The mathematical model and algorithms for calculating the position of GLONASS satellites by means of their broadcast ephemeris is presented in the paper. The algorithms are based on the generalized problem of two fixed centers. One of the advantages of the analytical solution obtained from the generalized problem of two fixed centers is the fact that it embraces perturbations of all orders, from the second and also part ly from the third zonal harmonics (Aksenov, 1969). GLONASS broadcast ephemeris - provided every 30 minutes - contain satellite position and velocities in the Earth fixed coordinate system PZ-90.02 (ICD, 2008), and acceleration due to luni-solar attraction. The GLONASS Interface Control Document recommends that a fourth order Runge-Kutta integration algorithm shall be applied. In the Department of Geomatics (AGH UST) a computer program has been established for fitting position and velocity of GLONASS satellites using their broadcast ephemeris. Intermediate GLONASS satellite orbits are calculated consider ing also the second and third zonal harmonics in the gravitational potential of the Earth. In this paper results of the analytical integration of the equation of the motion of the GLONASS satellites compared to the numerical solution are provided., Władysław Góral and Bogdan Skorupa., and Obsahuje bibliografické odkazy
For some purposes, such as for accurate orbit prediction, it seems to be useful to replace the large fields of harmonic coefficients, in the Earth gravity field models by a limited set of the lumped geopotential coefficients, tailored to the individual orbits. The lumped values absorb the orbital information to a high degree for the particular order of the harmonics, and a small set of the lumped coefficients, written for various orders, should be sufficient to describe the orbit as perturbed by the Earth. Some problems and questions concerning the application of this method for orbits similar to those of SEASAT or TOPEX are discussed and answered.