Calculation Of Position And Velocity Of GLONASS Satellite Based On Analytical Theory Of Motion

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.