Post-Newtonian effects on Lagrange’s equilateral triangular solution for the three-body problem
Year: 2011
Type: article
Abstract: Continuing work initiated in earlier publications [Yamada, Asada, Phys. Rev. D 82, 104019 (2010); Phys. Rev. D83, 024040 (2011)], we investigate the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that the equilateral triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if all three masses are equal. When a test mass is included, the equilateral configuration is possible for two cases: (1) one mass is finite and the other two are zero, or (2) two of the masses are finite and equal, and the third one is zero, namely, a symmetric binary with a test mass. The angular velocity of the post-Newtonian equilateral triangular configuration is always smaller than the Newtonian one, provided that the masses and the side length are the same.
Authors: Takumi Ichita, Kei Yamada, Hideki Asada
Institution: Hirosaki University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2000736574