Spacecraft Dynamics and Control
Peer reviewed
Abstract
Abstract
This study evaluates the impact of varying zonal harmonics up to J4 on the stability around out-of-plane equilibrium points (OEPs) of the restricted three-body problem coupled with mass variations of the primaries. The motion and mass variations of the primaries are defined by the Gylden- Meshchersky problem (GMP) and the Unified Meshchersky Law (UML), respectively, with further assumptions that the shapes of the primaries are varying oblateness with zonal harmonics coefficients up to J4 terms. The non-autonomous and autonomized dynamical differential equations are stated. Further, four OEPs denoted by and which exists because of the mass variation factor are obtained, and are defined by the mass variation factor, mass parameter, and oblateness up to J4, were obtained for the autonomized and non-autonomous systems. The linear stability of motion around the OEPs is investigated and confirmed to be unstable points. A numerical application is conducted for a particle placed in the vicinity of PQ Pegasi. It is observed that there exists at least a positive root which renders the points unstable. Additionally, the orbits and orbital stability are studied to further elucidate the complex nature of motion around the OEPs by analyzing the kinds of orbits and new phase-space characterization using Poincaré Surfaces of Section (PSS). The PSS reveals distinct dynamical regimes: quasi-periodic, periodic, chaotic (bounded/unbounded), and divergent trajectories due to the impacts of zonal harmonics together with the influence of the mass variation factor. The corresponding PSS reveals stable orbits for the quasi-periodic and periodic trajectories while the straight-line divergent trajectories are orbitally unstable. This study is directly applicable to cataclysmic variable binaries and evolving planetary systems, while also providing a basis for mission design by identifying regular phase-space regions that could support stable parking orbits.
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@article{John2026Effects,
title = {Effects of zonal harmonics up to J4 on dynamics near out-of-plane points in the restricted three-body problem with variable masses},
author = {Taura Joel John and L Oni and Singh Jagadish},
journal = {African Research Reports},
year = {2026},
doi = {10.65221/0295},
url = {https://doi.org/10.65221/0295}
}FAQ
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