Theona Theory of Relative Satellite Motion Flying in the Formation

Satellite formation flights are considered in the past few years as an effective alternative to large expensive satellites. The dynamics of relative satellite motion flying in the formation is complex and requires detailed study. This paper presents the approach based on the THEONA semi-analytical satellite theory and developed for orbits with arbitrary values of the eccentricity. The intermediary orbit corresponds to precise solution of the Generalized Problem of two fixed centers (GP2FC) which includes the effects of 2nd, 3rd and partially 4th zonal harmonics of the Earth gravity field. The osculating orbital elements (named Eulerian orbital elements) correspond to the intermediary orbit of GP2FC. The theory of relative perturbations of Eulerian orbital elements can take into account all essential perturbation effects. The analytical integrals use the special transcendental functions of orbital elements. Besides, THEONA allows predict the motion of both passive and active satellites. Therefore the proposed model considers all essential secular, long-periodic and short-periodic perturbations for these primary disturbances of relative satellite motion in a cluster.