On the Determination of the Orbital Elements of a Satellite from the Position and Velocity Components

摘要

Orbital problems of satellite geodesy are based on the assumption that the geocentric orbital elements, giving the geocentric position of the satellite being observed, are known for the moment of observation. The determination of such elements, however, is possible only if the observed topocentric quantities were, with sufficient accuracy, reduced to geocentric ones. The reduction assumes, however, that the position of the satellite stations with respect to the center of mass of the earth is known. This, however, is not known and the determination of the geocentric positions is substantially the main problem of present-day geodesy. In the case of natural celestial bodies, relatively far from the basic body, inaccuracies in correcting for the parallax practically do not influence the solution. But in the case of near artificial earth satellites, these inaccuracies are not negligible. The present paper analyzes from this aspect the case when the orbital elements are calculated from one position (three coordinates) and three velocity components. (Author)