Optimal Trajectory Design For Space Interception

Space technology becomes more and more important to politics, economy and military, as an ultimate guarantee of nation's power. Space interception is the key of space technology to protect space security and strategic dominance. Although it is complicated in technology, space-based interception, which can intercept a target in any low, middle and high orbit, has more strategic value than ground-based interception. Compare with same orbit interception and coplanar interception, space-based noncoplanar direct ascend interception has some advantages, such as covert purpose, the capability of intercepting targets in noncoplanar orbits. Moreover, a space-based platform with multiple interceptors can not only completely destroy the function of constellation, made up of targets in multiple orbit planes, but also save cost. Since noncoplanar interception will transfer out of initial plane, it consumes lots of fuel consequentially. Because fuel constraint is a crucial fact to design the transfer trajectory, optimal trajectory considering fuel constraint is a primary problem for noncoplanar interception.A calculated method of transfer angle considering interceptor initial velocity was presented. The relationship between transfer time of conic trajectory and semi-major axis was set up based on Lambert theorem. The effect of vacant focus location to shape of elliptical transfer trajectory and transfer angle to transfer time and eccentricity was analyzed using geometry. A method determining conic transfer trajectory between two points in space by a fixed semi-major axis was given. An arithmetic solving conic transfer trajectory by iterating semi-major axis with a specified launch time and transfer time was given. Some simulation proved that this arithmetic was valid to elliptic and hyperbolic transfer trajectory.For single impulse multiple-revolution interception, the relationship between characteristic velocity (?v) and semi-major axis of transfer trajectory was considered, It was proposed that the optimal solution actually is the less fuel trajectory among 2N+1 trajectories satisfying time constraint, but not the minimum fuel trajectory (MFT). A derivate formula between ?v of single impulse interception and semi-major axis was derived. As the single impulse was dissembled into two impulses with the same direction, a interceptor could consume the redundant transfer time by costing multiple-revolution on some specified elliptic orbit, and intercept a target on MFT in the rest transfer time. It was proved that ?v of this interception coincide with that of minimum fuel transfer in geometry. The existence of solutions was studied. Some simulations show that this intercept can save fuel and the existence of solutions is more loosely restrictive on the length of transfer time than single impulse multiple-revolution interception.A calculating method of minimum characteristic velocity curve for a fixed launch point to a target orbit was interpreted. Camparing the two minimum characteristic velocity curves of coplanar and noncoplanar interception study, it was proved that Hohmann transfer, which was the optimal solution of coplanar interception with transfer angle 180°, cost large mount of fuel in noncoplanar interception. The effect of the initial orbital elements of interceptor to minimum characteristic velocity curve is analyzed. A method of computing noncoplanar intercept range based on minimum characteristic velocity curve was proposed. Furthermore, arithmetics of calculating the defence range for lacking-one-revolution interception, single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception were given, respectively. Some simulations prove that single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception can cover the target into the defence range by more revolutions and launch interceptor immediately, but lacking-one-revolution interception often has to change the launch point to intercept the target.Contour of characteristic velocity for lacking-one-revolution interception can be calculated directly by using conic Lambert arithmetic. On the other hand, using the same process to draw contour of characteristic velocity, there will create singularities for single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception, whose solutions are not existed when transfer time is not long enough. Two methods calculating contour of characteristic velocity for single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception was presented, by using the solutions of lacking-one-revolution interception to replace the singularities. Comparing the launch conditions, although both single impulse multiple-revolution interception and impulse dissembled multiple-revolution interception can utilize intercept range well, the latter saves fuel. Finally, an example proves that the intercept trajectory, designed by contour of characteristic velocity for impulse dissembled multiple-revolution interception, can intercept targets of a constellation distributing on noncoplanar orbits.