Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: Continuing work initiated in earlier publications Yamada, Asada, Phys. Rev.D 82, 104019 2010, 83, 024040 2011, we investigate the post-Newtonianeffects on Lagrange-s equilateral triangular solution for the three-bodyproblem. For three finite masses, it is found that the equilateral triangularconfiguration satisfies the post-Newtonian equation of motion in generalrelativity, if and only if all three masses are equal. When a test mass isincluded, the equilateral configuration is possible for two cases: 1 one massis finite and the other two are zero, or 2 two of the masses are finite andequal, and the third one is zero, namely a symmetric binary with a test mass.The angular velocity of the post-Newtonian equilateral triangular configurationis always smaller than the Newtonian one, provided that the masses and the sidelength are the same.



Author: Takumi Ichita, Kei Yamada, Hideki Asada

Source: https://arxiv.org/







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