Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem
Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem
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DOI：
10.1103/physrevd.93.084027
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发表时间：
2015-12
影响因子：
5
通讯作者：
Kei Yamada;H. Asada
中科院分区：
文献类型：
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作者：
Kei Yamada;H. Asada
继续在早期出版物中开始的工作[H. Asada，Phys.Rev.D80，064021（2009）]中，以解析方法研究了对三体问题的拉格朗日的等边三角形解的引力辐射反应。以前的工作是基于能量平衡的论点，这是足够的两体系统，因为自由度的数量（半长轴和偏心率在准开普勒的情况下，例如）等于运动常数，如总能量和轨道角动量。然而，在一个有三个（或更多）物体的系统中，自由度的数目多于运动常数的数目。因此，本文直接从引力辐射反作用力的角度来讨论三角系统的演化。利用拉普拉斯变换技术求解扰动运动方程。结果表明，当质量比满足牛顿稳定性条件时，由于辐射反应，三角形构型会发生热收缩，并通过增加轨道频率而保持平衡.还讨论了涉及第一后牛顿修正的长期稳定性。
Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D 80, 064021 (2009)], the gravitational radiation reaction to Lagrange’s equilateral triangular solution of the three-body problem is investigated in an analytic method. The previous work is based on the energy balance argument, which is sufficient for a two-body system because the number of degrees of freedom (the semimajor axis and the eccentricity in quasi-Keplerian cases, for instance) equals that of the constants of motion such as the total energy and the orbital angular momentum. In a system with three (or more) bodies, however, the number of degrees of freedom is more than that of the constants of motion. Therefore, the present paper discusses the evolution of the triangular system by directly treating the gravitational radiation reaction force to each body. The perturbed equations of motion are solved by using the Laplace transform technique. It is found that the triangular configuration is adiabatically shrinking and is kept in equilibrium by increasing the orbital frequency due to the radiation reaction if the mass ratios satisfy the Newtonian stability condition. Long-term stability involving the first post-Newtonian corrections is also discussed.