Teardrop hovering formation for elliptical orbit considering J₂ perturbation

On-orbit service (OOS) technologies, applied to provide essential maintenance to prolong the lifetime of spacecraft and to extend their function, have received widespread attention recently. The hovering formation, as one of the core technologies, enables the relative motion state between an active spacecraft and chief spacecraft within a specified range. In this study, we proposed a teardrop hovering formation, which is suitable for elliptical reference orbit with a J₂ perturbation. We formulated a mathematical model of the teardrop hovering formation maintained by the impulse control and presented a rapid method based on the state transition matrix. With the triangles of the three tangent lines solved by the rapid method, we estimated the envelope of the multi-loop hovering formation. Furthermore, we analyzed the influence of the reference orbital elements and formation parameters on the hovering formation by numerical simulations, which demonstrated the efficiency of the proposed method and provided a reference for the preliminary design of hovering formations.