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

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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.

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Acknowledgements

I am thankful to Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India for supporting library visits and for the use of computing facilities.

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  1. Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar, 751024, Odisha, India

    Rajib Mia

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Mia, R. Lie-Series Solution of Restricted Three-Body Problem: Application to Binary Stellar Systems. J Astronaut Sci 67, 59–76 (2020). https://doi.org/10.1007/s40295-019-00172-5

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