Stability of Triangular Equilibrium Points in BiER4BP under the Radiation and Oblateness Effect of Primaries Applied for Sun–Earth–Moon System

IF 1.1 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS
A. Chakraborty, A. Narayan
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引用次数: 0

Abstract

The frame work of this study is the bi-elliptic restricted four body problem, where the largest primary \({{m}_{1}}\) is assumed to be a radiating body and the other two massive bodies \({{m}_{2}}\) and \({{m}_{3}}\) are assumed to be oblate spheroids. The problem is restricted in the sense that the fourth body is assumed to be of infinitesimal mass. The goal of the paper is to study the so-called equilibrium points by generalizing R3BP to a non-coherent but highly practical R4BP model. The location of the planar equilibrium points according to this model is numerically studied for Sun–Earth–Moon system. The position of the triangular equilibrium points are also obtained analytically and graphically compared with numerically obtained values. Both the graphical and analytical studies confirms the high dependence of the position of the triangular equilibrium points on radiation pressure, however the collinear points were found to be less affected. The collinear points were found to be more affected by the oblateness of the second primary. The triangular equilibrium points were found to be stable for the third and fourth order resonance cases when the mass ratio is less than equal to a critical mass ratio. This critical mass ratio is also found to be dependent on the radiation pressure and phase angle \({{\theta }_{0}}\). The transition curve in the (\(\mu - {{\epsilon }_{2}}\)) plane is plotted to find the value of \({{\epsilon }_{2}}\) for which the motion near triangular equilibrium points become unstable.

Abstract Image

应用于日-地-月系统的主星辐射和扁平效应下 BiER4BP 三角平衡点的稳定性
本研究的框架工作是双椭圆受限四体问题,其中最大的主({{m}_{1}}/)被假定为辐射体,其他两个大质量体({{m}_{2}}/)和({{m}_{3}}/)被假定为扁球体。问题的限制在于假设第四个天体的质量是无限小的。本文的目的是通过将 R3BP 推广到非连贯但非常实用的 R4BP 模型来研究所谓的平衡点。根据这一模型,对日-地-月系统的平面平衡点位置进行了数值研究。三角形平衡点的位置也是通过分析得到的,并用图形与数值进行了比较。图形研究和分析研究都证实了三角形平衡点的位置与辐射压力的高度相关性,但碰撞点受到的影响较小。研究发现,平行点受二次原电池扁平度的影响较大。当质量比小于等于临界质量比时,三角形平衡点在三阶和四阶共振情况下是稳定的。这个临界质量比还取决于辐射压力和相位角 \({\theta }_{0}}\)。绘制了 (\(\mu - {{\epsilon }_{2}}\))平面内的过渡曲线,以找到三角形平衡点附近的运动变得不稳定的 \({{\epsilon }_{2}}\)值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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