Semi-Analytical Assessment of Multiple Gravity-Assist Opportunities Based on Feasibility Domains

This paper proposes a semi-analytical method for multiple gravity-assist (MGA) opportunity assessment, which can judge the feasibility of MGA sequences and predict corresponding opportunities in terms of the relative phases between flyby planets. The proposed method features the feasible domains of gravity-assist states and the phase differences in MGA rather than focusing on a limited number of optimal solutions. First, the planet flyby departure and arrival conditions for successive gravity assist are analytically derived based on the planar circular model. Second, the feasible domain of gravity assist described by flyby parameters is established and pruned based on the conditions, and the corresponding relative phases between planets are calculated. Third, a MGA opportunity search algorithm via feasible domain is formulated to match the phase differences in the ephemeris. Lastly, the method is examined in two types of MGA missions: the rendezvous and flyby missions. The results from the semi-analytical approach can cover all optimized opportunities in the rendezvous mission and 94.44% optimized opportunities in the flyby mission under the accurate three-dimensional model. The results of the proposed semi-analytical method can serve as a good initial guess for further accurate trajectory optimization and provide reference for future MGA mission design.