Formation of the first oxidized iron in the solar system

For fayalite formation times of several thousand years, and systems enriched in water by a factor of ten relative to solar composition, 1 μm radius olivine grains could reach 2 mole% fayalite and 0.1 μm grains 5 mole% by nebular condensation, well short of the values appropriate for precursors of most chondrules and the values found in the matrices of unequilibrated ordinary chondrites. Even 10 μm olivine crystals could reach 30 mole% fayalite above 1100 K in solar gas if condensation of metallic nickel‐iron were delayed sufficiently by supersaturation. Consideration of the surface tensions of several phases with equilibrium condensation temperatures above that of metallic iron shows that, even if they were supersaturated, they would still nucleate homogeneously above the equilibrium condensation temperature of metallic iron. This phenomenon would have provided nuclei for heterogeneous nucleation of metallic nickel‐iron, thus preventing the latter from supersaturating significantly and preventing olivine from becoming fayalitic. Unless a way is found to make nebular regions far more oxidizing than in existing models, it is unlikely that chondrule precursors or the matrix olivine grains of unequilibrated ordinary chondrites obtained their fayalite contents by condensation processes. Perhaps stabilization of FeO occurred after condensation of water ice and accretion of icy planetesimals, during heating of the planetesimals and/or in hot, dense, water‐rich vapor plumes generated by impacts on them. This would imply that FeO is a relatively young feature of nebular materials.     

Formation of solar nebula and mass distribution in the planetary system

The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.     

Formation of the solar Hα profile

A series of non-LTE radiative transfer solutions for H was computed using the integrodifferential equation technique of Athay and Skumanich (1967). A model hydrogen atom consisting of three bound levels and a continuum was assumed. It was found that increasing the temperature of the chromosphere at the height of line formation decreases the central intensity of the line. The density structure of the atmosphere primarily affects the optical depth scale rather than the source function. The temperature minimum region of the atmosphere was found to be transparent to H radiation, so that the radiation in some part of the line will arise from two distinct layers of the atmosphere, one above the temperature minimum and one below it. The computed H profile was found to be highly sensitive to the assumed 2–3 collisional cross-section.     

Origin of the solar system

A theory for the origin of the solar system, which is based on ideas of supersonic turbulent convection and indicates the possibility that the original Laplacian hypothesis may by valid, is presented. We suggest that the first stage of the Sun's formation consisted of the condensation of CNO ices (i.e. H₂O, NH₃, CH₄,...) and later H₂, including He as impurity atoms, at interstellar densities to from a cloud of solid grains. These grains then migrate under gravity to their common centre of mass giving up almost two orders of magnitude of angular momentum through resistive interaction with residual gases which are tied, via the ions, to the interstellar magnetic field. Grains rich in CNO rapidly dominate the centre of the cloud at this stage, both giving up almost all of their angular momentum and forming a central chemical inhomogeneity which may account for the present low solar neutrino flux (Prentice, 1976). The rest of the grain cloud, when sufficiently compressed to sweep up the residual gases and go into free fall, is not threatened by rotational disruption until its mean size has shrunk to about the orbit of Neptune. When the central opacity rises sufficiently to halt the free collapse at central density near 10^?13 g cm^?3, corresponding to a mean cloud radius of 10⁴ R _⊙, we find that there is insufficient gravitational energy, for the vaporized cloud to acquire a complete hydrostatic equilibrium, even if a supersonic turbulent stress arising from the motions of convective elements becomes important, as Schatzman (1967) has proposed. Instead we suggest that the inner 3–4% of the cloud mass collapses freely all the way to stellar size to release sufficient energy to stabilize the rest of the infalling cloud. Our model of the early solar nebula thus consists of a small dense quasi-stellar core surrounded by a vast tenuous but opaque turbulent convective envelope. Following an earlier paper (Prentice, 1973) we show how the supersonic turbulent stress \((\rho _t v_t ^2 ) = \beta \rho GM(r)/r\) , where β is called the turbulence parameter, ρ is the gas density andM(r) the mass interior to radiusr causes the envelope to become very centrally condensed (i.e. drastically lowers its moment-of-inertia coefficientf) and leads to a very steep density inversion at its photosurface, as well as causing the interior to rotate like a solid body. As the nebula contracts conserving its angular momentum the ratio θ of centrifugal force to gravitational force at the equator steadily increases. In order to maintain pressure equilibrium at its photosurface, material is extruded outwards from the deep interior of the envelope to form a dense belt of non-turbulent gases at the equator which are free of turbulent viscosity. If the turbulence is sufficiently strong, we find that when θ→1 at equatorial radiusR _e=R₀, corresponding to the orbit of Neptune, the addition of any further mass to the equator causes the envelope to discontinuously withdraw to a new radiusR _e>R₀, leaving behind the circular belt of gas at the Kepler orbitR ₀. The protosun continues to contract inwards, again rotationally stabilizing itself by extruding fresh material to the equator, and eventually abandoning a second gaseous ring at radiusR ₁, and so on. If the collapse occurs homologously the sequence of orbital radiiR _n of the system of gaseous Laplacian rings satisfy the geometric progression $$R_n /R_{n + 1} = [1 + m/Mf]^2 = constant, n = 0, 1,2, \ldots ,$$ analogous to the Titius-Bode Law of planetary distances, wherem denotes the mass of the disposed ring andM the remaining mass of the envelope. Choosing a ratio of surface to central temperature for the envelope equal to about 10^?3 and adjusting the turbulence parameter β～~0.1 so thatR _n/R_n+1 matches the observed mean ratio of 1.73, we typically findf=0.01 and that the rings of gas each have about the same mass, namely 1000M _⊕ of the solar material. Detailed calculations which take into account non-homologous behaviour resulting from the changing mass fraction of dissociated H₂ in the nebula during the collapse do not appreciably disturb this result. This model of the contracting protosun enables us to account for the observed physical structure and mass distribution of the planetary system, as well as the chemistry. In a later Paper II we shall examine in detail the condensation of the planets from the system of gaseous rings.     

