The stability of orbit of a planet in the field of binary stars

In the paper, we consider the motion of a planet in the field of the binary stars in the theory of general relativity (GR), when all bodies have their own rotation. We consider that the third body moves in the plan of massive two bodies. The binary system orbit around the center of mass (sometimes referred to as the barycenter), in a circular orbit. The third body orbits closer to the primary star and does not affect the orbit of the secondary body. In fact, this problem belongs to the gravitational restricted three-body problem. We investigate the stability of the circular orbit of the planet in the binary system using the adiabatic theory of motion. The adiabatic theory of motion of bodies is the approach to study the evolutionary motion of bodies in the GR. The corresponding theory based on the vector elements of orbit to describe the motion of bodies and based on the asymptotic methods of nonlinear oscillations and in the method of adiabatic invariants.