Abstract The goal of the present manuscript is to determine the points of libration and their linear stability in the elliptic restricted synchronous three-body problem with a mass dipole model. The dipole system consists of two-point masses connected with a massless rod in a constant characteristic distance. To execute this study, we acquire the equations of motion of a spacecraft having negligible mass travelling in the system in which more massive primary is assumed to have a spherical shape, and the lesser one is irregular shaped and considered as a rotating mass dipole. The locations of the libration points are analyzed for various values of e, where e is the eccentricity of the orbit of one massive primary around other. Also, the stability of the libration points is investigated in linear sense, and it is observed that the collinear libration points are unstable while the non-collinear libration points are stable for the critical mass parameter μc. Further, we investigated the regions of motion around libration points.

中文翻译：

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具有质量偶极子模型的椭圆受限同步三体问题 (ERS3BP)

摘要本手稿的目标是确定具有质量偶极子模型的椭圆受限同步三体问题中的振动点及其线性稳定性。偶极子系统由以恒定特征距离与无质量杆连接的两点质量组成。为了执行这项研究，我们获得了在系统中运行的具有可忽略质量的航天器的运动方程，在该系统中，质量较大的初级被假定为球形，较小的初级为不规则形状并被视为旋转质量偶极子。针对不同的 e 值分析了振动点的位置，其中 e 是一个大质量初级围绕另一个的轨道偏心率。此外，在线性意义上研究了振动点的稳定性，并且观察到对于临界质量参数μc，共线的振动点是不稳定的，而非共线的振动点是稳定的。此外，我们研究了振动点周围的运动区域。