Models and Strategies for J₂-Perturbed Orbital Pursuit–Evasion Games

This paper discusses the modeling and solving of orbital pursuit–evasion games (OPEGs) under J₂ perturbation. The optimal long-range maneuver method under J₂ perturbation is designed, and it is proved that the effect of eccentricity can be ignored when transfer times and the ΔV budgets are fixed. It is discovered that when the inclination between the initial and target orbit is equal and is between 10° and 25°, the whole maneuver process can be simplified to a fixed-inclination transfer. Subsequently, a long-term OPEG model is provided under the assumption of fixed inclination, zero eccentricity, and impulsive thrust. Winning conditions of OPEGs under J₂ perturbation are then carefully derived, with long-time OPEG (J₂ dominated) and short-time OPEG (traditional) separated, and typical tactics of both sides formulated and verified. These studies are further extended to the “Arrival time matching game” for maintaining/avoiding resonant arrival time under J₂ perturbation, and the advantages and disadvantages of both sides are analyzed. The models and strategies obtained in this paper can be potentially used in practical applications of OPEGs, especially for evaders that have low thrust–weight ratios and are weak in traditional short-term OPEGs.