Relative hovering analysis about an elliptical perturbed orbit with consideration of dynamic air drag and oblate earth

Accurate model in close and far distance hovering operation is a crucial and important issue due to considerable perturbation effects in long time flights. In this paper a new close/far distance hovering model is proposed with consideration of non-simplified perturbed target in low earth orbit (LEO) that suitable for long-term accurate mission simulation. New equations are precisely extracted to express the dynamics of relative hovering for a perturbed elliptical reference orbit without any simplification, by employing all zonal harmonics perturbation of the Earth's oblateness and air drag force. These perturbation terms have a significant impact on operations in long-term hovering operation in low earth orbits. Thus, applying these terms in the equations can help to investigate the problem more precisely. To validate the presented model, another model has been built as an Earth-Centered-Inertial (ECI) based Relative Motion (ERM) model. After validating the presented model, several useful examples have been provided for analyzing the effect of several parameters such as the amount of fuel consumption, optimal positioning of the follower satellite, minimum and maximum required thrust. Furthermore, the location of the follower satellite will be determined using a hybrid Invasive Weed Optimization/Particle Swarm Optimization (IWO/PSO) algorithm, with the aim of finding minimum and maximum required thrust during the operation. High speed of convergence, not to be located in local minimums, and success in implementing of complex problems, are the advantages of the proposed algorithm.