Abozaid Ahmed A, Radwan M, Ibrahim A H, Bakry A
Astronomy and Meteorology Department, Faculty of Science Al-Azhar University, Cairo, Egypt.
Astronomy and Space Science Department, Faculty of Science Cairo University, Cairo, Egypt.
Sci Rep. 2024 May 23;14(1):11764. doi: 10.1038/s41598-024-61821-w.
In this work, we investigate the dynamics of a spacecraft near two primary bodies. The massive body is considered to have a spherical shape, while the less massive one is elongated and modeled as a dipole. The dipole consists of two connected masses, one is spherical and the other is an oblate spheroid. The gravitational potential of the elongated body is determined by four independent parameters. To study the dynamics, we construct the equations of motion of a spacecraft with negligible mass under the effect of the current force model. The existence and locations of the equilibrium points are analyzed for various values of the system parameters. We found that the existence and locations of the points are affected by the system parameters. Also, we studied the linear stability of the equilibrium points. We found some stable collinear points when the oblateness parameter is negative, otherwise the points are not stable. We used the curves of zero velocity to identify the regions of allowed motion. Furthermore, we discussed the 2001 SN263 asteroid system and found some stable collinear points when the oblateness parameter is negative. In addition, the triangular points of the system are stable in a linear sense.
在这项工作中，我们研究了航天器在两个主天体附近的动力学。质量较大的天体被认为是球形的，而质量较小的天体是细长的，并被建模为一个偶极子。该偶极子由两个相连的质量体组成，一个是球形的，另一个是扁球体。细长天体的引力势由四个独立参数确定。为了研究动力学，我们构建了在当前力模型作用下质量可忽略不计的航天器的运动方程。针对系统参数的不同值，分析了平衡点的存在性和位置。我们发现平衡点的存在性和位置受系统参数影响。此外，我们研究了平衡点的线性稳定性。当扁率参数为负时，我们发现了一些稳定的共线点，否则这些点不稳定。我们利用零速度曲线来确定允许运动的区域。此外，我们讨论了2001 SN263小行星系统，当扁率参数为负时发现了一些稳定的共线点。另外，该系统的三角形点在线性意义上是稳定的。
