The orbital stability of relativistic three-body problem in the fremework of general relativity

Abstract

In this paper, the stability conditions of a quasi-circular orbit of a test body in the field of two rotating bodies in the framework of general theory of relativity are investigated. The position of the central body coincides with the reference point of coordinates, the second body is moving in circular orbit around a central body (first body), and without inner mass distribution. The test body moves in a perturbed circular orbit. The equations of translational motion of a test body with rotation components are studied. The initial angular velocity allows the Lagrange equation to be supplemented with a member responsible for the uniform rotation of the test body itself. The physical Interpretation of the phenomenon as close as possible to the actually observed. In turn, the equations of motion are complicated, which inevitably leads to the use of numerical methods of analysis. The equations of motion are averaged over time using asymptotic methods of nonlinear mechanics.

We confine ourselves to zero terms of expansion in powers of the relations of the sizes of bodies to their mutual distances.