General Relativistic Approach to the Vis-viva Equation on Schwarzschild Metric
arXiv:2404.10302 · doi:10.1007/s10714-024-03235-7
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.
8 pages, 1 figure, Accepted for publication in General Relativity and Gravitation