| Issue |
A&A
Volume 705, January 2026
|
|
|---|---|---|
| Article Number | A61 | |
| Number of page(s) | 10 | |
| Section | Celestial mechanics and astrometry | |
| DOI | https://doi.org/10.1051/0004-6361/202555309 | |
| Published online | 07 January 2026 | |
Compact binary system dynamics at the second post-Newtonian order: Analytical formula of the coordinate time for eccentric and circular orbits
★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it.
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Received:
26
April
2025
Accepted:
17
November
2025
This work is based on our published letter, where we developed the analytical expression of the coordinate time in terms of the eccentric anomaly at the second post-Newtonian (PN) order in general relativity (GR) for a compact binary system moving on eccentric orbits. The aim of this paper is to provide more details about the performed calculations and to produce other new results. More specifically, we focus on deriving the analytical expression of the coordinate time at the second PN order for circular orbits, and then discuss two astrophysical applications involving binary neutron star and black hole systems.
Key words: gravitation / gravitational waves / methods: analytical / time / stars: black holes
© The Authors 2026
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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