The Mücket-Treder-type potential was initially introduced to explain the discrepancy between Mercury’s observed perihelion advance and the computed value based on Newton’s law, but it can also be used for many astronomical situations as, for instance, the study of the very eccentric cometary orbits in the neighborhood of the Sun. In this paper we tackle the two-body problem in the Mücket-Treder post-Newtonian field from the particular standpoint of orbits stability. Starting from the equations of motion and first integrals written in standard polar coordinates, we apply McGehee-type transformations of the second kind. Then we depict the phase-space structure considering the foliations by the energy constant and the angular momentum constant. Various stability regions are found for each case.

最初引入了Mücket-Treder型势能来解释水星观测到的近日点推进与基于牛顿定律的计算值之间的差异，但是它也可以用于许多天文情况，例如研究非常偏心的彗星在太阳附近旋转。在本文中，我们将从轨道稳定性的特定角度出发，解决Mücket-Treder牛顿后场中的两体问题。从运动方程式和用标准极坐标编写的第一个积分开始，我们应用第二种McGehee型变换。然后我们通过能量常数和角动量常数描述了考虑叶面的相空间结构。在每种情况下都可以找到各种稳定区域。