论文标题
在参数化的纽顿后形式主义中，针对共面和循环三体问题的共线和三角形解决方案
Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism
论文作者
论文摘要
本文研究了参数化后纽顿（PPN）形式主义中的共面和循环三体问题，我们专注于以Eddington-Robertson参数$β$和$γ$为特征的一类完全保守的理论。结果表明，仍然可以存在共线均衡构型和三角形构型，每个构型都是对牛顿后均衡构型的概括。共线构型可以以任意质量比，$β$和$γ$存在。另一方面，PPN三角构型取决于非线性参数$β$，但不取决于$γ$。对于任何$β$的任何值，当且仅当三个有限质量相等或两个有限质量的测试质量轨道时，就可以等边构型。对于一般的质量案例，PPN三角形不像牛顿后案例那样等边。还表明，牛顿重力$ l_1 $，$ l_2 $和$ l_3 $的Lagrange点的PPN位移取决于$β$和$γ$，而这些$ l_4 $和$ l_5 $仅依赖于$β$。
This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters $β$ and $γ$. It is shown that there can still exist a collinear equilibrium configuration and a triangular one, each of which is a generalization of the post-Newtonian equilibrium configuration in general relativity. The collinear configuration can exist for arbitrary mass ratio, $β$, and $γ$. On the other hand, the PPN triangular configuration depends on the nonlinearity parameter $β$ but not on $γ$. For any value of $β$, the equilateral configuration is possible, if and only if three finite masses are equal or two test masses orbit around one finite mass. For general mass cases, the PPN triangle is not equilateral as in the post-Newtonian case. It is shown also that the PPN displacements from the Lagrange points in the Newtonian gravity $L_1$, $L_2$ and $L_3$ depend on $β$ and $γ$, whereas those to $L_4$ and $L_5$ rely only on $β$.
