Minimum-Time Interception with a Tangent Impulse

Abstract

The minimum-time coplanar interception problem with an upper-bounded tangent impulse for a nonmaneuvering target is studied. This problem requires the same flight time for two spacecraft and a transfer orbit tangent to the initial orbit. For a given impulse point, the transfer time for any conic orbit is a function only of the true anomaly of the target orbit; then the minimum-time orbit is determined by comparing all feasible solutions that are obtained by the secant method in the range of solution existence. Moreover, the true-anomaly range of the target orbit is derived for an upper bound on the magnitude of the tangent impulse. Finally, the global minimum-time solution with initial coasting time is obtained by numerical optimization algorithms. An example is given to apply the proposed technique for all the minimum revolution-number solutions at different impulse points and the global minimum-time solution.