Triangular solution to the planar elliptic three-body problem in the parametrized post-Newtonian formalism

Abstract

A triangular solution [Phys. Rev. D 107, 044005 (2023)] has recently been found to the planar circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which they focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters $\beta$ and $\gamma$. The present paper extends the PPN triangular solution to quasi-elliptic motion, for which the shape of the triangular configuration changes with time at the PPN order. The periastron shift due to the PPN effects is also obtained.

arXiv comment5 pages, 2 figures, text improved for clarity, accepted for PRD

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