Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..794k&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Mathematics
Logic
Scientific paper
The statistical theory for a cosmological body forming (so-called the spheroidal body model) has been proposed in [1]-[9]. Within the framework of this theory, bodies have fuzzy outlines and are represented by means of spheroidal forms [1],[2]. In the work [3], it has been investigated a slowly evolving in time process of a gravitational compression of a spheroidal body close to an unstable equilibrium state. In the papers [4],[5], the equation of motion of particles inside the weakly gravitating spheroidal body modeled by means of an ideal liquid has been obtained. Using Schwarzschild's and Kerr's metrics a consistency of the proposed statistical model with the general relativity has been shown in [6]. The proposed theory follows from the conception for forming a spheroidal body from protoplanetary nebula [7],[8]; it permits to derive the form of distribution functions for an immovable [1]-[5] and rotating spheroidal body [6]-[8] as well as their density masses and also the distribution function of specific angular momentum of the rotating uniformly spheroidal body [7],[8]. It is well-known there is not a statistical equilibrium in a gas-dust proto-planetary cloud because of long relaxation time for proto-planets formation in own gravitational field. This proto-planetary system behavior can be described by Jeans' equation in partial derivations relative to a distribution function [9]. The problem for finding a general solution of Jeans' equation is connected directly with an analytical expression for potential of gravitational field. Thus, the determination of gravitational potential is the main problem of statistical dynamics for proto-planetary system [9]. This work shows this task of proto-planetary dynamics can be solved on the basis of spheroidal bodies theory. The proposed theory permits to derive the form of gravitational potential for a rotating spheroidal body at a long distance from its center. Using the obtained analytical expression for potential of gravitational field, the gravitational strength (as well as angular momentum space function) in a remote zone of a slowly gravitational compressed rotating spheroidal body is obtained. As a result, a distribution function describing mechanical state of proto-planetary system can be found from the Jeans' equation. References: [1] Krot AM. The statistical model of gravitational interaction of particles. Uspekhi Sovremennoï Radioelektroniki (special issue "Cosmic Radiophysics", Moscow) 1996; 8: 66-81 (in Russian). [2] Krot AM. Use of the statistical model of gravity for analysis of nonhomogeneity in earth surface. Proc. SPIE's 13th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 5-9, 1999; 3710: 1248-1259. [3] Krot AM. Statistical description of gravitational field: a new approach. Proc. SPIE's 14th Annual Intern.Symposium "AeroSense", Orlando, Florida, USA, April 24-28, 2000; 4038: 1318-1329. [4] Krot AM. Gravidynamical equations for a weakly gravitating spheroidal body. Proc. SPIE's 15th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 16-20, 2001; 4394: 1271-1282. [5] Krot AM. Development of gravidynamical equations for a weakly gravitating body in the vicinity of absolute zero temperature. Proc. 53rd Intern. Astronautical Congress (IAC) - The 2nd World Space Congress-2002, Houston, Texas, USA, October 10-19, 2002; Preprint IAC-02-J.P.01: 1-11. [6] Krot AM. The statistical model of rotating and gravitating spheroidal body with the point of view of general relativity. Proc. 35th COSPAR Scientific Assembly, Paris, France, July 18-25, 2004; Abstract-Nr. COSPAR 04-A- 00162. [7] Krot A. The statistical approach to exploring formation of Solar system. Proc. European Geoscinces Union (EGU) General Assembly, Vienna, Austria, April 02-07, 2006; Geophysical Research Abstracts, vol. 8: EGU06-A- 00216, SRef-ID: 1607-7962/gra/. [8] Krot AM. The statistical model of original and evolution planets of Solar system and planetary satellities. Proc. European Planetary Science Congress, Berlin, Germany, September 18-22, 2006; Planetary Research Abstracts, ESPC2006-A-00014. [9] Krot A. On the principal difficulties and ways to their solution in the theory of gravitational condensation of infinitely distributed dust substance. Proc. XXIV IUGG General Assembly, Perugia, Italy, July 2-13, 2007; GS002 Symposium "Gravity Field", Abstract GS002-3598: 143-144.
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