Small eccentricity satellite orbits: Linear perturbations

Abstract

The well known linearized theory of satellite motion given by Kaula in 1966 has proven to be very useful in categorizing the nature of gravitational perturbations associated with the mass distribution of the planet that defines the satellite orbits. The secular and periodic perturbations produced by zonal, tesseral and sectorial gravity coefficients can be readily identified. In fact, the expressions for secular variations and amplitude of some periodic variations are well represented by the theory. Nevertheless, potential problems exist when the eccentricity is small, for example, because of the use of classical orbit elements in Kaula's theory. This paper examines an alternate theory, based on nonsingular elements for small eccentricity, which is the typical case for most Earth observing and geodetic satellites.