Important perturbations relating to station-keeping of the Global Positioning System of satellites

A compact algorithm for maintaining the longitude of node crossing of GPS satellites has been developed. Fundamental to proper change of velocity selection for orbit sustenance is a detailed knowledge of the long-term behavior of certain classical orbital elements. Analysis of the perturbations include secular effects of zonal harmonics, secular and long period terms due to the sun and moon, and resonant perturbations due to tesseral and sectorial harmonics. The algorithm is based on numerical solutions to three first-order differential equations representing the time variation of semi-major axis, right ascension of the ascending node and longitude of node crossing. These three equations are cast in nondimensional form and simultaneously integrated via a fourth-order Runge-Kutta scheme. Comparison to the Advanced Orbit Ephemeris Subsystem indicates excellent agreement with detailed predictions.