Lambert-Free Solution of Multiple-Gravity-Assist Optimization Problem

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Lambert-Free Solution of Multiple-Gravity-Assist Optimization Problem

Gavira-Aladro, Miguel / Bombardelli, Claudio

A new method to find optimized multiple-gravity-assist (MGA) interplanetary trajectories that does not require the solution of Lambert’s problem is presented. The method, applicable to MGA sequences with ballistic transfer arcs and flybys, exploits Godal’s hyperbolic locus of incoming and outgoing velocities connecting the different trajectory legs combined with the $v_{\infty}$ sphere flyby constraint. The intersection between the two loci, when it exists, can be used to find feasible candidate solutions for each interplanetary trajectory segment and can be obtained analytically after solving a quartic equation. A time-of-flight compatibility condition can then be introduced that replaces the classical $C_{3}$ -matching constraint for locating properly phased transfer arcs, whereby opening the door to a very significant improvement in computational efficiency. The implementation of the method and its applicability to interplanetary trajectory optimization and moon tours are discussed in detail using representative test cases.