Fast calculation method for mission opportunities in orbital interception and rendezvous problems

This paper proposes a fast calculation method to solve all mission opportunities for orbital interception and orbital rendezvous under the impulse-magnitude constraint. Different from the existing search methods, the proposed method does not need to solve Lambert’s problem in the whole process. Three cases are considered for either departure time or transfer time being free, or both being free. For fixed departure time, the feasible windows of transfer time are obtained by solving a single-variable nonlinear equation only of terminal true anomaly. Similarly, for fixed interception (or rendezvous) time, the feasible windows of departure time are obtained. For free departure time and free transfer time, all mission opportunities are obtained by using a one-dimensional search strategy. The hyperbolic-transfer and the multiple-revolution cases are also analyzed. Numerical results show that the proposed method is superior to the typical pork-chop plot method and the two-dimensional launch window method in computational time.