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arXiv · 2608.20193

The 2PN Point-Mass N-Body Equations of Motion in Harmonic Gauge: A Computable Formulation

Hongkun Huang·Jie Yang·Wei-Tou Ni
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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.

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Hongkun Huang, Jie Yang, Wei-Tou Ni. 2026-08-20. The 2PN Point-Mass N-Body Equations of Motion in Harmonic Gauge: A Computable Formulation. https://arxiv.org/abs/2608.20193

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