In astrodynamics, the orbital-energy-invariance law or vis-viva equation, is one of the equations that model the motion of orbiting bodies.
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 (Latin meaning – living force) accumulated or lost in the system while the work is being done.
The formula for orbital-energy-invariance law or Vis-viva equation is given as,
v = the relative speed of the two bodies
G = the gravitational constant
M = mass of the central body
r = the distance between the orbiting bodies
a = the length of the semi-major axis(a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas,
and a < 0 for hyperbolas)