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This paper is devoted to binary stars belonging to the class of eclipsing-variable systems. Photometric and spectroscopic analysis of eclipses allows us to determine geometric parameters of the orbit and physical characteristics of stellar components as well as inclinations of stellar equators to the orbital plane. Estimations of inclinations can be obtained from measurement of the Rossiter-McLaughlin effect, which is discussed using examples of some eccentric binaries with an anomalous apsidal effect. Our task is to find the complete spectrum of solutions of the equation of apsidal motion, depending on the inclinations of the polar axes of the components to the orbital one for these systems, based on their individual spectroscopic and photometric observational data. The matrix of solutions allows us to select those pairs of polar inclinations that provide agreement with the observational apsidal period.

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We present the results of numerical simulation on the probability of formation of a Hypervelocity Star (HVS) in the scenario of dynamic capture of a close binary system by the central black hole in the Galaxy and on the probability of its survival in the strong tidal field in the vicinity of the black hole. The results have been obtained for a series of pericentric distances. We applied a two-level numerical simulation implemented at first in the framework of the three-body problem used for evaluation of the HVS ejection velocity and then as an

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