A Frequency-Based Hierarchy of Dynamical Models in Cislunar Space: Leveraging Periodically and Quasi-Periodically Perturbed Models

Abstract

Understanding the applicability of different dynamical models within cislunar space is a useful yet challenging problem. The current work constructs a hierarchy of dynamical models leveraging a common rotating reference frame that accommodates multiple dynamical models. In such a formulation, the Higher-Fidelity Ephemeris Model (HFEM) is approximated as quasi-periodically perturbed model with multiple frequencies in addition to the autonomous Circular Restricted Three-Body Problem (CR3BP) dynamics. Then, different intermediate models are evaluated within the hierarchy in terms of the types and numbers of the incorporated frequencies. The analysis focuses on three main topics. Firstly, coherent solar gravity modeling is properly defined with analytical and visual criteria that serve as useful metrics in assessing intermediate models. Secondly, two periodically perturbed models, i.e., Quasi Bi-Circular Problem (QBCP) and Hill Restricted Four-Body Problem (HR4BP), are investigated within the common rotating reference frame. The capabilities and limitations of these two models within the hierarchy between the CR3BP and HFEM are examined, focusing on the similarities and differences in the models. Thirdly, novel quasi-periodically perturbed models are introduced. Leveraging the insight from Hill's lunar theory, two models are designed denoted as In-plane Quasi-Hill Restricted Four-Body Problem (I-QHR4BP) and Out-of-plane Quasi-Hill Restricted Four-Body Problem (O-QHR4BP). These two models selectively introduce the eccentricity between the Earth-Moon system and the inclination of the lunar orbit with respect to the Earth ecliptic plane, respectively, in addition to the HR4BP. The global characteristics of these new models are analyzed within the common rotating reference frame. The capabilities of multiple models within the model hierarchy are analyzed for two sample transition cases from the CR3BP to HFEM: L2 Lagrange point and the L2 9:2 synodic halo orbit.