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Fractal basins of attraction in the restricted four-body problem when the primaries are triaxial rigid bodies

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Abstract

The planar equilateral restricted four-body problem, formulated on the basis of Lagrange’s triangular solutions is used to determine the existence and locations of libration points and the Newton-Raphson basins of convergence associated with these libration points. We have supposed that all the three primaries situated on the vertices of an equilateral triangle are triaxial rigid bodies. This paper also deals with the effect of these triaxiality parameters on the regions of motion where the test particle is free to move. Further, the regions on the configuration plane filled by the basins of attraction are determined by using the multivariate version of the Newton-Raphson iterative system. The numerical study reveals that the triaxiality of the primaries is one of the most influential parameters in the four-body problem.

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Acknowledgements

The authors would like to thank the anonymous referee for the careful reading of the manuscript and for all valuable suggestions and comments which helps us to improve the quality and the clarity of the manuscript.

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Authors and Affiliations

  1. Shri Guru Tegh Bahadur Khalsa College, University of Delhi, North Campus, New Delhi, 110007, India

    Md Sanam Suraj

  2. Research Scholar, P.G. Department of Physics, TMBU, Bhagalpur, Bihar, 812007, India

    Md Chand Asique

  3. Department of Physics, TNB College, TMBU, Bhagalpur, Bihar, 812007, India

    Umakant Prasad

  4. Department of Mathematics, S.M. College, TMBU, Bhagalpur, Bihar, 812007, India

    M. R. Hassan

  5. Department of Mathematics, Zakir Husain College, University of Delhi, New Delhi, India

    Kumari Shalini

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  1. Md Sanam Suraj
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  2. Md Chand Asique
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  3. Umakant Prasad
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  4. M. R. Hassan
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  5. Kumari Shalini
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Correspondence to Md Sanam Suraj.

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Suraj, M.S., Asique, M.C., Prasad, U. et al. Fractal basins of attraction in the restricted four-body problem when the primaries are triaxial rigid bodies. Astrophys Space Sci 362, 211 (2017). https://doi.org/10.1007/s10509-017-3188-7

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