Numerical simulation of evolution of a cluster of a finite number of gravitating bodies has been accomplished in the scope of classical mechanics taking into account accretion. The goal of the study was to reveal the basic characteristic phases of the intra-cluster distribution of material bodies. In solving the problem, the possibility of interbody collisions was taken into account. The collisions were assumed to be absolutely inelastic. Non-gravitational forces external with respect to the body cluster in question were ignored. Among all the internal force factors acting within the cluster, only the gravitational interaction was taken into account. To check the process of solution, the so-called “rotation curve” was used which presents a current radial distribution of orbital velocities of the cluster bodies. The Cauchy problem was considered. The issues of defining natural initial characteristics of the cluster bodies were touched upon. Conditions for commencement of rotation of gravitating bodies comprising the cluster about their common instantaneous center of mass were investigated. The numerical analysis showed that the characteristic shape of the “rotation curves” of stars of some galaxies depends only on the current configuration of the material body orbits. The “rotation curve” plateau characterizes the current redistribution phase of the intra-cluster matter. This means that invariance of radial distribution of star linear velocities in some of the observed clusters can be explained without considering the hypothesis of the “non-material gravitating dark matter” or modifying the classical Newton’s Law on gravitational interaction between two material bodies.
Comments: 14 Pages. Figs.8, russian
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