The use of vector interpretation of projective geometry invariants for analyzing dynamic spatial images

Abstract

Copyright © SGEM WORLD SCIENCE (SWS) Society 2020. This work focuses on the use of projective geometry methods to determine star positions produced on the basis of positional observations. As is known, projective geometry studies invariant projective transformations. The main feature of projective geometry is the principle of duality, which adds elegant symmetry to many designs. While the properties of the figures that Euclidean geometry deals with are metric, but there are figures that can be converted into one another by movement while maintaining the metric properties, that is, there are more complex properties of geometric figures, it is necessary to use the corresponding methods. The method novelty lies in the fact that the technique allows analyzing images of multiple systems of reference star positions having independent proper motions. The use of this projective geometry apparatus may have a wide application for the study of multi-parameter dynamic coordinate systems and the construction of the considered clusters' models. In this paper, the described method was used to analyze images of star clusters. When performing calculational procedures it was believed that non-linear distorting factors had been removed from the measured stars' coordinates. The determination of stars' proper motions is of particular practical importance as the inertial coordinate system is based on star positions catalogues, and it is necessary to know benchmarks' shift in time. In the practical part of the work a breadboard modeling of using the proposed method for determining stars' proper motions was performed. At the same time, it is implied that at the breadboard images scale of 90″/mm the proper motions do not exceed 0.050″ in absolute value over a time interval of 50 years. It should be noted the analysis of the numerical experiments results allows to conclude that there is the possibility of defining proper motions of independent objects, included in space clusters, with the method based on the vector interpretation of the projective geometry invariants - projective coordinates.