar modulation level, geomagnetic cut-off rigidity and zenith angle. A recent measurement by the INTEGRAL observatory of the atmospheric hard X-ray flux during the occultation of the cosmic X-ray background by the Earth agrees with our prediction within 10 per cent. This suggests that Earth observations could be used for in-orbit calibration of future hard X-ray telescopes. We also demonstrate that the hard X-ray spectra generated by cosmic rays in the crusts of the Moon, Mars and Mercury should be significantly different from that emitted by the Earth's atmosphere.     

Formation of Embryos of the Earth and the Moon from a Common Rarefied Condensation and Their Subsequent Growth

Embryos of the Moon and the Earth may have formed as a result of contraction of a common parental rarefied condensation. The required angular momentum of this condensation could largely be acquired in a collision of two rarefied condensations producing the parental condensation. With the subsequent growth of embryos of the Moon and the Earth taken into account, the total mass of as-formed embryos needed to reach the current angular momentum of the Earth–Moon system could be below 0.01 of the Earth mass. For the low lunar iron abundance to be reproduced with the growth of originally iron-depleted embryos of the Moon and the Earth just by the accretion of planetesimals, the mass of the lunar embryo should have increased by a factor of 1.3 at the most. The maximum increase in the mass of the Earth embryo due to the accumulation of planetesimals in a gas-free medium is then threefold, and the current terrestrial iron abundance is not attained. If the embryos are assumed to have grown just by accumulating solid planetesimals (without the ejection of matter from the embryos), it is hard to reproduce the current lunar and terrestrial iron abundances at any initial abundance in the embryos. For the current lunar iron abundance to be reproduced, the amount of matter ejected from the Earth embryo and infalling onto the Moon embryo should have been an order of magnitude larger than the sum of the overall mass of planetesimals infalling directly on the Moon embryo and the initial mass of the Moon embryo, which had formed from the parental condensation, if the original embryo had the same iron abundance as the planetesimals. The greater part of matter incorporated into the Moon embryo could be ejected from the Earth in its multiple collisions with planetesimals (and smaller bodies).     

Impacts of Large Planetesimals on the Early Earth

We considered the impacts of very large cosmic bodies (with radii in the range 100–200 to 1000–2000 km) on the early Earth, whose mass, radius and density distribution are close to the current values. The impacts of such bodies were possible during the first hundreds of million years after the formation of the Earth and the Moon. We present and analyze the results of a numerical simulation of the impact of a planetesimal, the size of which is equal to that of the contemporary Moon (1700 km). In three-dimensional computations, the velocity (15 and 30 km/s) and the angle (45°, 60°, and 90°) of the impact are varied. We determined the mass losses and traced the evolution of the shape of the Earth's surface, taking into account the self-consistent gravitational forces that arise in the ejected and remaining materials in accordance with the real, time-dependent mass distribution. Shock waves reflected from the core are shown to propagate from the impact site deep into the Earth. The core undergoes strong, gradually damped oscillations. Although motions in the Earth's mantle gradually decline, they have enough time to put the Earth in a rotational motion. As a result, a wave travels over the Earth's surface, whose amplitude, in the case of an oblique impact, depends on the direction of the wave propagation. The maximum height of this wave is tremendous—it attains several hundred kilometers. Some portion of the ejected material (up to 40% of the impactor mass) falls back onto Earth under the action of gravity. This portion is equivalent to the layer of a condensed material with a thickness on the order of ten kilometers. The appearance of this hot layer should result in a global melting of near-surface layers, which can limit the age of terrestrial rocks by the time of the impact under consideration. For lesser-sized impactors, say, for impactors with radii of about 160 km, the qualitative picture resembles that described above but the amplitude of disturbances is considerably smaller. This amplitude, however, is sufficient to cause a crustal disruption (if such a crust has already formed) and intense volcanic activity.     

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.     

