Numerical Assessment of a Frequency-Based Hierarchy for the Cislunar Domain

A frequency-based hierarchy of dynamic models in cislunar space is introduced in the recent literature, where multiple models between the circular restricted three-body problem (CR3BP) and a higher-fidelity ephemeris model (HFEM) are investigated within a common rotating reference frame. Intermediate models selectively introduce perturbations associated with specific frequencies, enabling a systematic assessment of their influence on dynamic structures. This study conducts an extensive numerical investigation across cislunar space to complement the hierarchy and evaluate the suitability of various intermediate models. A total of six intermediate models, rendering (quasi-)periodically forced systems within the common frame, are analyzed. The numerical analysis examines key CR3BP structures, including Lagrange points and periodic orbits, and compares their counterparts in the intermediate models and the HFEM. Frequency-domain analysis is leveraged to assess capabilities and limitations of each model. The findings supply a criterion for selecting appropriate intermediate models, improving i) the characterization of perturbations inherent in higher-fidelity models and ii) transitions between models within the cislunar domain.