Delivery of Water and Volatiles to the Terrestrial Planets and the Moon

From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two?three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s orbit could be less than that for the Earth by a factor not more than 20.     

A history of the determination of Pluto's mass

Lowell's value for the mass of Planet X was about seven times that of the Earth. Postdiscovery determinations of the mass of Pluto from analysis of the observed motions of Uranus and Neptune reduced this value to about one Earth mass. More extended analyses in the past 10 years have lowered this value to about one-tenth of an Earth mass. The mass so derived, however, fails to agree by a factor of 50 with that determined from the motion of the newly discovered satellite Charon. The discrepancy may arise from unmodeled effects in the motions of the outer planets.     

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).     

Gas capture and rare gas retention by accreting planets in the solar nebula

In this paper, the physico-chemical effects of the nebula gas on the planets are reviewed from a standpoint of planetary formation in the solar nebula.The proto-Earth growing in the nebula was surrounded by a primordial atmosphere with a solar chemical composition and solar isotopic composition. When the mass of the proto-Earth was greater than 0.3 times the present Earth mass, the surface was molten because of the blanketing effect of the atmosphere. Therefore, the primordial rare gasses contained in the primordial atmosphere dissolved into the molten Earth material without fractionation and in particular the dissolved neon is expected to be conserved in the present Earth material. Hence, if dissolved neon with a solar isotopic ratio is discovered in the Earth material, it will indicate that the Earth was formed in the nebula and that the dissolved rare gases were one of the sources which degassed to form the present atmosphere.     

The Dynamical Evolution of the Atens

In this investigation the orbits of 21 Atens (semimajor axes smaller than the Earth) are studied with the aid of numerical integrations over the time interval of one million years. The dynamical model was a 6-body Solar System, where the perturbations of Uranus and Neptune were ignored, and where Mercury's mass was added to the Sun's mass. Thus mean motion resonances, secular resonances and the Kozai resonance were fully taken into account. The evolution of the semimajor axes shows the typical step function like pattern which we know also from comets although some Atens have a very fuzzy development of the orbital elements, and some of them stay in a mean motion resonance for very long time. The evolution from Atens to Apollos (with semimajor axes larger than the Earth) and vice versa is also a phenomenon which we could observe. The main goal was the study of encounters of the Atens with the Earth and Venus. We found out that Venus encounters occur somewhat more often than Earth encounters (approximately one within the distance Earth - Moon every 40000 years with Venus, one every 50000 years with the Earth). This revised version was published online in July 2006 with corrections to the Cover Date.     

Sub-brown dwarfs as seats of life based on non-polar solvents: Thermodynamic restrictions

Sub-brown dwarfs (SBD) might originate either around a star or in solitary fashion. These bodies can retain atmospheres composed of molecular gases, which, upon cooling, have basal pressures of tens of bars or more. Pressure-induced opacity of these gases prevents such a body from eliminating its internal radioactive heat and its surface temperature can exceed the melting point of the life-supporting solvent for an extended period of time. Earth life uses water as a solvent but synthesis of observational data makes it possible to conceive chemical reactions that might support life involving non-carbon compounds, occurring in solvents other than water. In this paper a non-polar solvent is considered: ethane. Thermodynamic requirements to be fulfilled by a hypothetic gas constituent of a life-supporting SBD atmosphere are studied. Three gases are analyzed: nitrogen, carbon dioxide and methane. For thermodynamic reasons carbon dioxide is excluded from the list of candidate gases. We show that bodies with ethane oceans are possible in interstellar space. This may happen on SBD of (significantly) smaller or larger mass than the Earth. Generally, in case of SBD smaller in size than the Earth, the atmosphere exhibits a convective layer near the surface and a radiative layer at higher altitudes while the atmosphere of SBDs larger in size than Earth does not exhibit a convective layer. The prescribed thermodynamic state of ethane on the surface has some influence on the features of the atmosphere. The atmospheric mass of a life-hosting SBD of Earth size is two or three orders of magnitude larger than the mass of Earth atmosphere.     

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.     

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.     

关于章动序列计算中的地球动力学扁率的取值

刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．     

On the capture of the Moon

This paper studies the possibility of lunar capture depending on variations of the solar mass under certain well specified conditions and assumptions regarding the behaviour of the three-body dynamical system formed by the Sun, Earth and Moon. It is found that a large amount of decrease in the solar mass (approximately 37%) would be required to allow capture if the model of the planar restricted problem of three bodies is assumed, if the masses of the Earth and Moon did not change and if the angular momentum of the Sun-Earth system did not change. Such large mass-changes of the Sun can not be associated with radiation mass losses only with catastrophic events, such as stellar close approaches.     

Source regions and timescales for the delivery of water to the Earth

Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.     

Did the moon form as a result of a thermonuclear explosion?

The proposed model explains the Moon formation as a result of a thermo-nuclear explosion due to which a big land mass was torn off from the Earth. Within the model framework, on the one hand, the data on the Moon’s physical and chemical parameters are in good agreement. On the other hand, this model corresponds to modern ideas about the dynamism of the Earth’s geological structure which presupposes the presence of a powerful energy source in the Earth’s core, which might have thermonuclear origin.     

Atmospheric entry heating of micrometeorites at Earth and Mars: Implications for the survival of organics

The atmospheric entry heating of micrometeorites (MMs) can significantly alter their pre‐existing mineralogy, texture, and organic material. The degree of heating depends predominantly on the gravity and atmospheric density of the planet on which they fall. For particles falling on Earth, the alteration can be significant, leading to the destruction of much of the pre‐entry organics; however, the weaker gravity and thinner atmosphere of Mars enhance the survival of MMs and increase the fraction of particles that preserve organic material. This paper investigates the entry heating of MMs on the Earth and Mars in order to examine the MM population on each planet and give insights into the survival of extraterrestrial organic material. The results show that particles reaching the surface of Mars experience a lower peak temperature compared to Earth and, therefore, experience less evaporative mass loss. Of the particles which reach the surface, 68.2% remain unmelted on Mars compared to only 22.8% on Earth. Due to evaporative mass loss, unmelted particles that reach the surface of Earth are restricted to sizes <70 μm whereas particles >475 μm survive unmelted on Mars. Approximately 10% of particles experience temperatures below ~800 K, that is, the sublimation temperature of refractory organics found in MMs. On Earth, this fraction is significantly lower with less than 1% expected to remain below this temperature. Lower peak temperatures coupled with the larger sizes of particles surviving without significant heating on Mars suggest a much higher fraction of organic material surviving to the Martian surface.     

Astronomical Engineering Revisited: Planetary Orbit Modification Using Solar Radiation Pressure

As the Sun evolves along the main sequence its luminosity will grow, leading to a steadily increasing solar flux at the Earth with corresponding catastrophic consequences for the biosphere. A novel means of avoiding this terminal route to human evolution has recently been proposed by Korycansky et al. which utilises a series of grazing fly-pasts of the Earth with a small solar system body to increase the orbit radius of the Earth over a timescale of order 10⁹ years. This short paper will propose an alternative strategy which utilises a large reflective sail to generate a propulsive thrust due to solar radiation pressure. It will be shown that if the sail is configured to be in static equilibrium relative to the Earth, the centre-of-mass of the Earth-sail system slowly accelerates. This scheme offers some advantages in that the mass of the sail is four orders of magnitude less than the mass to be processed in the scheme of Korycanskyet al. for trajectory correction manoeuvres alone. In addition, the severe hazard posed by multiple grazing fly-pasts of the Earth by a small solar system body is avoided. Although offering significant advantages, any thoughts of engineering on an astronomical scale clearly requires a leap of the imagination and a ready use of liberal assumptions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chemical composition of the Earth after the giant impact

The giant impact hypothesis for the origin of the Moon has been widely accepted. One of the most important features of this hypothesis is that the impactor's metallic core was incorporated in the Earth after impact. If the mass of the impactor is 0.82 × 10²⁷ g, the mass of the impactor core was estimated to be 0.19 × 10²⁷ g, which is about 1/10 of present Earth's core. Liu (1982) derived the bulk composition of the Earth from CI chondrites, and concluded that the Fe content of his model appears to be low in comparison with the present Earth, which, however, can be rationalized by the addition of impactor core into the proto-Earth developed by Liu (1982). If the impactor's mantle contains 14 wt% FeO as suggested, the mass ratio of impactor/proto-Earth should not exceed 0.22. The same ratio is not likely to exceed 0.30, if a giant blowoff did not occur during impact.     

Determining the possible building blocks of the Earth and Mars

Abstract— To determine the possible building blocks of the Earth and Mars, 225,792,840 possible combinations of the bulk oxygen isotopic and chemical compositions of 13 chondritic groups at 5% mass increments were examined. Only a very small percentage of the combinations match the oxygen isotopic composition, the assumed bulk FeO concentration, and the assumed Fe/Al weight ratio for the Earth. Since chondrites are enriched in silicon relative to estimates of the bulk Earth, none of the combinations fall near the terrestrial magmatic fractionation trend line in Mg/Si‐Al/Si space. More combinations match the oxygen isotopic composition and the assumed bulk FeO concentration for Mars. These combinations fall near the trend for shergottite meteorites in Mg/Si‐Al/Si space. One explanation for the difficulty in forming Earth out of known chondrites is that the Earth may be composed predominately of material that did not survive to the present day as meteorites. Another explanation could be that significant amounts of silicon are sequestered in the core and/or lower mantle of the Earth.     

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.     

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University.     

On the internal structures of mercury and venus

Recent radar measures of the radius and mass of Mercury imply a composition for the planet containing about 60% iron. One or other of two conclusions seems inescapable: either that Mercury is a highly exceptional object among terrestrial planets, or that all measures to date of the planet involve substantial systematic error. In either case the situation is such that independent checking of the radius and mass of Mercury by some entirely different means has become of the greatest importance to planetary physics and cosmogony.The recent radar and other determinations of the solid radius of Venus imply an internal structure similar to that of the Earth, namely a liquid core surrounded by a solid mantle and outer-shell zone. The theory also implies that the temperatures within Venus should be slightly higher than at the corresponding parts of the Earth. The proportion of mass in the core of Venus (about 25% of the whole) is entirely consistent with the phase-change hypothesis as to its nature, as of course is also the absence of any liquid or iron core in both Mars and the Moon. On the older iron-core hypothesis, Venus with considerably less iron content by mass than the Earth, and Mars and the Moon with none, would all present problems in different degrees to account for the differences of composition.If Venus began as an all-solid planet, the initial radius would have been about 6300 km, and the total amount of surface reduction to date owing to contraction of the planet would have been almost 40 million km², and as a proportion of the total area only slightly less than the contraction of the Earth. The theory thus predicts the existence of folded and thrusted mountain-systems of terrestrial type at the surface of Venus.     

The origin of the moon and the single-impact hypothesis I

Recently the single-impact hypothesis for forming the Moon has gained some favorable attention. We present in this paper a series of three-dimensional numerical simulations of an impact between the protoearth and an object about 0.1 of its mass. For computational convenience both objects were assumed to be composed of granite. We studied the effects on the outcome of the collision of varying the impact parameter, the initial internal energy, and the relative velocity. The results show that if the impact parameter is large enough so that the center of the impactor approximately grazes the limb of the protoearth, the impactor is not completely destroyed; part of it forms a clump in a large elliptical orbit about the Earth. This clump does not collide with the Earth, since the effects, first, of vapor pressure gradients during the impact, and later, of angular momentum transfer due to the rotation of the deformed Earth, have modified the ballistic trajectory. However, since the orbit of the clump comes close to the Earth (within the Roche limit) the clump will be destroyed and spread out to form a disk around the Earth. The amount of angular momentum in the Earth-Moon system thus obtained tends to fall short of the observed amount; this deficiency would be eliminated if the mass of the impactor were somewhat greater than the one assumed here. The scenario for making the Moon from a single-impact event is supported by these simulations.