At the second post-Newtonian (2PN) order, the secular pericenter precession ${\dot{\omega }}^{2\mathrm{PN}}$ of either a full two-body system made of well-detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computing ${\dot{\omega }}^{2\mathrm{PN}}$ in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration ${\mathit{A}}^{2\mathrm{PN}}$ , and also an indirect part arising from the self-interaction of the 1PN acceleration ${\mathit{A}}^{1\mathrm{PN}}$ in the orbital average accounting for the instantaneous shifts induced by ${\mathit{A}}^{1\mathrm{PN}}$ itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity e. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericenter precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

中文翻译：

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鉴于可能的未来测量方法，重新审视2PN周边中心进动

在第二个牛顿后阶（2PN），世俗性的中心点进动 ${\dot{\omega }}^{2\mathrm{PN}}$ 迄今为止，已经通过各种方法对由可分离大小的可分离的非旋转单极质量构成的完整两体系统和由围绕固定中心质量运行的点粒子组成的受限两体系统进行了分析。我们通过分析计算提供我们的贡献 ${\dot{\omega }}^{2\mathrm{PN}}$ 通过显式计算两个2PN加速度引起的直接贡献，用椭圆形元素的变化方法来摄动 ${\mathit{一种}}^{2\mathrm{PN}}$ 以及由1PN加速度的自相互作用引起的间接部分 ${\mathit{一种}}^{\mathrm{1个}\mathrm{PN}}$ 在轨道平均中解释了由瞬时引起的瞬时位移 ${\mathit{一种}}^{\mathrm{1个}\mathrm{PN}}$ 本身。对于点粒子和完整的两体情况，都可以直接获得显式公式，而无需重复简化偏心率e的假设。运动方程的两个不同的数值积分证实了我们对直接和间接进动的分析结果。水银和某些二元脉冲星产生的影响值在测量/约束其中心点进动方面面临着当今实验精度水平。还考虑了BL Lac对象OJ 287中的超质量二元黑洞。与文献中出现的一些结果进行了比较。