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The orbital evasion problem is getting increasing attention because of the increase of space maneuvering objects. In this paper, an escape-zone-based optimal orbital evasion guidance law for an evading spacecraft on near circular reference orbit is proposed against multiple pursuing spacecraft with impulsive thrust. The relative reachable domain is introduced first and approximated as an ellipsoid propagating along the nominal trajectory under the short-term assumption. The escape zone for the impulsive evasion problem is presented herein as a geometric description of the set of terminal positions for all the impulsive evasion trajectories that are not threatened by the maneuvers of pursuers at the maneuver moment. A general method is developed next to calculate the defined escape zone through finding the intersection of two relative reachable domain approximate ellipsoids at arbitrary intersection moment. Then, the two-sided optimal strategies for the orbital evasion problem are analyzed according to whether the escape zone exists, based on which the escape value is defined and used as the basis of the proposed orbital evasion guidance scheme. Finally, numerical examples demonstrate the usefulness of the presented method for calculating escape zone and the effectiveness of the proposed evasion guidance scheme against multiple pursuing spacecraft. 1

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