Ballistic gravity-assist trajectory search by analytical reachability assessment pruning

This paper presents an exact analytical formulation for assessing post–gravity-assist reachability in three-dimensional space under ballistic flyby constraints. By extending prior two-dimensional geometric feasibility analyses to fully three-dimensional configurations using vector algebra, the proposed method avoids case-dependent trigonometric constructions and provides a closed-form feasibility certification of post-flyby reachable velocity domains. This analytical characterization enables rigorous determination of whether a target position is dynamically admissible under exact ballistic gravity-assist constraints, independent of trajectory construction or encounter epoch sampling. Building on this analytical reachability assessment, a reachability-driven pruning framework is introduced as an application to support gravity-assist trajectory exploration. In this framework, dynamically infeasible candidates are eliminated a priori based on analytical reachability conditions, while only candidates confirmed reachable are subjected to a subsequent local one-dimensional time-matching refinement to enforce ephemeris consistency. This reachability-driven strategy enables systematic identification of families of feasible ballistic gravity-assist opportunities within prescribed time windows and sampling resolutions, which could provide broad structural insight into admissible transfer opportunities under full ephemeris models, rather than an unconditional global optimum. Numerical examples demonstrate the effectiveness of the proposed analytical reachability formulation and its utility for early-phase mission analysis, mission window identification, and assessment of ballistic gravity-assist trajectories.