Study of Stokes Drag and Radiation Pressure in the Restricted Four-Body Problem with Variable Mass

IF 1.1 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS
Krishan Pal, Amit Mittal, Rajiv Aggarwal
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Abstract

This manuscript illustrates the existence, locations, and stability of equilibrium points under the effect of Stokes drag in the restricted four-body problem (R4BP) with variable mass when all the primaries are source of radiation. The motion of the fourth body of negligible mass (infinitesimal mass) is effected by the motion of the primaries, and its motion is perturbed by the radiation pressure and Stokes drag. All the primaries are established at the vertices of an equilateral triangle and known as Lagrangian configuration. The dynamics of an infinitesimal body has been studied under the influences of radiation pressure of all the primaries with Stokes drag and variable mass. Jeans’ law and space time transformations of Meshcherskii have been used to formulate the equations of motion of the infinitesimal body. We have numerically investigated the existence and locations of the equilibrium points in the theoretical ranges of the parameters. The numerical investigations delved that all the equilibrium points are non-collinear, the collinear equilibrium points do not exist due to the presence of Stokes drag. Further, we have observed that all the equilibrium points are unstable for all values of the parameters considered. Moreover, the regions of motion have been drawn for different values of the parameters, i.e., for the radiation parameters \({{q}_{i}} (0 < {{q}_{i}} < 1),\) \(i = 1,2,3\), the proportionality constant \(\alpha (0 < \alpha \leqslant 2.2)\) occurs due to Jeans’ law, the mass parameter \(\mu (0 < \mu \leqslant 1{\text{/}}3)\), and for the dissipative constant \(k (0 < k < 1)\). This model has novelty in the sense that we have studied this problem first time by combining the concept of Stokes drag in the restricted four-body problem, considering all primaries as the source of radiation and the fourth body having variable mass. This paper is applicable in various di-sciplines of celestial mechanics as space mission planning, satellite dynamics, and fundamental astrodynamics research. Finally, we have justified the importance of our model by applying it to an appropriate stellar system.

Abstract Image

质量可变的受限四体问题中的斯托克斯阻力和辐射压力研究
本手稿说明了在质量可变的受限四体问题(R4BP)中,当所有基体都是辐射源时,平衡点在斯托克斯阻力作用下的存在、位置和稳定性。质量可忽略不计(质量无限小)的第四体的运动受主体运动的影响,其运动受辐射压力和斯托克斯阻力的扰动。所有基体都位于等边三角形的顶点,称为拉格朗日构型。在带有斯托克斯阻力和可变质量的所有基元的辐射压力的影响下,研究了无穷小体的动力学。Jeans' law 和 Meshcherskii 的时空变换被用来制定无穷小体的运动方程。我们对理论参数范围内平衡点的存在和位置进行了数值研究。数值研究发现,所有的平衡点都是非共线的,由于斯托克斯阻力的存在,共线平衡点并不存在。此外,我们还观察到,在考虑的所有参数值下,所有平衡点都是不稳定的。此外,我们还绘制了不同参数值下的运动区域,即辐射参数 \({{q}_{i}}(0 < {{q}_{i}} < 1),\)\(i=1,2,3),比例常数(\alpha (0 < \alpha \leqslant 2.2)\),质量参数(\mu (0 < \mu \leqslant 1{/text{/}}3)\),以及耗散常数(\k (0 < k < 1)\)。这个模型的新颖之处在于,我们首次将斯托克斯阻力的概念结合到受限四体问题中进行了研究,将所有原初体视为辐射源,第四体质量可变。本文适用于天体力学的多个学科,如太空任务规划、卫星动力学和基础天体动力学研究。最后,我们将模型应用于一个适当的恒星系统,从而证明了模型的重要性。
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来源期刊
Astronomy Reports
Astronomy Reports 地学天文-天文与天体物理
CiteScore
1.40
自引率
20.00%
发文量
57
审稿时长
6-12 weeks
期刊介绍: Astronomy Reports is an international peer reviewed journal that publishes original papers on astronomical topics, including theoretical and observational astrophysics, physics of the Sun, planetary astrophysics, radio astronomy, stellar astronomy, celestial mechanics, and astronomy methods and instrumentation.
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