К определению элементов орБиты спутника по положению и скорости

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 centre 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. Relations are derived (14, 15, 19, 22, 32, 38) giving the exactly geocentric elements. The way in which they differ from the well-known relations of classical celestial mechanics (10, 11, 17, 20, 24-26, 36), giving only certain approximate elements (we call them quasi-geocentric) consists in considering parameters defining the position of the origin and direction of the axes of the used reference system in the Earth's body. In the derivation we neglected expressions equal in order to the squares of the coordinates of the centre of the reference ellipsoid with respect to the centre of mass of the Earth and to the squares of the angles between the axis of rotation of the ellipsoid and the mean rotation axis of the Earth's inertia as well between the planes of the initial (Greenwich) astronomic and geodetic meridians. [ABSTRACT FROM AUTHOR]