Precision Analytical Calculation of Geodynamical Effects on Satellite Motion

Abstract

A new analytical method for calculating satellite orbital perturbations due to different disturbing forces is developed. It is based on the Poincare method of small parameter but takes advantages of modern high-performance computers and of the tools of computer algebra. All perturbations proportional up to and including the 5th-order of small parameters are obtained. The method can precisely calculate the effects of all geodynamical forces on satellite motion given by the most up-to-date IAU and IERS models, such as non-central Earth gravity potential, precession and nutation of the geoequator, polar motion and irregularities in the Earth's rotation, effect of ocean and solid Earth tides, pole tide, and secular variations of gravity coefficients. Numerical tests prove the method's accuracy to be equivalent to 1–2 cm when calculating positions of high altitude geodetic satellites (like ETALON), and/or of GLONASS navigational spacecraft. The accuracy is stable over 1 year at least and comparable to that of the best tracking measurements of satellites. Positions of low altitude geodynamical satellites (like STARLETTE) by the analytical method are calculated to an accuracy of about 70 cm over a month's interval. The method is developed for future use in GLONASS/GPS on-board ephemeris computation where it can improve the current scheme of their flight control.