Singh Jagadish, Ahmad Shitu Muktar
Department of Mathematics, Faculty of Physical Science, Ahmadu Bello University, Zaria, Nigeria.
Sci Rep. 2022 Feb 18;12(1):2819. doi: 10.1038/s41598-022-06328-y.
This paper studies the position and stability of equilibrium points in the circular restricted three-body problem under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear [Formula: see text] and two triangular [Formula: see text]. It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for [Formula: see text] and unstable for [Formula: see text], where [Formula: see text] is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.
本文研究了在质心为辐射状且形状为非均匀扁球体的情况下，受科里奥利力和离心力小扰动影响的圆形限制性三体问题中平衡点的位置和稳定性。可以看出，与经典限制性三体问题一样，存在五个平动点，三个共线的[公式：见正文]和两个三角形的[公式：见正文]。还可以看出，三角形点不再与质心构成等边三角形，而是与连接质心的直线构成简单三角形。进一步观察到，尽管存在所有扰动，但共线点仍然不稳定，而三角形点对于[公式：见正文]是稳定的，对于[公式：见正文]是不稳定的，其中[公式：见正文]是取决于上述参数的临界质量比。值得注意的是，科里奥利力的小扰动、辐射以及两个质心的非均匀扁率都有使系统不稳定的趋势。还进行了它们的数值检验。
