Collinear solution to the general relativistic three-body problem

Details Collinear solution to the general relativistic three-body problem Collinear solution to the general relativistic three-body problem

2010-10-12

arxiv.org/abs/1010.2284v1

Phys.Rev.D82:104019,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures, accepted for publication in PRD

Scientific paper

10.1103/PhysRevD.82.104019

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L1, L2 and L3 are also evaluated.

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