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

Abstract

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

10 pages, 1 figure; including test mass; accepted by PRD

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Cited by in corpus (12)

• The three-body problem
• Quantum Schwarzschild geometry in effective-field-theory models of gravity
• Dynamical features and shadows of quantum Schwarzschild black hole in effective field theories of gravity
• Gravitational wave forms, polarizations, response functions and energy losses of triple systems in Einstein-Aether theory
• Triangular solution to general relativistic three-body problem for general masses
• Stability and chaos of hierarchical three black hole configurations
• Post-Newtonian effects on the stability of the triangular solution in the three-body problem for general masses
• Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem
• Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism
• The linear stability of the post-Newtonian triangular equilibrium in the three-body problem
• Triangular solution to the planar elliptic three-body problem in the parametrized post-Newtonian formalism
• Lagrange point stability for a rotating host mass binary