Checking the possibility of determining the relative orbits of stars rotating around the center body of the Galaxy

Abstract The results of observations of selected stars orbiting the central body of our Galaxy, which, according to the latest data, has a mass of about 4 million of solar mass, are considered. Using the methods of observation and processing of binary stars used at the Pulkovo Observatory and the published exact relative positions of the star-central body obtained with the Keck and VLT telescopes, we checked the possibility of determining the preliminary orbits of the above objects in some cases from observations covering sufficient short arc in relation to the turnover period. Examples are the stars S02 and S102 with published positions and the graphical data for S27 and S4711. We attempted to calculate the assumed relativistic effects in accordance with the orbital elements obtained by Pulkovo methods. In this case, the estimates of the O–C errors for these orbits turned out to be comparable with the O–C errors for the orbits published by the Keck and VLT observers, in some cases about several milliarcseconds. The theoretical relativistic parameters also turned out to be of the same order of value with the results of these authors.