On the Principal Difficulties and Ways to Their Solution in the Theory of Gravitational Condensation of Infinitely Distributed Dust Substance

Abstract

The gravitational condensation problem of infinitely distributed substance is directly connected with gravitational instability problem. The linearized theory of gravitational instability leads to the well-known Jeans’ criterion. The main difficulty of Jeans’ theory is connected with a gravitational paradox: for an infinite homogeneous substance there exists no potential of gravitational field in accord with the Poisson equation. Since the classic gravitational theory did not give good solution of the gravitational condensation problem, the statistical theory for a cosmological body forming (so-called the spheroidal body model) has been proposed. In this model the forming cosmological bodies are shown to have fuzzy contours and are represented by spheroidal forms. This work considers a gas-dust protoplanetary cloud as a rotating and gravitating spheroidal body. The distribution functions and the mass densities for an immovable spheroidal body as well as rotating one have been derived. This work explains a slowly evolving process of gravitational condensation of a spheroidal body from an infinitely distributed substance. The equation for initial evolution of distribution function of a gas-dust protoplanetary cloud is derived. Because of the specific angular momentums are averaged during a conglomeration process, the specific angular momentum for a protoplanet in the protoplanetary cloud is found in this paper. As a result, a new law for planetary distances gives a very good estimation of observable planetary distances for our solar system