发表机构
School of Physical Science and Technology, Lanzhou University; Institute of Theoretical Physics & Research Center of Gravitation, Lanzhou University; Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University; Lanzhou Center for Theoretical Physics & Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University; Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology (APM), Chinese Academy of Sciences; International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（兰州大学物理科学与技术学院; 兰州大学理论物理研究所与引力研究中心; 教育部量子理论与应用重点实验室，兰州大学; 兰州大学兰州理论物理中心与甘肃省理论物理重点实验室; 中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所; 中国科学院大学亚太理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在阿达马正则化下构建谐和规范2PN N体运动方程的可计算形式，应用于两个太阳系基准系统，分析非闭合项的贡献与相对距离摄动特性。
AI 中文摘要
我们在阿达马正则化框架内，针对一般点质量N体系统，构建了谐和规范下二阶后牛顿（2PN）运动方程的半解析半数值公式化表述。该运动方程被拆分为闭合解析贡献项与非闭合积分贡献项；我们分析了后者的奇异结构，并将其进一步正则化为可数值计算的形式。我们将该公式应用于太阳-木星-土星系统与太阳-水星-金星系统，沿牛顿轨道计算瞬时非闭合2PN加速度，以及通过对应摄动方程计算其领先阶有限时间相对距离响应。在两个基准测试中，非闭合加速度仅占完整2PN加速度的一小部分，而诱导的相对距离摄动呈振荡状态，且在后期可达到更大的振荡幅度。
英文摘要
We develop a semi-analytic and semi-numerical formulation of the harmonic-gauge second post-Newtonian (2PN) equations of motion for a general point-mass N-body system within Hadamard regularization. The equations of motion are separated into a closed analytic contribution and a non-closed integral contribution. We analyze the singular structure of the latter and further regularize it into a numerically evaluable representation. We apply the formulation to the Sun-Jupiter-Saturn and Sun-Mercury-Venus systems, evaluating the instantaneous non-closed 2PN acceleration along Newtonian trajectories and its leading finite-time relative-distance response through the corresponding perturbation equations. In both benchmarks, the non-closed acceleration remains a small fraction of the complete 2PN acceleration, while the induced relative-distance perturbation remains oscillatory and can reach larger oscillation amplitudes at later times.
Comments48 pages, 3 figures, 4 tables
