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This research addresses the problem of formulating and analyzing the single vehicle path planning problem for radar exposure minimization. A single vehicle with given initial and final positions is exposed to a threat radar and optimal paths are sought. The calculus of variations and optimal control are applied to formulate optimal trajectories and numerical optimization algorithms are utilized to solve for the optimal paths. A sensitivity study of the objective cost is performed for flight against one radar utilizing two different geometries and several numerical approaches. A second threat radar is then included in the formulation and the optimal trajectory for fight between the radars is found for several symmetric threat radar geometries.