Lie-Series Solution of Restricted Three-Body Problem: Application to Binary Stellar Systems

The purpose of this present paper is to find the Lie-series solutions of the photo-gravitational restricted three-body problem and to apply this Lie-series theory in binary stellar systems. In this paper, we have taken four stellar binary systems namely Kepler-34, Kepler-35, Kepler-413 and Kepler-16. Firstly, the zero-velocity curves are studied in the four binary stellar systems. The Lie-integration method is a concept to deal with the system of ordinary differential equations(ODEs) with the help of Lie-series. We have applied this method to solve the equations of motion of restricted three-body problem with radiating primaries and obtained the solutions of the equations of motion. Then the solution obtained by Lie-series method is compared with that of obtained from the well known Runge-Kutta method. In addition, we have shown the absolute errors graphically for Lie-series method and Runge-Kutta method.