# Origin of the solar system

- Received:

DOI: 10.1007/BF00898829

- Cite this article as:
- Prentice, A.J.R. The Moon and the Planets (1978) 19: 341. doi:10.1007/BF00898829

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## Abstract

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. H_{2}O, NH_{3}, CH_{4},...) and later H_{2}, 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 10^{4}*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.

*M(r)*the mass interior to radius

*r*causes the envelope to become very centrally condensed (i.e. drastically lowers its moment-of-inertia coefficient

*f*) 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 radius

*R*

_{e}=R

_{0}, corresponding to the orbit of Neptune, the addition of any further mass to the equator causes the envelope to discontinuously withdraw to a new radius

*R*

_{e}>R

_{0}, leaving behind the circular belt of gas at the Kepler orbit

*R*

_{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 radius

*R*

_{1}, and so on. If the collapse occurs homologously the sequence of orbital radii

*R*

_{n}of the system of gaseous Laplacian rings satisfy the geometric progression

*m*denotes the mass of the disposed ring and

*M*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 that

*R*

_{n}/R

_{n}+1 matches the observed mean ratio of 1.73, we typically find

*f*=0.01 and that the rings of gas each have about the same mass, namely 1000

*M*

_{⊕}of the solar material. Detailed calculations which take into account non-homologous behaviour resulting from the changing mass fraction of dissociated H

_{2}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.