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.     

Formation of the solar system

Prentice (1978a, b), in his modern Laplacian theory of the origin of the solar system, has established a scenario in which he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant 1.69. In an attempt to understand this law in an alternative way, Rawal (1984a) assumes that during the collapse of the solar nebula the halts at various radii are brought about by the supersonic turbulent convection and arrives at the relation of the formR _p=Ra^p, whereR is the radius of the present Sun anda=1.422, is referred to, here, as the Roche constant. Kepler's third law assumes the form:T _p=T₀(a ^3/2) ^p ,T ₀ being the rotational period of the Sun at the time it attained its present radius.R _p satisfy Laplace's resonance relation without any exception. The present paper investigates inter-relations among the concepts of supersonic turbulent convection, rotational instability, and Roche limit.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

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 galaxies as based on the spatial distribution of matter

A morphological box for the space distribution of galaxies and dark matter as the consequence of various types of cosmogonical hypotheses is presented. A short review of concepts of clustering of galaxies is given. One has to distinguish between the phenomena of “clusters of galaxies” and of “clustering of galaxies”. The second notion is more general. The investigations of KIANG , FLIN , and PEEBLES speak in favour of general clustering rather than overal existence of individual clusters. Individuals such as our Supergalaxy, Coma cluster etc. seem rather to be exceptional features.     

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.     

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.     

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.     

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.     

Short-lived radionuclides in the early solar system — A meteoritic perspective of the solar system formation

This paper reviews the evidence for short-lived radionuclides in the early solar system and evaluates the models of their origin. The stellar model requires that some freshly-nucleosynthesized radionuclides were injected into the proto-solar cloud shortly before it began to collapse. The spallation theory suggests that these nuclides were the products of interaction between energetic particles and gas/dust in the proto-solar cloud or solar nebula. A brief discussion is given to a new theory for the X-wind model of solar system formation.     

HIPPARCOS and the dynamics of the solar system

The HIPPARCOS program may contribute to dynamical astronomy in two different ways: by determining the positions of some bodies of the solar system or by improving the positions of the reference stars with respect to which observations of members of the solar system are made.It is shown that only minor planets may be observed validly by HIPPARCOS but these observations alone cannot contribute significantly to the determination of a reference frame. However, they can be useful for the improvement of orbits and as a complement to a major observational effort in preparation of a new determination of dynamical system of reference.HIPPARCOS will provide a new global reference frame and improved proper motions of stars. This may be used to rediscuss earlier observations and provide corrections to the theory of motion of the Moon and planets. Such corrections may be rather large and their possible effect is indicated for several cases. Furthermore, the celestial reference system of HIPPARCOS will allow to avoid, in future observations, many of the presently existing biases.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.     

The influence of solar system oscillation on the variability of the total solar irradiance

Total solar irradiance (TSI) is the primary quantity of energy that is provided to the Earth. The properties of the TSI variability are critical for understanding the cause of the irradiation variability and its expected influence on climate variations. A deterministic property of TSI variability can provide information about future irradiation variability and expected long-term climate variation, whereas a non-deterministic variability can only explain the past.This study of solar variability is based on an analysis of two TSI data series, one since 1700 A.D. and one since 1000 A.D.; a sunspot data series since 1610 A.D.; and a solar orbit data series from 1000 A.D. The study is based on a wavelet spectrum analysis. First, the TSI data series are transformed into a wavelet spectrum. Then, the wavelet spectrum is transformed into an autocorrelation spectrum to identify stationary, subharmonic and coincidence periods in the TSI variability.The results indicate that the TSI and sunspot data series have periodic cycles that are correlated with the oscillations of the solar position relative to the barycenter of the solar system, which is controlled by gravity force variations from the large planets Jupiter, Saturn, Uranus and Neptune. A possible explanation for solar activity variations is forced oscillations between the large planets and the solar dynamo.We find that a stationary component of the solar variability is controlled by the 12-year Jupiter period and the 84-year Uranus period with subharmonics. For TSI and sunspot variations, we find stationary periods related to the 84-year Uranus period. Deterministic models based on the stationary periods confirm the results through a close relation to known long solar minima since 1000 A.D. and suggest a modern maximum period from 1940 to 2015. The model computes a new Dalton-type sunspot minimum from approximately 2025 to 2050 and a new Dalton-type period TSI minimum from approximately 2040 to 2065.