On the determination of the position of an earth satellite in the geodetic coordinate system

Abstract

The present theory of the determination of the position of an Earth satellite from simultaneous measurements of the topocentric coordinates at 2 or more geodetic satellite points is not exact. The inaccuracy is caused by the fact that the measured topocentric coordinates of the satellite are defined in a system in which the directions of the axes are not exactly parallel to the directions of the corresponding axes of the geodetic system in which the coordinates of the satellite points are given; this difference in direction is not respected in the solution. The paper gives an exact solution of the problem. The concepts (4) of geodetic topocentric declination and geodetic hour angle of the satellite, i.e. the declination and hour angle in the geodetic reference system, are introduced. With these quantities the problem of determining the position of the satellite is then solved exactly. There always exist superabundant observations so that the method of least squares can be used. The procedure is outlined for the case of conditioned observations (suitable for 2 satellite geodetic points) and for the case of intermediate observations (suitable for >2 satellite geodetic points).