A Theory of Low Eccentricity Earth Satellite Motion

Earth satellite motion is considered from the point of view of periodic orbits and Floquet theory in the Earth's zonal potential field. Periodic orbits in the zonal potential are nearly circular, except near the critical inclination. The local linear solution near the periodic orbit includes two degenerate modes that locally mirror the global invariance to time and nodal rotation, at least in the zonal potential. Since the Earth's oblateness is included in the periodic orbit, perturbations generally begin at one part in 10(5), not one part in 10(3). Perturbations to the periodic orbit are calculated for sectoral and tesseral potential terms, for air drag, and for third body effects. The one free oscillatory mode of the periodic orbit is the eccentricity / argument of perigee analogues, and this can be extended past the first order in small quantities. There results a compact, purely numerical set of algorithms that may rival numerical integration in their accuracy, but have the usual "general perturbations" advantage of calculation directly at the time of interest, without having to perform a long propagation.