The design of interplanetary trajectories often involves a preliminary searchfor options later refined/assembled into one final trajectory. It is this broadsearch that, often being intractable, inspires the international event calledGlobal Trajectory Optimization Competition. In the first part of this chapter,we introduce some fundamental problems of space flight mechanics, buildingblocks of any attempt to participate successfully in these competitions, and wedescribe the use of the open source software PyKEP to solve them. In the secondpart, we formulate an instance of a multiple asteroid rendezvous problem,related to the 7th edition of the competition, and we show step by step how tobuild a possible solution strategy. In doing so, we introduce two newtechniques useful in the design of this particular mission type: the use of anasteroid phasing value and its surrogates and the efficient computation ofasteroid clusters. We show how the basic building blocks, sided to theseinnovative ideas, allow designing an effective global search for possibletrajectories.
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