In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.
Vis viva (Latin for "living force") is a term from the history of mechanics and the name given to the orbital equation originally derived by Isaac Newton. is as follows:
<math display="block">v^2 = GM \left({ 2 \over r} - {1 \over a}\right)</math>
where:
- is the relative speed of the two bodies
- is the distance between the two bodies' centers of mass
- is the length of the semi-major axis ( for ellipses, or for parabolas, and for hyperbolas)
- is the gravitational constant
- is the mass of the central body
The product of can also be expressed as the standard gravitational parameter using the Greek letter .