Vis-Viva Orbital Velocity Calculator
Orbital mechanics & astrodynamics: Compute instantaneous orbital velocity, specific mechanical energy, orbital period, and escape velocity using the Vis-Viva equation.
Central Body & Orbit Geometry
Gravitational parameter μ = GM
Conic section geometry
Height above surface (e.g., ISS ~420 km, LEO 200–2,000 km)
The Vis-Viva Equation
Derived from the conservation of specific mechanical energy $\varepsilon = \frac{v^2}{2} - \frac{\mu}{r} = -\frac{\mu}{2a}$:
$$v^2 = \mu \left( \frac{2}{r} - \frac{1}{a} \right)$$
Where $r$ is the distance from the body center and $a$ is the semi-major axis.
Orbital Velocity Results
Orbital Velocity (v)
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Escape Velocity (v_esc)
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Energy & Period
Orbital Period (T)
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Specific Mechanical Energy (ε)
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Apsidal Extremes & Parameters
Semi-Major Axis (a):
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Eccentricity (e):
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Periapsis Velocity (v_p):
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Apoapsis Velocity (v_a):
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