Stability of the solar system

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.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.     

Cosmogony of the solar system

In Sections 1–6, we determine an approximate analytical model for the density and temperature distribution in the protoplanetary could. The rotation of the planets is discussed in Section 7 and we conclude that it cannot be determined from simple energy conservation laws.The velocity of the gas of the protoplanetary cloud is found to be smaller by about 5×10³ cm s^–1 in comparison to the Keplerian circular velocity. If the radius of the planetesimals is smaller than a certain limitr ₁, they move together with the gas. Their vertical and horizontal motion for this case is studied in Sections 8 and 9.As the planetesimals grow by accretion their radius becomes larger thanr ₁ and they move in Keplerian orbits. As long as their radius is betweenr ₁ and a certain limitr ₂ their gravitational interaction is negligible. In Section 10, we study the accretion for this case.In Section 11, we determine the change of the relative velocities due to close gravitational encounters. The principal equations governing the late stages of accretion are deduced in Section 12, In Section 13 there are obtained approximate analytical solutions.The effect of gas drag and of collisions is studied in Sections 14 and 15, respectively. Numerical results and conclusions concerning the last and principal stage of accretion are drawn in Section 16.     

Organics in the solar system

Complex organics are now commonly found in meteorites, comets, asteroids, planetary satellites and interplanetary dust particles. The chemical composition and possible origin of these organics are presented. Specifically, we discuss the possible link between Solar System organics and the complex organics synthesized during the late stages of stellar evolution. Implications of extraterrestrial organics on the origin of life on Earth and the possibility of existence of primordial organics on Earth are also discussed.     

Chaos in the solar system

We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T _c ,is a function of the Lyapunov time, T _ty .The relation is log (T _c /T _o )= a + b log (T _ly T _o )where T _o is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T _o .This is the case of interest for the planets in the solar system.     

Formation of solar system as a result of evolution of protostar of second or subsequent generation

The formation of the solar system is considered from the physico-chemical point of view. The main role in the process is ascribed to heavy metals and to the surface tension that had arisen as a result of appearance of a liquid layer of fused substance in the equatorial region of the protostar. The formation of the liquid layer was caused by the transfer of fused substance droplets under the action of centrifugal forces in the direction of the protostar surface. Due to the surface tension the prevalence of the centrifugal forces over the gravitational ones was able to reach the value when the density differentiation of the substance began to take place under the effect of the centrifugal forces, and accumulation of heavy metals proceeded in outermost equatorial region of the protostar. As a result the disk has been formed and a liquid ring was separated from the protostar. Later explosions on the young Sun sent parts of the hardened ring which possessed the first cosmic velocity to different distances away from the Sun. In such a way planets, their satellites, asteroids, meteorites and comets were formed. The physical characteristics of planets, the parameters of their orbits, and the data on the structure of meteorites are consistent with ideas developed in the paper.     

