Keywords
Restricted 3-body problem
Nonlinear dynamics
Orbital classification
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Abstract
In this paper, we examine the extent to which the circular restricted three-body problem provides a reliable framework for the orbital classification in the Earth-Moon-satellite system without explicitly integrating the gravitational influence of the Sun. To this end, we compared three dynamical models: the circular restricted three-body problem (CR3BP), the bicircular restricted four-body problem (BCR4BP), and an approximate formulation of the latter, denoted as BCR4BP-A. Trajectories were classified using qualitative and quantitative numerical methods according to their asymptotic behavior, including escape to infinity, bounded motion, and collision with a primary. The numerical results revealed substantial differences in orbital outcomes among the models, demonstrating that solar perturbations can significantly alter the predicted dynamical behavior. While the BCR4BP-A reproduced the main features of the full BCR4BP in the vicinity of the Earth-Moon region, solar effects became dominant for circumbinary orbits extending beyond approximately two lunar distances. A comparative analysis over a range of Jacobi constant values showed that, beyond this threshold distance, the CR3BP systematically overestimated the persistence of bounded motion, whereas the BCR4BP-A provided a more accurate description of escape and collision dynamics.
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