The development of projective metric method for analyzing star positions

In this work, the projective geometry method was used for analyzing star clusters. When carrying out the calculation procedures, it was considered that non-linear distortion factors had been removed from the measured stars' coordinates. Determination of stars' proper motions is of great practical importance, as the inertial coordinate system relies on catalogues of star positions, and it is necessary to be aware of the stellar reference marks' time shift. In the practical part of the work, the breadboard simulation of the use of the proposed method for determining stars' proper motions is performed. At the same time, it is supposed that at 90"/mm breadboard image scale the absolute values of proper motions do not exceed 0.050" over a period of 50 years. As result, determined that the standard deviation of the calculated proper motions μ_α, μ_β from their true value is 0.0065 arcseconds for the first model (when the proper motions of the reference "stars" are negligible and equal to 0) and 0.0072 arcseconds or the second model (when the reference stars do have real proper motions). These values indicate the high accuracy of the used method.