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arXiv · 1212.0754

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

Kei Yamada·Hideki Asada
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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.

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Kei Yamada, Hideki Asada. 2012-12-03. Triangular solution to general relativistic three-body problem for general masses. https://doi.org/10.1103/physrevd.86.124029

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