Constraint-Sensitive Pre-Analysis in Gravity-Assist Trajectory Design Structural Identification of Sensitivity and Robustness Prior to Numerical Dispersion

This deposit presents a methodological framework for early-stage analysis of gravity-assist trajectories, focused on identifying structural sensitivity and robustness prior to full numerical dispersion and optimization. The work does not propose new physical laws, propulsion concepts, or trajectory optimization techniques. Instead, it introduces a constraint-sensitive pre-analysis schema that makes implicit structural features of gravity-assist encounters explicit, including coupling conditions, phase alignment, anisotropic sensitivity, and robustness regions. The framework is demonstrated using two historical Earth gravity-assist cases with complementary failure shapes: Cassini–Huygens (1999), where multiple trajectory solutions with comparable ΔV and arrival energy exhibited sharply different robustness to timing perturbations, revealing fragile versus robust optima within the primary trajectory design space. Galileo (1990, 1992), where trajectories were numerically robust with respect to mission feasibility, yet exhibited unanticipated sensitivity in secondary dimensions such as radiation exposure, thermal conditions, and spacecraft–environment interaction, demonstrating fragility orthogonal to the primary optimization objectives. In both cases, standard numerical tools ultimately identified these sensitivities correctly, but only after extensive dispersion analysis and post hoc interpretation. The contribution of this work is to show that key sensitivity structures can be identified earlier using geometric and coupling considerations alone, enabling improved decision hygiene, clearer risk interpretation, and more targeted use of computational resources. The framework is intended as a complementary analytical instrument rather than a replacement for existing methods. Its value lies in discriminating failure shapes, clarifying where numerical robustness may mask structural fragility, and improving early-stage reasoning about complex, phase-dependent dynamical systems. This deposit is part of the broader body of work associated with the Copeland Resonant Harmonic Formalism (Ψ-formalism), which functions here as a reference and continuity identifier across related analytical publications. No claims of new physics, experimental validation, or engineering implementation are made. Keywords gravity assist trajectory design sensitivity analysis robustness phase alignment B-plane targeting orbital mechanics mission design methodology constraint-sensitive analysis structural pre-analysis License: Copeland Resonant Harmonic Formalism (CRHC v1.0) This work is licensed under the Copeland Resonant Harmonic Copyright (CRHC v1.0). Attribution is required for all uses. Collaboration, academic discussion, and non-commercial use are permitted. Commercial use, resale, or incorporation into proprietary systems is not permitted without explicit written permission from the author. Derivative works must preserve attribution and must not remove or alterbthe stated license terms.