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E. Griv, M. Gedalin (Dept. of Physics, Ben-Gurion University, Israel), E. Liverts (Dept. of Mechanical Engineering, Ben-Gurion University, Israel)
Planetary formation is thought to start with dust particle settling to the central plane of a rotating nebula to form a thin dust layer. During the early evolution of such a rotationally flattened disk it is believed that the dust particles coagulate into numerous kilometer-sized rocky planetesimals. In this investigation we use the Boltzmann kinetic and Poisson equations to study the evolution of the self-gravitating disk of randomly colliding planetesimals. We examine the possibility of obtaining the law of planetary distances on the basis of the concept of gravitational Jeans-type instability in sufficiently flat rapidly rotating systems (cf. Lin and Shu's idea which already led to promising results in the problem of the origin of spiral structure of galaxies). It is shown that as a result of an almost aperiodic Jeans instability of small-amplitude gravity disturbances the disk is subdivided into numerous dense fragments. These can eventually condense into the planetary sequence with mathematical regularity in the spacing formulated empirically by Titius and Bode.
In addition, we analyze the evolution of many-body models (N-body models) of self-gravitating disks of planetesimals by direct integration over a time span of the equations of motion of randomly colliding particles. We show that in agreement with the theory, during the first rotation, Jeans-unstable perturbations break the system into several macroscopic fragments. Finally, after 2-3 rotations the quasi-stable system of the very massive sun and several planets is developed. Interestingly, the distances of the planets from the sun are described rather well by the Titius--Bode rule.
Acknowledgements. This work was performed under the auspices of the Israel Science Foundation, the Israel--U.S. Binational Science Foundation, and the Israeli Ministry of Immigrant Absorption.
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The author(s) of this abstract have provided an email address for comments about the abstract: griv@bgumail.bgu.ac.il
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Bulletin of the American Astronomical Society, 34
© 2002. The American Astronomical Soceity.