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Rotational wobble effects on equilibrium structure and Floquet stability in the circular restricted three body
M Javed Idrisi1, M Shahbaz Ullah2, Worku Tenna3
1Centre for Material and Applied Sciences, Manav Rachna University, Faridabad, Haryana, 121004, India.
Scientific Reports
|July 17, 2026
Summary
Celestial mechanics: rotational wobble in the circular restricted three-body problem (CR3BP) creates time-dependent dynamics. This perturbation causes significant trajectory deviations, impacting space mission modeling.
Area of Science:
- Celestial mechanics
- Astrodynamics
- Perturbation theory
Background:
- The circular restricted three-body problem (CR3BP) traditionally assumes time-independent gravitational fields for primaries.
- Realistic celestial bodies can have rotational variability, especially with non-spherical mass distributions, causing time-dependent gravitational reorientation.
Purpose of the Study:
- To extend the CR3BP by incorporating rotational wobble of the smaller primary as a perturbation.
- To analytically determine time-dependent equilibrium configurations and investigate their stability.
- To assess the impact of rotational wobble on trajectory dynamics and deviations.
Main Methods:
- Modeling rotational wobble as a first-order perturbation in the CR3BP.
- Analytical derivation of time-dependent equilibrium configurations using perturbation theory.
- Floquet analysis for investigating the linear stability of the perturbed system.
- Numerical simulations of the Sun-Earth system to observe trajectory modulations and deviations.
Main Results:
- The CR3BP with rotational wobble becomes non-autonomous, replacing classical libration points with time-dependent configurations.
- Floquet analysis shows moderate modifications to the stability spectrum near libration regions.
- Numerical simulations reveal persistent motion modulation and cumulative trajectory deviations, reaching 10^5-10^6 m over extended periods for the Sun-Earth system.
Conclusions:
- Rotational wobble is a physically motivated perturbation mechanism for restricted three-body dynamics.
- This effect introduces time-dependent perturbations with potential implications for high-precision trajectory modeling.
- The findings are relevant for long-duration space missions requiring accurate orbital predictions.
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