Relative satellite motion in a formation Original Research Article

The paper concerns the analytical description of the relative motion of satellites flying in a formation. We study the relative satellite motion without any restriction as to the plane of the satellite orbits as well as their eccentricity and inclination. In our analysis, we take into account the influence of geopotential and luni-solar perturbations. Two completely different methods for analytical calculation of differential perturbations are presented. The first method (Method A) contains analytical formulas for differential perturbations in orbital elements. In the second one (Method B) formulas for differential perturbations in the radial, transverse and normal components of the position vector were applied. The paper presents some numerical results of differential perturbations for different formations with the use of different force models. Exemplary calculations show a good agreement, on a level of 0.1%, between results obtained from the two methods.