Dynamical Structures and Trajectory Families in the J2 – Extended Neptune–Triton System

Abstract

The Neptune–Triton system represents one of the most dynamically compelling targets for future deep-space exploration, yet the trajectory design infrastructure needed to support a long-duration orbital mission remains largely undeveloped. This thesis addresses that gap by constructing a systematic dynamical framework for identifying, classifying, and evaluating trajectories suitable for a Neptune–Triton tour mission, using tools drawn from nonlinear dynamical systems theory. The analysis is conducted within the planar Circular Restricted Three-Body Problem (CR3BP), formulated in the rotating barycentric frame of the Neptune–Triton system and extended to include Neptune's J2 oblateness perturbation as a correction to the gravitational potential. Large trajectory sets are generated across selected energy levels and analyzed using three complementary tools. Poincaré maps characterize the geometric structure of phase space, frequency analysis identifies resonance families through spectral decomposition of trajectory time histories, and linear stability analysis evaluates periodic-orbit candidates via the monodromy matrix and Floquet multipliers. All numerical workflows are implemented within ORBIT, a computational framework developed as part of this work that integrates trajectory generation, phase-space mapping, spectral analysis, stability evaluation, and data visualization into a unified and reproducible pipeline. The analysis identifies trajectory families supporting Neptune-bounded operations, system-wide touring, bottleneck-crossing transfer into the Triton region, and Triton-bounded terminal orbits. These families are synthesized into a conceptual tour architecture demonstrating how the natural phase-space structure of the Neptune–Triton system can be directly leveraged for mission design. The results establish a reproducible dynamical foundation for future trajectory optimization, higher-fidelity modeling, and mission concept development in the Neptune–Triton system.