How to Calculate Orbital Velocity for Elliptical Orbits Using the Vis-Viva Equation

[@AstroPhil2000]

Here is is the derivation for the vis-viva equation: kzbin.info/www/bejne/iH7InI2NqLSHpJY

[@karhukivi]

Interesting! If M1>>M2 and r=a, the the two formulae are identical. Is this an empirical formula or is it derived from the equation of an ellipse?

[@AstroPhil2000]

Yes, it becomes the circular velocity equation when r =a. It is derived from the specific orbital energy and the fact that it is a balance between the kinetic and potential energy.