This work analyzes the capturability of the true proportional navigation (TPN) guidance law applied in circular orbital pursuit-evasion, which is a new view compared to the prior method used in orbital pursuit-evasion. The saddle point is a rather difficult problem to resolve when the orbital pursuit-evasion problem is formulated as a zero-sum differential game. The research in this paper focuses on analyzing the capture capability of the pursuer and the escape capability of the evader. The relative motion equations for the line-of-sight (LOS) coordinate and the modified polar coordinate (MPC) system are united. Then, nonlinear transformation is used in the dynamic equations so as to acquire the relative motion equation. The optimal strategies of both satellites are determined and expression of the analytical capture-escape equation is proposed. The capture-escape region of an orbital pursuit-evasion game is defined. The simulation clearly shows the capture region of the pursuer, and the results are in agreement with the analysis. The results of the analytic capturability method proposed in this paper are visual and understandable, which means that it will be very convenient to use in analyzing capturability in orbital pursuit-evasion problems.

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