Vis-Viva Equation Calculator

Vis-Viva Calculator

Property to Calculate:

Relative orbital speed of the two bodies (v):

Mass of the central body (M):

Distance between bodies center of mass (r):

Length of the semi-major axis (a):

How This Is Calculated

$$ v^2 = G M \left( \frac{2}{r} - \frac{1}{a} \right) $$ where:

v = Relative orbital speed of the two bodies (m/s)

G = Gravitational Constant (6.674 x 10^-11 Nm²kg^-2)

M = Mass of the central body (kg)

r = Distance between bodies center of mass (m)

a = Length of the semi-major axis (m)

Assumptions

The objects are treated as point masses.
The mass distribution of the objects are spherically symmertric.
The bodies are in stable orbits.
The system is simplied to the interaction between two bodies.

Related Calculators

Orbital Period for Circular Orbits

Orbital Velocity

Radius from True Anomaly

Specific Orbital Energy

Sphere of Influence