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arXiv · 2404.10302

General Relativistic Approach to the Vis-viva Equation on Schwarzschild Metric

Qi Peng·Shuichiro Yokoyama·Kiyotomo Ichiki
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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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Qi Peng, Shuichiro Yokoyama, Kiyotomo Ichiki. 2024-04-16. General Relativistic Approach to the Vis-viva Equation on Schwarzschild Metric. https://doi.org/10.1007/s10714-024-03235-7

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