Evaluation of Light Flashes Caused by Impacts of Small Comets on the Surface of the Moon

Images of the dayglow of the Earth's atmosphere in the ultraviolet wavelength region obtained by the photometer of the spacecraft Dynamics Explorer revealed dark spots of the order of 50 km in diameter. These atmospheric holes were interpreted by the American physicist Frank as concentrations of water vapor formed as a result of the disintegration and vaporization of so-called small comets at high altitudes. An analysis of the same images showed that their explanation requires a frequency of comet collisions with the Earth as high as 20 events a minute! This sensational hypothesis evoked a heated scientific debate. The paper below contains an analysis of the possibility of observing Frank's hypothetical comets during their collisions with the Moon. By solving a two-dimensional radiative–gasdynamic problem, the authors demonstrate that the flashes occurring during such impacts can be observed from the Earth with ordinary telescopes.     

A new variant of the large-impact hypothesis for the origin of the Moon

The hypothesis is advanced that after collision of a Mars-sized impact with the Earth, collisions between debris particles themselves are able to place enough material into Earth orbit, to form the Moon. Collision probability estimates show that the collision frequency is high enough to place about one lunar mass into Earth orbit, if the average semimajor axis is of order of the Earth's Roche limit of 18 500 km.     

Formation of the terrestrial planets

The early phases of formation in the inner solar system were dominated by collisions and short-range dynamical interactions among planetesimals. But the later phases, which account for most of the differences among planets, are unsure because the dynamics are more subtle. Jupiter's influence became more important, leading to drastic clearing out of the asteroid belt and the stunting of Mars's growth. Further in, the effect of Jupiter-- both directly and indirectly, through ejection of mass in the outer solar system-- was probably to speed up the process without greatly affecting the outcome. The great variety in bulk properties of the terrestrial bodies indicate a terminal phase of great collisions, so that the outcome is the result of small-N statistics. Mercury, 65 percent iron, appears to be a residual core from a high-velocity collision. All planets appear to require a late phase of high energy impacts to erode their atmospheres: including the Earth, to remove CO₂ so that its ocean could form by condensation of water.Consistent with this model is that the largest collision, about 0.2 Earth masses, was into the proto-Earth, although the only property that appears to require it is the great lack of iron in the Moon. The other large differences between the Earth and Venus, angular momentum (spin plus satellite) and inert gas abundances, must arise from origin circumstances, but neither require nor forbid the giant impact. Venus's higher ratio of light to heavy inert gases argues for it receiving a large icy impactor, about 10^–6 Earth masses from far out, requiring some improbable dynamics to get a low enough approach velocity. Core formation in both planets probably started rather early during accretion.Some geochemical evidences argue for the Moon coming from the Earth's mantle, but are inconclusive. Large scale melting of the mantle by the giant impact would plausibly have led to stratification. But the "lock-up" at the end of turbulent mantle convection is a trade-off between rates: crystallization of constituents of small density difference versus overall freezing. Also, factors such as differences in melting temperatures and densities, melt compressibilities, and phase transitions may have had homogenizing effects in the subsequent mantle convection.     

Utilisation of the lunar field for interplanetary travel by the Oslo system

This paper presents preliminary results of orbital investigations by a data processing machine aimed at the utilisation of the lunar gravitational field in interplanetary travel. The lunar field is utilised in two successive steps. In the first step a spacecraft in an Earth-bound orbit is deviated into an orbit similar to but separated from the Earth's orbit around the Sun. In a successive approach between the spacecraft and the Earth-Moon system the combined fields of the Earth and the Moon are utilised as a means to convey to the spacecraft a main portion of the momentum required in order to carry it to the proximity of Venus.A substantial portion of the fuel required for space travel can be saved by this kind of procedure.The CD 3300 machine time needed for this investigation was supplied by the computing facility of the University of Oslo at Blindern.     

Visibility of the new Moon at two sites I: Maryland situated at northern geographical latitude. II: Sacramento peak situated at high altitude above sea level

The optimum conditions to see the crescent of the new Moon have been obtained at Sacramento Peak and Maryland. We have used the data of the sky twilight brightness given by Koomenet al. (1952) for the two sites. The results show that the crescent can not be seen at the two sites for sun's depression less than 4° and 8° elongation between Sun, Moon and Earth confirming the results obtained before by Asaadet al. (1976). The visibility conditions at Maryland and Sacramento Peak are better than that obtained before for the three sites Misallat, Helwan and Daraw at Egypt. The reason is mainly due to the decrease in the sky twilight brightness at sites having higher geographical northern latitudes and high elevation above sea level.     

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.     

Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system

In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration.