On the origin of the solar system,I

The principal dynamical properties of the planetary and satellite systems listed in Section 2 require these bodies to have condensed in highly-flattened nebulae which provided the dissipation forces that produced the common directions of orbital motion, and the lowe andi values. Minimum masses of these nebulae can be estimated on the assumption that the initial solar abundances apply, starting from the empirical data on present planetary and satellite compositions and masses. The asteroids and comets are assumed to be direct condensations and accretion products in their respective zones (2–4 AU and 20–50 AU), without the benefit of gravitational instability in the solar nebula, owing to the comparatively low density there; with gravitational instability accelerating and ultimately dominating the accretion of the planets and major satellites, in zones approaching and exceeding the local Roche density. Only in the case of Jupiter, gravitational instability appears to have dominated from the outset; the other planets are regarded as hybrid structures, having started from limited accretions. In Section 3 the empirical information on protostars is reviewed. ‘Globules’ are described, found to have the typical range of stellar masses and with gaseous compositions now well known thanks largely to radio astronomy. They contain also particulate matter identified as silicates, ice, and probably graphite and other carbon compounds. The measured internal velocities would predict a spread of total angular momenta compatible with the known distribution of semi-major axes in double stars. The planetary system is regarded as an ‘unsuccessful’ binary star, in which the secondary mass formed a nebula instead of a single stellar companion, with 1–2% of the solar mass. This mass fraction gives a basis for an estimate of thefrequency of planetary systems. The later phases of the globules are not well known empirically for the smaller masses of solar type; while available theoretical predictions are mostly made for non-rotating pre-stellar masses. Section 5 reviews current knowledge of the degree of stability of the planetary orbits over the past 4.5×10⁹ yr, preparatory to estimates of their original locations and modes of origin. The results of the Brouwer and Van Woerkom theory and of recent numerical integrations by Cohenet al. indicate no drastic changes in Δa/a over the entire post-formation history of the planets. Unpublished numerical integrations by Dr P. E. Nacozy show the remarkable stability of the Jupiter-Saturn system as long as the planetary masses are well below 29 times their actual values. Numerical values of Δa/a are collected for all planets. The near resonances found for both pairs of planets and of satellites are briefly reviewed. Section 6 cites the statistics on the frequency and masses of asteroids and information on the Kirkwood gaps, both empirical and theoretical. An analogous discussion is made for the Rings of Saturn, including its extension observed in 1966 to the fourth Saturn satellite, Dione. The reality, or lack of it, of the divisions in the Rings are considered. The numbers of Trojan asteroids are reviewed, as is the curious, yet unexplained, bimodal distribution of their orbital inclinations. Important information comes from the periods of rotation of the asteroids and the orientation of their rotational axes. The major Hirayama families are considered as remnants of original asteroid clusterings whose membership has suffered decreases through planetary perturbations. Other families with fewer large members may be due to collisions. The three main classes of meteorites, irons, stones, and carbonaceous chondrites all appear to be of asteroidal origin and they yield the most direct evidence on the early thermal history of the solar system. While opinion on this subject is still divided, the author sees in the evidence definite confirmation of thecold origin of the planetary system, followed by ahot phase due to the evolving sun that caused the dissolution of the solar nebula. This massive outward ejection, that included the smaller planetesimals, appears to have caused the surface melting of the asteroids by intense impact, with the splashing responsible for the formation of the chondrules. The deep interiors of the asteroids are presumably similar to the C1 meteorites which have recently been found to be more numerous in space by two orders of magnitude than previously supposed.     

Structure and evolutionary history of the solar system,I

1. Introduction and Survey. The method for studying the structure and evolution of the solar system is discussed. It is pointed out that theories that account for the origin of planets alone are basically insufficient. Instead one ought to aim for a general theory for the formation of secondary bodies around a central body, applicable both to planet and satellite formation. A satisfactory theory should not start from assumed properties of the primitive Sun, which is a very speculative subject, but should be based on an analysis of present conditions and a successive reconstruction of the past states.
2. Orbits of Planets and Satellites. As a foundation for the subsequent analysis, the relevant properties of planets and satellites are presented.
3. The Small Bodies. The motion of small bodies is influenced by non-gravitational forces. Collisions (viscosity) are of special importance for the evolution of the orbits. It is pointed out that the focusing property of a gravitational field (which has usually been neglected) leads to the formation of jet streams. The importance of this concept for the understanding of the comet-meteoroid relations and the structure of the asteroidal belt is shown.
4. Resonance Structure. A survey is given of the resonances in the solar system and their possible explanation. It is concluded that in many cases the resonances must already be produced at the times when the bodies formed. It is shown that resonance effects put narrow limits on the post-accretional changes of orbits.
5. Spin and Tides. Tidal effects on planetary spins and satellite orbits are discussed. It is very doubtful if any satellite except the Moon and possibly Triton has had its orbit changed appreciably by tidal effects. The isochronism of planetary and asteroidal spins is discussed, as well as its bearing on the accretional process.
6. Post-accretional Changes in the Solar System. The stability of the solar system and upper limits for changes in orbital and spin data are examined. It is concluded that much of the present dynamic structure has direct relevance to the primordial processes.

     

A co-accretional model of satellite formation

Numerical calculation of a simple accretion model including the effects of tidal friction indicate that coformation is tenable only if the planet's Q is less than about 10³. The parameter which most strongly affects the final mass ratio of the pair is the time at which the secondary embryo is introduced. Our model yields the proper Moon-Earth mass ratio if the Moon embryo is introduced when the Earth is only about $\text{1}\text{10}$ of its final mass. The lunar orbit remains at about 10 Earth radii throughout most of the growth.This model of satellite formation overcomes two difficulties of the “circumterrestrial cloud” model of Ruskol (1960, 1963, 1972): (1) The difficulty of accumulating a mass as great as the entire Moon before gravitational instability reduces the cloud to a small number of moonlets is removed. (2) The differences between terrestrial and outer planet satellite systems is easily understood in terms of the differences in Q between these planets. The high Q of the outer planets does not allow a satellite embryo to survive a significant portion of the accretion process, thus only small bodies which formed very late in the accumulation of the planet remain as satellites. The low Q of the terrestrial planets allows satellite embryos of these planets to survive during accretion, thus massive satellites such as the Earth's Moon are expected. The present lack of such satellites of the other terrestrial planets may be the result of tidal evolution, either infall following primary despinning (Burns, 1973) or escape due to increase in orbit eccentricity.     

Gravitational N-body problem on the accretion process of terrestrial planets

Numerical integration of the gravitational N-body problem has been carried out for a variety of photoplanetary clusters in the range N = 100 to 200. Particles are assumed to coagulate at collisions irrespective of relative velocity and mass ratio of the particles. It is shown graphically how the dispersed N-bodies accumulate to a single planet through mutual collisions. The velocity distribution and size distribution of bodies are also investigated as functions of time in the accretion process. The root mean square velocity of bodies in a cluster increases with time in an early stage of accretion but decreases with time in a late stage of accretion. Accretion rates of planets are found to be dependent strongly on the initial number density distribution, the initial size distribution, and the initial velocity distribution of bodies. Formation of satellites of about 10% in the planet mass is common to most cases in the present study. A substantial mass of bodies also escapes from the cluster. Many satellites and escapers formed during the accretion process of planets may be source materials of heavy bombardment in the early history of planets.     

Origin and evolution of the solar system,II

(7)Formation of celestial bodies. The basic concepts of the accretional process are discussed, and the inadequacy of the contractional model is pointed out. A comparison is made between the general pre-planetary state on the one hand and the present state in the asteroidal region on the other. A model for accretion of resonance-captured grains leading to the formation of resonance-captured planets and satellites is suggested.(8)Spin and accretion. The relation between the accretional process and the spin of planets is analyzed.(9)Accretion of planets and satellites. It is shown that jet streams are a necessary intermediate stage in the formation of celestial bodies. The time sequence of planet formation is analyzed, and it is shown that the newly accreted bodies have a characteristic internal heat structure; the cases of the Earth and the Moon are considered in detail. A region of high initial temperature is found at 0.4 of the present Earth radius, whereas the culminating temperature of the Moon is near its present surface. An accretional heat wave is found to proceed outwards, and may produce the observed differentiation features.     

