Rotational wobble effects on equilibrium structure and Floquet stability in the circular restricted three body problem

The circular restricted three-body problem (CR3BP) is a fundamental model in celestial mechanics, typically formulated under the assumption that the gravitational fields of the primaries are time independent in the rotating frame. In realistic systems, however, celestial bodies may exhibit rotational variability, particularly when their mass distribution deviates from spherical symmetry, leading to a time-dependent reorientation of the gravitational field. In this work, we extend the classical CR3BP by incorporating a small periodic rotational wobble of the smaller primary, modeled as a first-order perturbation associated with orientation-dependent gravitational effects. The resulting system becomes non-autonomous, and classical libration points are replaced by time-dependent equilibrium configurations whose displacement is obtained analytically using perturbation theory. Linear stability is investigated using Floquet analysis, revealing systematic but moderate modifications to the stability spectrum near libration regions. Numerical simulations for the Sun–Earth system demonstrate that rotational wobble induces persistent modulation of motion and leads to cumulative trajectory deviations over time. When expressed in physical units, these deviations can reach magnitudes of 10 5 –10 6 m over extended integration periods, depending on the wobble amplitude. These results highlight rotational wobble as a physically motivated mechanism for introducing time-dependent perturbations into restricted three-body dynamics, with potential implications for high-precision trajectory modeling and long-duration space missions.