State Space Analysis for The Relative Spacecraft Motion in Geopotential fields

The paper offers an approach to the relative orbital motion from a new point of view, which introduces a unified way to approach both the relative position and the relative velocity with the help of a single appropriately defined tensor operator. In the situation of an unperturbed gravitational field, this operator is written with respect to the eccentric anomaly associated to the deputy spacecraft inertial orbit. In the situation of the relative equatorial motion around an oblate planet, the operator may be written with the help of elliptic integrals. The six dimensional curve in the state space (position and velocity) is completely described with the help of the parametrization which emerges from the present approach. The applications are in orbit initialization, rendezvous and docking maneuvers, as well as it constitutes a basis for propagating nominal integrable orbits when dealing with perturbations. © 2011 by Daniel Condurache and Vladimir Martinusi.