$$v^2=GM\left(\frac{2}{r}-\frac{1}{a}\right)$$

The so called

*vis-viva*equation. Where ##a## is the length of the semi-major axis of the orbit. For Schwarzschild metric it should be similar, except I guess for a perihelion term. I understand that perihelion term complicates maths, however I'm not interested on that term, so it would be fine if it's ignored. Would you know about any bibliography/video where it is explained? Or would you like to help? Thanks!