Year: 2026
Type: article
Abstract: 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.
DOI: 10.1103/y8nj-tmz3
Authors: Hongkun Huang, Jie Yang, Wei-Tou Ni
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Natural Science Foundation of China, Natural Science Foundation of Gansu Province, National Key Research and Development Program of China, Fundamental Research Funds for the Central Universities, Overseas Expertise Introduction Center for Discipline Innovation of Food Nutrition and Human Health (111 Center)
OpenAlex ID: W7221835638