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Triple collision orbits in the free-fall three-body system without binary collisions

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Abstract

We numerically investigate triple collision orbits of the free-fall three-body system which has no double collisions before three bodies collide. Triple collision is an important property of the three-body system. Tanikawa, Saito, Mikkola (Celest Mech Dyn Astron 131(6):24, 2019) obtained 11 triple collision orbits without double collision for the free-fall three-body problem. In this paper, we present 1658 triple collision orbits including the Lagrange’s homothetic solution, 11 ones found by Tanikawa et al. (2019) and 1646 new triple collision orbits. The symbol sequences of these 1646 new triple collision orbits have digits that range between 1 and 120. With our high-precision results, numerical evidences of the asymptotic property of triple collision orbits are given.

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Acknowledgements

This work was carried out on TH-1A at National Supercomputer Center in Tianjin, China. It is partly supported by National Natural Science Foundation of China (Approval Nos. 12002132, 11702099 and 91752104).

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Authors and Affiliations

  1. School of Mechanics and Construction Engineering, MOE Key Laboratory of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou, 510632, China

    Xiaoming Li & Linghui He

  2. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, China

    Xiaochen Li

  3. Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Linghui He

  4. Center of Advanced Computing, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Shijun Liao

  5. School of Physics and Astronomy, Shanghai Jiaotong University, Shanghai, 200240, China

    Shijun Liao

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  1. Xiaoming Li
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  2. Xiaochen Li
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  3. Linghui He
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  4. Shijun Liao
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Correspondence to Xiaochen Li or Shijun Liao.

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Li, X., Li, X., He, L. et al. Triple collision orbits in the free-fall three-body system without binary collisions. Celest Mech Dyn Astr 133, 46 (2021). https://doi.org/10.1007/s10569-021-10044-6

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