On the photogravitational R4BP when the third primary is an oblate/prolate spheroid
On the photogravitational R4BP when the third primary is an oblate/prolate spheroid
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DOI：
10.1007/s10509-015-2522-1
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发表时间：
2015-10
影响因子：
1.9
通讯作者：
Md Chand Asique;U. Prasad;M. Hassan;Md Sanam Suraj
中科院分区：
文献类型：
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作者：
Md Chand Asique;U. Prasad;M. Hassan;Md Sanam Suraj
本文研究了限制性四体问题，当限制性三体问题的三角平动点处的第三质点为扁球体时。第三原色3不影响主导原色m1和m2的运动。我们已经研究了m4的运动，它在三个原色mi，i= 1，2，3的影响下运动，但原色的运动不受无穷小质量m4的影响。本研究的目的是找到平衡点的位置和它们的稳定性。我们得到了三个共线和五个非共线平衡点。对于所有的质量参数，共线平衡点都是不稳定的。对于不同的质量参数和扁率因子，非共线点是稳定的。此外，我们还考虑了小推力航天器的具有无穷小质量的自主共面圆形限制性四体问题。人工平衡点是通过使用持续的低推力推进来创建的。结果表明，在没有推力的情况下，在第三原色附近存在不稳定的平衡点。此外，使用恒定的低推力，可以产生从自然平衡点移动的人工平衡点。进一步证明了在靠近第三准素性的一定区域内，这些点是稳定的。我们已经画出了零速度面，以确定可能允许的边界区域。我们观察到，随着扁率系数A值的增加，相应的可能的边界区域增加，其中颗粒可以自由地从一侧移动到另一侧。此外，对于不同的Jacobi常数C值，我们可以找到粒子可以在可能的允许分区中移动的边界区域。由于扁率系数和C值的变化，平衡点的稳定区域扩大。
The present paper deals with the restricted four-body problem, when the third primary placed at the triangular libration point of the restricted three-body problem is an oblate body. The third primarym3is not influencing the motion of the dominating primariesm1andm2. We have studied the motion ofm4, moving under the influence of the three primariesmi,i=1,2,3, but the motion of the primaries is not being influenced by infinitesimal massm4. The aim of this study is to find the locations of equilibrium points and their stability. We obtain three collinear and five non-collinear equilibrium points. The collinear equilibrium points are unstable for all the mass parameter. The non-collinear points are stable for different mass parameter and oblateness factor. Also, we have considered the autonomous coplanar circular restricted four-body problem with the infinitesimal mass as a low-thrust spacecraft. Artificial equilibrium points are created with the use of continuous low-thrust propulsion. The obtained results show that, in absence of thrust there are unstable equilibrium points close to the third primary. Also, using the constant low-thrust, the artificial equilibrium points can be generated, which move from the natural equilibrium points. Further, it is proved that in certain region closed to the third primary, these points are stable. We have drawn the zero velocity surfaces to determine the possible allowed boundary regions. We observed that for increasing values of oblateness coefficientA, the corresponding possible boundary regions increase where the particle can freely move from one side to another side. Further, for different values of Jacobi constantC, we can find the boundary region where the particle can move in possible allowed partitions. The stability regions of the equilibrium points expanded due to presence of oblateness coefficient and various values ofC.