论文标题
鉴于可能的未来测量值
Revisiting the 2PN pericentre precession in view of possible future measurements of it
论文作者
论文摘要
在第二个北顿（Newtonian）（2pn）订单中，世俗的围地方进攻$ \dotΩ^\ mathrm {2pn} $是一个完整的两体系统，该系统由良好的非旋转单极质量制成，具有可比大小的良好型单极质量，并且是由固定的固定中心质量组成的限制性粒子组成的限制性粒子系统，该固定中的中央质量已与固定的中心质量组成，该方法是在分析的方法，该方法是在分析的，同样是一致相同的一定的方法。我们通过分析计算$ \dotΩ^\ mathrm {2pn} $以一种扰动的方式与椭圆形元素变化的方法通过明确计算2pn Acceleration $ {\ boldsymbol a}^\ mathrm and and Ind and An Ind and and and and and and and and and and的直接贡献，并概括了2pn加速$ { 1pn加速度$ {\ boldsymbol a}^\ mathrm {1pn} $在轨道平均值的瞬时偏移中，由$ {\ boldsymbol a}^\ mathrm {1pn} $本身引起的瞬时偏移。对于点粒子和完整的两体案例，可以直接获得明确的公式，而无需重复出现以简化对偏心$ e $的假设。运动方程式的两个不同数值整合证实了我们直接和间接进攻的分析结果。汞和某些二元脉冲星的产生效果的值面临着当今的实验精度水平，以测量/约束其围胎预次预读。也考虑了Bl lac对象中的超质量二进制黑洞OJ 287。与文献中出现的一些结果进行了比较。
At the second post-Newtonian (2PN) order, the secular pericentre precession $\dotω^\mathrm{2PN}$ 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 $\dotω^\mathrm{2PN}$ in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration ${\boldsymbol A}^\mathrm{2PN}$, and also an indirect part arising from the self-interaction of the 1PN acceleration ${\boldsymbol A}^\mathrm{1PN}$ in the orbital average accounting for the instantaneous shifts induced by ${\boldsymbol A}^\mathrm{1PN}$ 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 pericentre 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.
