Mean Orbital Elements of a Near-Circular Orbiting Artificial Satellite due to the Earth's Zonal Potentials

Abstract

The short and long periodic perturbations and secular perturbation due to the geopotentials of degree J2 and J3 which affect orbital elements of a near-circular satellite are obtained by the analytical method. The singular points due to a small denominator e in the perturbation equations can be excluded using one of the methods introduced by Taff(1985), which substitutes es = esinω, ec = ecosω and l = ω+M for the orbital elements e, ¥ø and M. We determined the mean orbital elements of the meteorological satellite NOAA-10 using the Walter(1967)'s iterative procedure and compared with Brouwer's mean orbital elements determined at NASA. The mean orbital elements a, i and Ω are consistent with those of NASA but the mean orbital elements e, Ω and M have some deviations from those of NASA. According to the our results, it is not suitable for the polar orbiting satellites to use the Taff's proposal for excluding the singular points, which substitutes e, Ω and M by es = esin(Ω+ω) and L = Ω+ω+M.