A new approach to derive a formation flying model in the presence of a perturbing body in inclined elliptical orbit: relative hovering analysis

In this paper, the modeling of satellites' relative motion has been investigated in the presence of a third body and with consideration of main-body's obliquity. The proposed model is based on non-simplified perturbed relative dynamic equations of satellites and combined with perturbed target orbit. From a new point of view, in the present work, the relative dynamic equations of a disturbing body in an elliptic inclined three-dimensional orbit are derived using Lagrangian mechanics. The Main-body Center based Relative Motion (MCRM) model has been introduced for validating the presented model. Furthermore, for relative hovering analysis, the parameters such as the fuel consumption, proper positioning of follower, minimum and maximum values of required thrust, and the proper timing for performing the hovering operation based on the target satellite's position have been addressed in this study. Also, the effects of eccentricity and inclination of the third body on the abovementioned parameters have been studied. The findings of this research show the effect of obliquity on the relative hovering. In this study, several useful practical examples related to the Earth-Moon system have been provided for analyzing the abovementioned factors. Furthermore, the hybrid IWO/PSO algorithm has been applied to find the desired hovering location, and also the minimum and maximum amounts of thrust.