English

Triangular solution to general relativistic three-body problem for general masses

General Relativity and Quantum Cosmology 2015-06-12 v1 Earth and Planetary Astrophysics Mathematical Physics math.MP

Abstract

Continuing work initiated in an earlier publication [Ichita, Yamada and Asada, Phys. Rev. D 83, 084026 (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that a triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if it has the relativistic corrections to each side length. This post-Newtonian configuration for three finite masses is not always equilateral and it recovers previous results for the restricted three-body problem when one mass goes to zero. For the same masses and angular velocity, the post-Newtonian triangular configuration is always smaller than the Newtonian one.

Keywords

Cite

@article{arxiv.1212.0754,
  title  = {Triangular solution to general relativistic three-body problem for general masses},
  author = {Kei Yamada and Hideki Asada},
  journal= {arXiv preprint arXiv:1212.0754},
  year   = {2015}
}

Comments

12 pages, 1 figure, 1 table; accepted by PRD

R2 v1 2026-06-21T22:48:34.317Z