New dynamical system for circular satellites relative motion

In this work, a new perturbed dynamical system to describe the satellites relative motion is derived considering that the gravitational attractive force is generated by the continued fraction potential. In this context, the parameter of continuation fraction creates an additional force which is the source of perturbation for motion. Aiming to find a simple and precise mathematical model to characterize this motion while maintaining high accuracy results, a new circular linear perturbed system is also derived under the effect of this parameter. Furthermore, the perturbed linear dynamical system of satellites relative motion is studied, along with finding the conditions of stable and periodic solutions. Finally, these solutions are calculated and their graphical simulation is introduced. We emphasize that the new proposed system could be applied in space rendezvous missions aiming at getting precise descriptions of satellites relative motion.