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arXiv · 2011.12533

Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries

Shounak De·Suparna Roychowdhury·Roopkatha Banerjee
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Abstract

The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perjés procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $ε$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $ε$ is also studied. The dynamics of the particle is studied using the Poincaré map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $ε$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $ε$.

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Shounak De, Suparna Roychowdhury, Roopkatha Banerjee. 2020-11-25. Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries. https://doi.org/10.1093/mnras%2Fstaa3733

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