A natural physical approach to the analysis of the structure of closed gravitating systems has been formulated in the scope of classical mechanics. The approach relies on the interrelation between densities of nested spheres inscribed in the circular orbits of the system bodies. An empirical law has been defined for the evolution of closed gravitating systems differing in mass, time scale and distance from the ground-based Observer. The gravitating systems undergo modifications and evolve from their initial state, namely, a gas-and-dust formation of almost constant density over the entire volume, to a certain terminal phase of the process when the system structure becomes similar to the planetary system (like the Solar system) where almost all the gravitating mass is concentrated in the vicinity of the system center of gravity. Using the proposed method of nested spheres, it is possible to reveal for the gravitating system the character of radial distribution of matter density in the system symmetry plane, quantitatively evaluate the density of medium containing the gravitating system under consideration, and assess the current phase of the system evolution. The research results have led us to a conclusion that introduction into the scientific practice of such an entity as “dark matter” has no physical background since it is based on a wrong interpretation of an “unordinary” distribution of star orbital velocities in galaxies.

"Advanced Problems in Mechanics (APM 2017)", International Conference (45; 2017; St. Petersburg, Russia). Proceedings of the XLV Summer School-Conference "Advanced problems in mechanics (APM 2017)" [Электронный ресурс] / Russian Academy of Sciences, Institute for Problems in Mechanical Engineering ; Peter the Great St. Petersburg Polytechnic University. — Электрон. текстовые дан. (1 файл : 49,8 МБ). — St. Petersburg, 2017. — Загл. с титул. экрана. — Текст на англ. яз. — Электронная версия печатной публикации. — Свободный доступ из сети Интернет (чтение, печать, копирование). — Adobe Acrobat Reader 7.0. — <URL:http://elib.spbstu.ru/dl/2/k17-24.pdf>. — <URL:http://doi.org/10.18720/SPBPU/2/k17-24>.