This paper focuses on the impulsive orbital pursuit–evasion game (OPEG) with limited action sets for the pursuer and evader. Initially, a mathematical model is developed by combining game theory and orbital dynamics, forming a finite-round impulsive OPEG problem. The problem is then formulated as a bilateral optimization problem, employing a minimum-maximum optimization index based on terminal distance. To tackle this problem, an algorithm based on game tree search is designed, enabling the determination of the optimal pursuit–evasion strategy with limited action sets. Additionally, we explore the influence of the initial pursuing orientation on OPEG. The optimal initial pursuit orientation is analytically derived using relative motion dynamics under uncontrolled conditions. Furthermore, considering factors such as the initial status of the pursuit spacecraft, initial relative distance, transfer time, and maneuverability, the impulsive OPEG problem with limited action sets is numerically solved using game tree search. The findings of this study showcase the efficacy of game tree search in addressing impulsive OPEG problems with limited action sets. The study also demonstrates that the initial pursuing orientation selection at the start of the game plays a crucial role in increasing the success rate of pursuit. The research findings of this study have important implications for future practical engineering applications.

This paper discusses the modeling and solving of orbital pursuit–evasion games (OPEGs) under J ₂ perturbation. The optimal long-range maneuver method under J ₂ perturbation is designed, and it is proved that the effect of eccentricity can be ignored when transfer times and the Δ V 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 J ₂ perturbation are then carefully derived, with long-time OPEG ( J ₂ 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 J ₂ 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.