Chaos Study On Celestial-body Motion In Post-Newtonian Approximation

When the bodies is very close to the gravitational source,Newton theory cannot accurately describe the bodies' motion.We need better theories,such as general relativity,to deal with the motion of the bodies.The post Newtonian approximation is an important method to deal with the bodies' motion in the strong gravitational field.We study the chaos of celestial motion in the Newtonian approximation.The main contents are as follows.We employ the Runge-Kutta method to solve the geodesic equation of the test particles.In order to reduce the integration error,we also use the single-factor-correction method to ensure the accuracy of the integration and the dynamic properties of the long-time integration.The chaos of the test particles is judged by the Poincare-section method and the fast Lyapunov-index method.Firstly,we study the chaos of the test particles in the Brans-Dicke theory under the first-order post-Newtonian approximation.The numerical results show that there is no chaos in the particles' motion.Secondly,we study the chaos of the test particles in the post-Newtonian gravitational field with the quadrupoles in the framework of general relativity,and obtain some intervals for the chaotic motion.