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arxiv: 1707.02088 · v2 · pith:K6LLGXBBnew · submitted 2017-07-07 · 🌀 gr-qc

Solving post-Newtonian accurate Kepler Equation

Yannick Boetzel , Abhimanyu Susobhanan , Achamveedu Gopakumar , Antoine Klein , Philippe Jetzer This is my paper
classification 🌀 gr-qc
keywords pn-accuratesolutionaccuratecompactequationkepleranalyticanalytically
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We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional analytic solution is presented to check the correctness of our compact solution and we perform comparisons between our PN-accurate analytic solution and a very accurate numerical solution of the PN-accurate Kepler equation. We adapt our approach to compute crucial 3PN-accurate inputs that will be required to compute analytically both the time and frequency domain ready-to-use amplitude-corrected PN-accurate search templates for compact binaries in inspiralling eccentric orbits.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order

    gr-qc 2025-11 unverdicted novelty 8.0

    Derives the 4PN conservative map between constants of motion and fundamental frequencies for eccentric orbits, resummed over eccentricity and validated against circular-orbit and self-force results.