Pursuit-evasion barrier of two spacecrafts under minute continuous radial thrust in coplanar orbit

The pursuit-evasion game of two coplanar near-earth orbiters is investigated based on orbital element equations. Under the assumption of radial, minute, continuous and variable thrust for both spacecrafts, the condition of barrier existence is established, which takes into account of thrust index. The optimum control parameter of the variable thrust is deduced based on the condition of the existence of the barrier, together with the expressions of the barriers in terms of eccentricity and argument. In numerical examples, the barrier curves of the eccentricity are obtained under given capture radius and it is shown that at the end of the game, the evader is right above or below the pursuer.