Collinear and triangular solutions to the coplanar and circular three-body problem in the parametrized post-Newtonian formalism

Abstract

This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters $\beta$ and $\gamma$. It is shown that there can still exist a collinear equilibrium configuration and a triangular one, each of which is a generalization of the post-Newtonian equilibrium configuration in general relativity. The collinear configuration can exist for arbitrary mass ratio, $\beta$, and $\gamma$. On the other hand, the PPN triangular configuration depends on the nonlinearity parameter $\beta$ but not on $\gamma$. For any value of $\beta$, the equilateral configuration is possible, if and only if three finite masses are equal or two test masses orbit around one finite mass. For general mass cases, the PPN triangle is not equilateral as in the post-Newtonian case. It is shown also that the PPN displacements from the Lagrange points in the Newtonian gravity $L_1$, $L_2$ and $L_3$ depend on $\beta$ and $\gamma$, whereas those to $L_4$ and $L_5$ rely only on $\beta$.

arXiv comment8 pages, 2 figures, typos corrected, version matched with publication in PRD

References in corpus (23)

• The Confrontation between General Relativity and Experiment
• Progress in Lunar Laser Ranging Tests of Relativistic Gravity
• A millisecond pulsar in a stellar triple system
• Testing the universality of free fall by tracking a pulsar in a stellar triple system
• Accretion dynamics in neutron star black hole binaries
• An improved test of the strong equivalence principle with the pulsar in a triple star system
• Relativistic Celestial Mechanics with PPN Parameters
• The Lagrange Equilibrium Points L_4 and L_5 in a Black Hole Binary System
• Collinear solution to the general relativistic three-body problem
• Gravitational waveforms for 2- and 3-body gravitating systems
• Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system
• Relativistic Astrophysics with Resonant Multiple Inspirals
• Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity
• Triangular solution to general relativistic three-body problem for general masses
• Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test
• Precession resonances in hierarchical triple systems
• Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
• Post-Newtonian effects on the stability of the triangular solution in the three-body problem for general masses
• Effective two-body approach to the hierarchical three-body problem
• Uniqueness of collinear solutions for the relativistic three-body problem
• The three body first post-Newtonian effects on the secular dynamics of a compact binary near a spinning supermassive black hole
• Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem
• General Relativistic Effects on Hill Stability of Multi-Body Systems I: Stability of Three-Body Systems Containing a Massive Black Hole

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