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.

中文翻译：

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受限三体问题的Lie级数解：在二元恒星系统中的应用

本文的目的是找到光引力约束三体问题的李级数解，并将该李级数理论应用于二元恒星系统。在本文中，我们采用了四个恒星二进制系统，即Kepler-34，Kepler-35，Kepler-413和Kepler-16。首先，在四个双星系统中研究了零速度曲线。Lie积分法是借助Lie级数处理常微分方程（ODE）系统的概念。我们已经将该方法应用于求解具有辐射原色的受限三体问题的运动方程，并获得了运动方程的解。然后将通过李系列方法获得的溶液与从众所周知的龙格-库塔方法获得的溶液进行比较。此外，