The presented algorithms of computation of orbital elements and positions of GLONASS satellites are based on the asymmetric variant of the generalized problem of two fixed centers. The analytical algorithm embraces the disturbing acceleration due to the second J2 and third J3 coefficients, and partially fourth zonal harmonics in the expansion of the Earth’s gravitational potential. Other main disturbing accelerations – due to the Moon and the Sun attraction – are also computed analytically, where the geocentric position vector of the Moon and the Sun are obtained by evaluating known analytical expressions for their motion. The given numerical examples show that the proposed analytical method for computation of position and velocity of GLONASS satellites can be an interesting alternative for presently used numerical methods.
Aksenov E.P., Grebenikov E.A., Demin V.G. (1963). The generalized problem of motion about two fixed centers and its application to the theory of artificial Earth satellites, Soviet Astron. – AJ, Vol. 7, No. 2, American Institute of Physics, 276-283.
Aksenov E.P. (1977). Theory of motion artificial Earth’s satellites (in Russian), Nauka Press, Moscow, p.360.
Demin V.G. (1970). Motion of an artificial satellite in an eccentric gravitation field, translated and published as NASA Technical translation, TT F-579, Wshington D.C. (Translation from Dvizheniye Iskusstvennogo Sputnika v Netsentral’nom Pole Tyagoteniya, Nauka Press, Moscow, 1968).
GLONASS Interface Control Document (ICD), Edition 5.1, Moscow, 2008.
Golikov A. R. (2012). THEONA – a numerical-analytical theory of motion of artificial satellites of celestial bodies, Cosmic Research, Vol. 50, No. 6, 449-458.
Góral W., Skorupa B. (2012). Determination of intermediate orbit and position of GLONASS satellites based on the generalized problem of two fixed centers, Acta Geodynamica et Geomaterialia, Vol. 9, No. 3 (167), 283–290.
Lukyanov L. G., Emelyanov N. V., Shirmin G. I. (2005). Generalized problem of two fixed centers or the Darboux-Gredeaks problem, Cosmic Research, Vol. 43, No. 3, 186-191.
Van Flandern T., Pulkkinen K. (1979). Low precision formulae for planetary positions, Astrophysical Journal Supplement Series, 41, 391-411.