Abstract

This work investigates the dynamics of the modified circular restricted three-body problem. The triaxial shape of the massive body, a modified gravitational parameter, quantum correction effect, radiation pressure and small perturbations in the Coriolis and centrifugal forces are all taken into account. The impact of the considered parameters in the equilibrium points and their linear stability is studied. Some new significant results in the critical mass parameter, \(\mu _c\) , are observed in the presence of perturbing parameters. It is found that the critical mass parameter, \(\mu _c\) , increases in the presence of modified gravitational potential, and it slightly decreases due to the quantum correction effect. Analytical construction of periodic orbits around the collinear equilibrium points is performed. Additionally, analysis of the impact of perturbations on the shape of these periodic orbits is conducted.

中文翻译：

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具有量子校正和修正引力势的摄动受限三体问题的动力学

摘要

这项工作研究了改进的圆形受限三体问题的动力学。大质量物体的三轴形状、修正的引力参数、量子校正效应、辐射压力以及科里奥利力和离心力的小扰动都被考虑在内。研究了平衡点中所考虑参数的影响及其线性稳定性。在存在扰动参数的情况下，观察到临界质量参数\(\mu _c\)的一些新的重要结果。研究发现，临界质量参数\(\mu _c\)在修正引力势的存在下增加，并由于量子校正效应而略有下降。围绕共线平衡点进行周期轨道的解析构造。此外，还分析了扰动对这些周期性轨道形状的影响。