Digital 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 material bodies intra-cluster distribution. In solving the problem, the possibility of interbody collisions was taken into account. The collisions were assumed to be inelastic. Non-gravitational force impacts external with respect to the body cluster in question were ignored. Among all the internal force factors acting within the cluster, only the gravitational impact was taken into account. To check the process of solution, the so-called “rotation curve” was used, which demonstrates the current radial distribution of the cluster body orbital velocities. The Cauchy problem was considered. The issues of defining natural initial conditions for the cluster bodies were touched upon. Conditions for commencement of rotation of gravitating bodies comprising the cluster about the common center of mass were investigated. The computer 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 speed curve plateau characterizes the current redistribution phase of the cluster matter. This means that it is not necessary to consider the hypothesis of the “non-material gravitating dark matter” as well as to modify the classical Newton law on the gravitational interaction between two material bodies for the purpose of explaining the invariance of radial distribution of star linear velocities in some of the observed clusters.
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