Assessment of dynamical models for transitioning from the Circular Restricted Three-Body Problem to an ephemeris model with applications

Abstract

While the Circular Restricted Three-Body Problem (CR3BP) provides useful structures for various applications, transitioning the solutions from the CR3BP to a higher-fidelity ephemeris model while maintaining specific characteristics remains non-trivial. An analytical approach is leveraged to provide additional insight on the perturbations that are present in an ephemeris model. For the Earth–Moon CR3BP, pulsation of the Earth–Moon distance and solar gravity are identified as key components contributing to the additional accelerations, where patterns are illustrated through simplified mathematical relationships and graphics. Utilizing these findings, capabilities and limitations of two intermediate models, the Elliptic Restricted Three-Body Problem and the Bi-Circular Restricted Four-Body Problem, are assessed within the context of transitioning from the CR3BP to a realistic ephemeris model. A sample transition process for Earth–Moon L2 halo orbits is provided, leveraging the insight from the proposed analytical approach.