Long-term effects of main-body's obliquity on satellite formation perturbed by third-body gravity in elliptical and inclined orbit

A new non-simplified model of formation flying is derived in the presence of an oblate main-body and third-body perturbation. In the proposed model, considering the perturbation of the third-body in an inclined orbit, the effect of obliquity (axial tilt) of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J ₂ perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion (MCRM) model. Finally, the importance of the main-body's obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body's obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit (PCO) formations. (paper)