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.

Graphical abstract

中文翻译：

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Schwarzschild 度量上 vis-viva 方程的广义相对论方法

摘要

对解释广义相对论效应的 vis-viva 方程进行了修改，以提高轨道运动和进动预测的准确性。更新后的方程简化为牛顿条件下的传统vis-viva方程，并且是比传统方程更准确的天体动力学工具。初步仿真结果证明了改进的 vis-viva 方程对于更复杂的 n 体系统的应用潜力。该方法假设球对称；然而，这种限制可能会在未来的研究中被消除。这项研究是连接经典力学和相对论力学的关键一步，因此对天体动力学领域做出了重要贡献。

图形概要