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General relativistic approach to the vis-viva equation on Schwarzschild metric

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Abstract

A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation under Newtonian conditions and is a more accurate tool for astrodynamics than the traditional equation. Preliminary simulation results demonstrate the application potential of the modified vis-viva equation for more complex n-body systems. Spherical symmetry is assumed in this approach; however, this limitation could be removed in future research. This study is a pivotal step toward bridging classical and relativistic mechanics and thus makes an important contribution to the field of celestial dynamics.

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Acknowledgements

SY is supported in part by the JSPS KAKENHI Grant Number JP20K03968 and JP 23H00108. KI is supported by the JSPS Grant Number 21H04467, JST FOREST Program JPMJFR20352935, and by JSPS Core-to-Core Program (Grant Number: JPJSCCA20200002, JPJSCCA20200003).

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Author notes

  1. Shuichiro Yokoyama and Kiyotomo Ichiki have contributed equally to this work.

Authors and Affiliations

  1. Division of Particle and Astrophysical Science, School of Science, Nagoya University, Chikusa-Ku, Nagoya, Aichi, 464-8602, Japan

    Qi Peng, Shuichiro Yokoyama & Kiyotomo Ichiki

  2. Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Chikusa-Ku, Nagoya, Aichi, 464-8602, Japan

    Shuichiro Yokoyama & Kiyotomo Ichiki

  3. Kavli IPMU (WPI), UTIAS, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8583, Japan

    Shuichiro Yokoyama

Authors
  1. Qi Peng
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  2. Shuichiro Yokoyama
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  3. Kiyotomo Ichiki
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Correspondence to Qi Peng.

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Peng, Q., Yokoyama, S. & Ichiki, K. General relativistic approach to the vis-viva equation on Schwarzschild metric. Gen Relativ Gravit 56, 48 (2024). https://doi.org/10.1007/s10714-024-03235-7

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  • DOI: https://doi.org/10.1007/s10714-024-03235-7

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