A statistical approach to investigate the formation of the solar system

Abstract

A model describing a gravitational effect into a forming gravitating and rotating cosmological body based on the statistical theory has been proposed. In this model, the forming cosmological bodies are shown to have fuzzy contours and are represented by spheroidal forms. The proposed theory starts from the conception for forming a spheroidal body from a gas-dust protoplanetary nebula. The distribution functions together with the mass densities and gravitational field potentials for an immovable spheroidal body as well as rotating one have been derived. This work also considers problem of gravitational condensation of a gas-dust protoplanetary cloud with a view to protoplanet formation in its own gravitational field. It is known a protoplanetary system behavior can be described by Jeans’ equation in partial derivations relative to a distribution function. The paper derives a more general evolutional equation which generalizes the Jeans’ equation. Since the determination of gravitational potential (and mass density) is the main problem of statistical dynamics for protoplanetary system, then the work shows how this task of protoplanetary dynamics can be solved on the basis of the proposed spheroidal body theory. Within the framework of this theory, the distribution function of a specific angular momentum of a rotating uniformly spheroidal body has been found. As the specific angular momentums are averaged during a conglomeration process, the specific angular momentum of a protoplanet for a planetary system is found in this paper. The proposed theory is also applied to investigate formation of planets in our solar system. As a result, a new law for the solar system planetary distances (which generalizes the well-known Schmidt law) is derived in this paper. It has been shown that the new law gives a very good estimation of observable planetary distances in the solar system.