An aircraft exposed to illumination by a tracking radar is considered and the problem of determining an optimal planar trajectory connecting two prespecified points is addressed. An analytic solution yielding the trajectory that minimizes the radar energy reflected from the target is derived using the Calculus of Variations. The solution is shown to exist only if the angle θ _f , formed by the lines connecting the radar to the two prespecified trajectory end points, is less than 60°. In addition, expressions are given for the path length and optimal cost.