Distribution of gravitational potential energy within the solar system

The orbital gravitational potential energies of the planets and of the satellites have been estimated and compared to the gravitational potential energies of the bodies themselves and to the gravitational potential energy of the Sun. From the point of view of the gravitational potential energy distribution two quite different groups of the planets can be distinguished clearly. However, the gravitational potential energy of the systems is mainly concentrated within the central bodies, only about 10^–5 in orbiting bodies.     

Structure and evolutionary history of the solar system,III

Parts I and II of our analysis of the evolution of the solar system were devoted mainly to the mechanical processes. The present part (Part III) deals primarily with the plasma processes and the hydromagnetic aspects.Much confusion in the cosmogonic field is due to the treatment of the early phases of the evolution of a circumstellar medium by pre-hydromagnetic methods, or by erroneous application of magnetohydrodynamics. In order to reduce the speculative element as far as possible the present analysis tries to connect the cosmogonic processes as directly as possible to laboratory plasma physics and to space phenomena actually observed today (Section 10).Models of the Laplacian type have been made obsolete by magnetohydrodynamics. Furthermore they are in conflict with observations. A new model is suggested (Section 11).A plasma surrounding a rotating central body may attain a state of partial corotation which is determined by the balance between gravitation and the centrifugal force acting on a plasma in a dipole field. Condensation from a partially corotating plasma results in grains orbiting in ellipses withe=1/3 and finally accreting to bodies at 2/3 of the central distance of the point of condensation (Section 12).An application of the theory to the Saturnian rings and to the asteroidal belt shows that the falldown ratio 2/3 (derived from the geometry of a dipole field) is essential for the understanding of their structure. The structure of the groups of planets and satellites is also discussed but only in a preliminary way. The behavior of volatile substances is a major problem which still awaits an appropriate treatment (Section 13).     

Numerical simulation of the final stages of terrestrial planet formation

Three representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative-velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross section is unnecessary. These simulations indicate that the growth of bodies with final masses approaching those of Venus and the Earth is possible, at least for the case of a two-dimensional system. Simulations assuming an initial uniform distribution of orbital eccentricities on the interval from 0 to e_max are found to produce final states containing too many bodies with masses which are too small when e_max < 0.10, while simulations with e_max > 0.20 result in too many catastrophic collisions between bodies thus preventing rapid accretion of planetary-size bodies. The e_max = 0.15 simulation ends with a state surprisingly similar to that of the present terrestrial planets and, therefore, provides a rough estimate of the range of radial sampling to be expected for the terrestrial planets.     

Exobiology, the study of the origin, evolution and distribution of life within the context of cosmic evolution: a review

The primary goal of exobiological research is to reach a better understanding of the processes leading to the origin, evolution and distribution of life on Earth or elsewhere in the universe. In this endeavour, scientists from a wide variety of disciplines are involved, such as astronomy, planetary research, organic chemistry, palaeontology and the various subdisciplines of biology including microbial ecology and molecular biology. Space technology plays an important part by offering the opportunity for exploring our solar system, for collecting extraterrestrial samples, and for utilizing the peculiar environment of space as a tool. Exobiological activities include comparison of the overall pattern of chemical evolution of potential precursors of life, in the interstellar medium, and on the planets and small bodies of our solar system; tracing the history of life on Earth back to its roots; deciphering the environments of the planets in our solar system and of their satellites, throughout their history, with regard to their habitability; searching for other planetary systems in our Galaxy and for signals of extraterrestrial civilizations; testing the impact of space environment on survivability of resistant life forms. This evolutionary approach towards understanding the phenomenon of life in the context of cosmic evolution may eventually contribute to a better understanding of the processes regulating the interactions of life with its environment on Earth.     

Searching for the source of short-period comet nuclei: The direction of the spatial migration of comets

An attempt is made to determine the spatial location of the main source of short-period comet nuclei. Numerical calculations for the orbital evolution of Jupiter family comets, medium-period comets, and Centaurs are used to show that the orbits of small solar system bodies tend to evolve in the direction of increasing semimajor axes. This relates to bodies that can experience encounters with planets and whose orbital evolution is shaped by gravitational perturbations. It is concluded that there is good reason to search for the main source of the nuclei of Jupiter family comets at distances of 6 AU or less from the sun.     

