Drag-perturbed bounded relative trajectories in low Earth orbit: A semi-analytical approach

摘要

Although recent numerical studies have demonstrated the possibility to obtain entire families of bounded relative trajectories in the Earth zonal problem, it is still unclear whether such initial conditions can cope with mismodeled dynamics such as atmospheric drag, luni-solar attraction, and solar radiation pressure. In the attempt to deal with the dynamical perturbations caused by the Earth's atmosphere, this paper offers a semi-analytical approach that combines previous work developed by the authors with newly found analytical relationships describing the effects of drag on the nodal and sidereal periods of a satellite. It is shown that both of these quantities change in a secular fashion due to the variations in the semi-major axis of spacecraft. Nevertheless, bounded relative motion can be guaranteed over the course of several days by either initializing the satellites on the same invariant curve of a stroboscopic mapping or by design of appropriate ballistic coefficients. These conclusions are supported by numerical simulations that prove the feasibility of our approach for spacecraft formations in low Earth orbit.