Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem

Journal Article · Fri Apr 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.084026· OSTI ID:21541492

Ichita, Takumi; Yamada, Kei; Asada, Hideki ^[1]

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1. Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561 (Japan)

Continuing work initiated in earlier publications [Yamada, Asada, Phys. Rev. D 82, 104019 (2010); ibid.83, 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.

• OSTI ID: 21541492
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR VELOCITY
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
GENERAL RELATIVITY THEORY
MANY-BODY PROBLEM
MASS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
RELATIVITY THEORY
SYMMETRY
THREE-BODY PROBLEM
TRIANGULAR CONFIGURATION
VELOCITY