  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.