Deuterium in the early solar system

An attempt is made to construct a self-consistent picture of the deuterium abundance in the early Solar System based on the assumption of chemical equilibrium in the solar nebula. A recent determination of the $\text{D}\text{H}$ ratio for the atmosphere of Jupiter is consistent with a previous estimate of the $\text{D}\text{H}$ ratio for the proto-Sun. The high (> 1.5 × 10^?4) $\text{D}\text{H}$ ratios determined from analyses of carbonaceous meteorites imply an equilibrium temperature < 270°K, in marked disagreement with the equilibrium temperature determined for the same material by oxygen isotope cosmothermometry.     

Mass distribution in the solar system

The present-day observed mass distribution in the solar system including the Sun is shown to be compatible with the idea of the splitting of a number of ring-shaped rotating clouds of particles in the equatorial plane of a single contracting nebula. The formation of such a nebula is discussed and it is inferred that during the course of contraction this nebula has remained a sphere of uniform density spinning with the Keplerian velocity of its surface layer. The mass of a planet is taken as the portion of this spherical solar nebula gained at the time of splitting by its gaseous ring of dimensions satisfying Roche and accretional limits.     

Angular momenta in the solar system

A statistical study of the orbital parameters of comets, asteroids and meteor streams shows that the vectors representing their angular momenta per mass unit (or the average angular momentum for meteor streams) are not arbitrarily distributed in the space: They are clustered around determinated values of angles . This synthesizes the eccentricities and inclinations of the orbital planes in a unique parameter adequated for the statistical purposes of the present work being defined by cos = cos (arc sin e) cos i.The discreteness of the obtained distribution N() and its relation with the components of the angular momenta per mass unit is analysed having this distribution common features for objects of different nature and located in different places in the solar potential well. Some hypotheses concerning to these effects are discussed.     

Interstellar dust in the solar system

Dust is an important component of galactic stucture and the cyclic processing of particulate matter leads to stellar and planetary formation. Though astronomical methods using analysis of dust-penetrating starlight can provide some limited information about the dust, the prospect of its in-situ sampling within the Solar System by spacecraft and its remote sensing by ground-based techniques open up a new field in galactic exploration.     

Resonant structures in the solar system

The resonance theory is discussed with respect to the Solar System with a view to show that every triad of successive planets in the Solar System follows Laplace's resonance relation. With rings now known to exist around three of the four major planets, scientists have begun to speculate about the possible existence of ring structure and one or two small planets going around the Sun itself. It is also believed that the ring systems may exist around the planets Neptune and Mars. In this paper an attempt is made to provide a basis to these beliefs using Laplace's resonance relation. The triads of successive innermost objects (rings and/or satellites) in the satellite — systems of Jupiter, Saturn and Uranus are also shown to follow Laplace's resonance relation.     

Nanoparticles in the inner solar system

We discuss different scenarios for the formation and dynamics of nanoparticles in the inner solar system. Particles up to a few tens of nanometer size, if formed at a distance larger than several 0.1 AU from the Sun, are picked up by the solar wind and therefore do not reach the regions closer to the sun. At distances ⩽0.1 AU particles of several tens of nanometer in size can stay in bound orbits and, aside from the Lorentz force, the plasma and the photon Poynting–Robertson effect determine their spatial distribution. Local sources of nanometer-sized particles in the inner solar system are collisional fragmentation and sublimation of dust and meteoroids. The most likely materials to survive in the very vicinity of the Sun are MgO particles from the sublimation of cometary and meteoritic silicates, nanodiamonds originating from meteoroid material, and possibly carbon structures formed by thermal alteration of organics. The nanoparticles may produce spectral features in a limited spectral interval, and this spectral interval varies with particle size, composition and temperature. Bearing in mind the wide size distribution of solar system dust and the preponderance of larger particles, it is unlikely that nanoparticles can be detected in thermal emission or scattered light brightness and we are unable to predict observable features for these nanoparticles. If the nanodust produced observable features, they are most likely to appear in the blue or near infrared. We suggest a more promising option is the in situ detection of the particles.     

Stability of frosts in the solar system

Calculations on the stability of various frosts (against evaporation) for solar system objects in circular and elliptical orbits are made. It is found that the stability of these frosts is dependent on the rate of rotation of the object, the latitude of the area on the object being considered, and the eccentricity of the orbit as well as its mean distance from the Sun. These factors greatly influence the amount of solar radiation incident and reradiated from a given area on the object. The likelihood of finding these frosts on the surfaces of objects and the lifetimes of objects composed of these frosts is discussed.