On the anomalous secular increase of the eccentricity of the orbit of the Moon

Kerr时空中一般束缚轨道轨道参数的长期演化

Secular evolution of orbital parameters for general bound orbits in Kerr spacetime

研究Kerr时空一般束缚轨道的轨道参数长期变化，通过6PN阶和16阶轨道偏心率展开，验证公式并评估偏心率对精度和PN收敛性的影响，提出混合近似方法提升计算效率。

Classical and relativistic orbital motions around a mass-varying body

I calculate the classical effects induced by an isotropic mass loss of a body on the orbital motion of a test particle around it; the present analysis is also valid for a variation of the Newtonian constant of gravitation. I perturbatively obtain negative secular rates for the osculating semimajor axis, the eccentricity and the mean anomaly, while the argument of pericenter does not undergo secular precession; the node and the inclination i remain unchanged. The anomalistic period is different from the Keplerian one, being larger than it. The true orbit, instead, expands, as shown by a numeric…

后牛顿层级三体系统的长期动力学 I. 多尺度公式的偏心率、倾角与节点依赖性及其正则一致性

Post-Newtonian secular dynamics of hierarchical triples. I. Eccentricity-, inclination- and node-dependence of the multiple-scale formulation, and its canonical consistency

本文重新检验层级三体系统的1PN交叉项，指出LR多尺度展开中的天平动项源于平均测度错误，修正后与KST有效场论一致，且移除该项不影响共振ZLK调制但消除加速并合。

Secular evolution of compact binaries revolving around a spinning massive black hole

The leading order effect of the spin of a distant supermassive black hole (SMBH) on the orbit of compact binary revolving around it appears at the 1.5 post Newtonian (PN) expansion through coupling with the inner and outer orbital angular momenta, and makes an oscillating characteristic contribution to the secular evolution of the compact binary eccentricity over a long time scale compared to the Kozai-Lidov dynamics caused by a non-spinning SMBH.

The three body first post-Newtonian effects on the secular dynamics of a compact binary near a spinning supermassive black hole

The binary black holes (BBHs) formed near the supermassive black holes (SMBHs) in the galactic nuclei would undergo eccentricity excitation due to the gravitational perturbations from the SMBH and therefore merger more efficiently. In this paper, we study the coupling of the three body 1st post-Newtonian (PN) effects with the spin effects from the SMBH in the hierarchical triple system. We extend previous work by including the coupling between the de Sitter precession and the Lense-Thirring precession from the SMBH spin. This coupling includes both the precessions of the inner orbit angular mo…

Relativistic orbits around spinning supermassive black holes. Secular evolution to 4.5 post-Newtonian order

We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the conservative dynamics that are valid through 3PN order, including spin-orbit, quadrupole and (spin)$^2$ effects, and with radiation-reaction contributions linear in the mass of the body that are valid through 4.5PN order, including the 4PN damping effects of spin-orbit coupling. The evolution equations for the osculating orbit elements are iterated to high PN orders us…

Anomalous Post-Newtonian terms and the secular increase of the Astronomical Unit

In the last decade a major debate has emerged on the astrophysics community concerning the anomalous behaviour of the astronomical unit, the fundamental scale of distances in the Solar system. Several independent studies have combined radar ranging and optical data from the last four decades to come to the conclusion that the astronomical unit is increasing by several meters per century. It is abundantly clear that General Relativity cannot account for this new effect, although an still undefined angular momentum transfer mechanism could provide the simpler and more conventional explanation. H…

非保守李级数：2.5PN二体动力学

Nonconservative Lie series: post-Newtonian binary dynamics at 2.5PN

本文提出利用李级数方法求解非保守二体动力学问题，实现长期和短期行为的解析解，并适用于引力波模板。