Abstract
We derive the second-order post-Newtonian solution for the quasi-Keplerian motion of a nonspinning compact binary system in the Wagoner–Will–Epstein–Haugan representation. This adds a new formulation to the literature in which the motion solution has been formulated in the Brumberg–Damour–Deruelle–Schäfer representation and the osculating-element parametrization. We also show that the orbital period and the pericenter precession in the Wagoner–Will–Epstein–Haugan representation are identical to those in the other formulations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Brumberg, Relativistic Celestial Mechanics (Nauka, Moscow, 1972)
S. Kopeikin, M. Efroimsky, and G. Kaplan, Relativistic Celestial Mechanics of the Solar System (Wiley, New York, 2012).
S. M. Kopeikin, Eur. Phys. J. Plus 135, 466 (2020).
R. V. Wagoner and C. M. Will, Astrophys. J. 210, 764 (1976).
R. Epstein, Astrophys. J. 219, 92 (1977).
M. P. Haugan, Astrophys. J. 296, 1 (1985).
V. Brumberg, Essential Relativistic Celestial Mechanics (Taylor and Francis Group, Abingdon, 1991).
T. Damour and N. Deruelle, Ann. Inst. H. Poincaré 43, 107 (1985).
T. Damour and G. Schäfer, Nuovo Cim. B 101, 127 (1988).
S. A. Klioner and S. M. Kopeikin, Astrophys. J. 427, 951 (1994).
M. H. Soffel, Relativity in Astrometry, Celestial Mechanics and Geodesy (Springer, Berlin, 1989).
M. H. Soffel, H. Ruder, and M. Schneider, Celestial Mech. 40, 77 (1987).
M. H. Soffel and W. B. Han, Applied General Relativity: Theory and Applications in Astronomy, Celestial Mechanics and Metrology (Springer, Berlin, 2019).
B. Yang and W. Lin, Grav. Cosmlo. 26, 273 (2020).
L. Kidder, Phys. Rev. D 52, 821 (1995).
T. Damour, in 300 Years of Gravitation, Ed. S. Hawking and W. Israel (Cambridge University Press, Cambridge, 1987).
G. Schäfer and N. Wex, Phys. Lett. A 174, 196 (1993).
R. M. Memmesheimer, A. Gopakumar, and G. Schäfer, Phys. Rev. D 70, 104011 (2004).
ACKNOWLEDGMENT
We thank the referees for providing helpful suggestions to promote the quality of this work.
Funding
This study was supported in part by the National Natural Science Foundation of China (no. 11973025).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gao, W., Yang, B. & Lin, W. The 2PN Motion of a Non-spinning Compact Binary: the Wagoner–Will–Epstein–Haugan Representation. Gravit. Cosmol. 27, 240–246 (2021). https://doi.org/10.1134/S0202289321030075
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0202289321030075