The 1/1 resonance in extrasolar systems

We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves around the star. The stability regions around periodic orbits along the family are studied. Next, we study the dynamical evolution in time of a planetary system with two planets which is initially trapped in a stable 1/1 resonant periodic motion, when a drag force is included in the system. We prove that if we start with a 1/1 resonant planetary system with large eccentricities, the system migrates, due to the drag force, along the family of periodic orbits and is finally trapped in a satellite orbit. This, in principle, provides a mechanism for the generation of a satellite system: we start with a planetary system and the final stage is a system where the two small bodies form a close binary whose center of mass revolves around the star.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

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.     

Interplanetary dust dynamics: I. Long-term gravitational effects of the inner planets on zodiacal dust

Whereas the inner planets' perturbations on meteoroids' and larger interplanetary bodies' orbits have been studied extensively, they are usually neglected in studies of the dynamics of smaller particles producing the zodiacal light through scattering of sunlight. Forces acting on these dust particles are fairly well known and include radiation forces and interaction with the solar wind. This article is the first in a series aimed at improving our knowledge of the dynamical evolution of dust in interplanetary space by studying the combined effects of these perturbations including gravitational perturbations by the planets Venus, Earth, Mars, and Jupiter. The necessity of including effects of the inner planets in dust dynamics investigations is established. Sample trajectories are presented to illustrate commonly occurring phenomenae, such as nonmonotonic changes in semimajor axis, eccentricity, inclination, and in the line of nodes. These perturbations are shown to be due to the inner planets as opposted to Jupiter or nongravitational forces.     

The origin of the solar system: Implications for transneptunian planets and the nature of the long-period comets

If the solar system origin is considered within the framework of the author's hypothesis on the binary stars formation as a result of rotational-exchange break-up of the rotating protostar, then difficulties involved in the usual nebular hypotheses are automatically removed (unclear aspects of the possibility of formation of the gas disc proper, the problems of the angular momentum including slow rotation of the Sun and coplanarity of the planetary orbits, of differences in planetary masses and composition, the need, for the disc remnants to be swept out, the long time of planetary formation as compared with the possible lifetime of a turbulized disc etc.).The major stages of division and evolution of the Jupiter-Sun system are described. Similarities between the massive rotating proto-Jupiter (PJ) and the classical protoplanetary discs are pointed out. The process of planetoid condensation inside PJ is discussed. The most probable site of the condensation is the region of the first Lagrangian point. The planetoids condensed were lost by PJ as a result of its fast mass decrease. A gas dynamic consideration of the motion of planetoids in PJ yields 1000–3000 yr as a time scale for the PJ's mass loss. The number of the moonlike bodies lost (the remaining Galilean satellites fixing their lower mass limit) could reach 10⁴.Evolution of such interacting bodies results in the formation beyond Neptune of a cloud (up to 10³) of moonlike (and more massive) planets.The excess concentration of the long-period comets aphelia in this area implies their genetic relation to the planets. A concept of a joint planeto-cometary cloud is introduced. A concrete hydrodynamic mechanism of ice ejection from planets into space, viz. the formation of cumulative (Monroe) jets, is pointed out.A program of further investigations is outlined and recommendations given for an experimental check on the implications of the new cosmogonic concepts.     

Planetary close encounters: geometry of approach and post-encounter orbital parameters

Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle—planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

Astrometric observations of planetary satellites at the Abastumani Astrophysical Observatory

We present and discuss the results of the astrometry project during which we observed the satellites of Mars, Jupiter, Saturn, Uranus, and Neptune at the Abastumani Astrophysical Observatory (Georgia) between 1983 and 1994. Observations at the Abastumani Observatory were performed with the double Zeiss astrograph (DZA: D/F = 400/3024 mm) and AZT-11 telescope (F = 16 m). We processed a large array of observations and determined exact coordinates of the planets and their satellites in a system of reference stars of modern catalogues as well as relative coordinates of the satellites. The results were compared with modern ephemerides using the MULTI-SAT software. The comparison enabled us to estimate the accuracy of observations (their random and systematic uncertainties) and the accuracy of modern theories of the motion of planets and their satellites. Random uncertainties of observations are estimated to be 0.10??C0.40?? for various objects and observational conditions. Observational results obtained for Uranus, Neptune and the satellites Titania and Oberon were shown to deviate appreciably and systematically from theories of their motion. The results of observations are presented in the Pulkovo database for Solar System bodies that is available at the website http://www.puldb.ru.