Analysis of multiple gravity-assist solution space based on feasible domains

Multiple gravity assist (MGA) is a widely used and highly effective technique in deep space exploration; however, its solution space remains insufficiently characterized. This paper characterizes the MGA solution space by the orbital energy, the total time of flight (TOF), and the MGA opportunity based on a semi-analytical method. Firstly, the gravity-assist state feasible domain and a semi-analytical method for assessing MGA opportunities are introduced. Then, the solution space, defined in terms of orbital energy, total TOF, and MGA opportunity, is mapped from these feasible domains. The interdependence among the three dimensions reveals intrinsic structural features within the solution space. Finally, representative rendezvous and interstellar mission scenarios are examined. Results indicate that MGA opportunities for a given sequence can be classified into windows and cycles based on their repeating periods. A higher initial energy yields more and wider windows, while a stricter ending energy constraint results in fewer and narrower windows. Numerical computation shows that the Earth–Jupiter–Saturn and Earth–Jupiter–Neptune sequences exhibit cycle periods of 20 years and 12 years, respectively. A comprehensive catalog of MGA sequences with varying energy requirements and opportunities is provided. A potential fast interstellar mission under a realistic configuration is identified with launch in 2038 and fuel consumption of 73.1 kg.