In this work, the nutation momentum acting upon the Earth from the Moon's perigee mass that has not been taken into account in the Earth's precession-nutation theory was revealed. This missing momentum exhibits itself in the so-called "local latitude variation" with the Chandler's period. The results of our work raise the question of updating the Earth's precession-nutation theory and revising some postulates of the time service, astronomy, geophysics, satellite navigation, etc.
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 gasand-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.
Numerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial distribution of material bodies constituting the cluster. In solving the problem, the possibility of interbody collisions was taken into account, the collisions being assumed to be absolutely inelastic. Forces external to the body cluster under consideration were ignored. Among all the internal force factors acting within the cluster, only the gravitational interaction was taken into account. The total mass of all the gravitating bodies of the cluster was assumed to remain constant during the entire evolution. The Cauchy problem with natural initial conditions was considered. To check the process of solution, the so-called rotation curve was used which represents the current radial distribution of orbital velocities of the cluster bodies. The numerical analysis showed time variations of the model cluster rotation curve and, particularly, the fact that the rotation curve horizontal section is only a short moment in evolution of the gravitating bodies cluster. The results obtained within the scope of classical mechanics show that it is possible to represent all the rotation curve variations for the observed galaxies without appealing to the hypothesis of non-observable gravitating "dark matter".
Term "gravitational constant" was for the first time introduced more than 200 years ago, and since that time attempts have been made to refine its value. As per the materials of Committee on Data for Science and Technology (CODATA), all indirect measurements of the "gravitational constant" obtained by various research groups exhibit in the SI system equality of two first decimals and spread in subsequent decimals. We have analyzed this situation by using the torsion balance mathematical model. This paper shows that this situation might be explained by solving the direct metrological problem, namely, calculation of the necessary measurement accuracies of each of the torsion balance parameters from the preset accuracy of the "gravitational constant" value. Decimal-by-decimal analysis of the torsion balance sensitivity, jointly with the CODATA data, has lead us to the assumption that all the variety of the "gravitational constant" values was obtained at experimental setups without appropriately planning the final result accuracy.
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