Post-Newtonian effects on the stability of the triangular solution in the three-body problem for general masses

Kei Yamada, Takuya Tsuchiya, and Hideki Asada

Phys. Rev. D 91, 124016 – Published 3 June 2015

Abstract

Continuing work initiated in earlier publications [T. Ichita et al., Phys. Rev. D 83, 084026 (2011); K. Yamada and H. Asada, Phys. Rev. D 86, 124029 (2012)], we examine the post-Newtonian (PN) effects on the stability of the triangular solution in the relativistic three-body problem for general masses. For three finite masses, a condition for stability of the triangular solution is obtained at the first post-Newtonian (1PN) order, and it recovers previous results for the PN restricted three-body problem when one mass goes to zero. The stability regions still exist even at the 1PN order, though the PN triangular configuration for general masses is less stable than the PN restricted three-body case as well as the Newtonian one.

Received 8 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.124016

Authors & Affiliations

Kei Yamada^3,*, Takuya Tsuchiya², and Hideki Asada¹

¹Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
²School of Fundamental Science and Engineering, Waseda University, Shinjuku 169-8555, Japan
³Department of Physics, Kyoto University, Kyoto 606-8502, Japan

^*yamada@tap.st.hirosaki-u.ac.jp

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

Kei Yamada and Hideki Asada

Phys. Rev. D 86, 124029 (2012)

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Vol. 91, Iss. 12 — 15 June 2015

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covering particles, fields, gravitation, and cosmology