Vis-Viva Equation with standard gravitational parameter


In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the motion of orbiting bodies. It is the direct result of the law of conservation of energy, which requires that the sum of kinetic and potential energy is constant at all points along the orbit.

Vis viva (Latin for “live force”) is a term from the history of mechanics, and it survives in this sole context. It represents the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done.

This formula is an alternative version of the “Vis-Viva Equation (orbital speed)” and it uses the standard gravitational parameter instead of the Newtonian constant of gravitation and the mass of the central body.

Related formulas


vrelative speed of the two bodies (m/s)
μstandard gravitational parameter(Earth:3.986004418e+14) (m3/s2)
rdistance between the two bodies (m)
asemi-major axis (m)