Orbital Velocity Calculator

Calculate orbital velocities for circular and elliptical orbits using the vis-viva equation

Calculate Orbital Velocity

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Solar System Planets:

Vis-viva Equation

v² = μ(2/r - 1/a)
v: Orbital velocity
μ: Standard gravitational parameter
r: Distance from central body
a: Semi-major axis

The vis-viva equation relates orbital velocity to position in any orbit, circular or elliptical.

Orbit Types

Circular Orbit

Eccentricity = 0, constant velocity

Elliptical Orbit

0 < Eccentricity < 1, variable velocity

Parabolic Orbit

Eccentricity = 1, escape trajectory

Hyperbolic Orbit

Eccentricity > 1, unbound trajectory

Quick Facts

Earth's orbital velocity: ~29.8 km/s around the Sun

ISS velocity: ~7.66 km/s around Earth

Objects move faster at periapsis (closest point)

Escape velocity is √2 times orbital velocity

Understanding Orbital Velocity

What is Orbital Velocity?

Orbital velocity is the speed needed for an object to orbit around a celestial body. It depends on the mass of the central body and the distance from it. For circular orbits, this velocity is constant, but for elliptical orbits, it varies throughout the orbit.

Circular vs Elliptical Orbits

In circular orbits, objects maintain constant distance and velocity. In elliptical orbits, objects speed up when closer to the central body (periapsis) and slow down when farther away (apoapsis), following Kepler's Second Law.

Circular Orbit

v = √(μ/r)

  • v: Orbital velocity
  • μ: Standard gravitational parameter
  • r: Orbital radius

Elliptical Orbit Parameters

Elliptical orbits are characterized by their semi-major axis (a), semi-minor axis (b), and eccentricity (e). The eccentricity determines how elongated the ellipse is, ranging from 0 (perfect circle) to close to 1 (very elongated).

Applications

  • Spacecraft mission planning and trajectory design
  • Satellite orbit determination and maintenance
  • Planetary motion analysis and prediction
  • Asteroid and comet trajectory calculation

Key Relationships

Eccentricity: e = √(1 - b²/a²)
Periapsis: rₚ = a(1 - e)
Apoapsis: rₐ = a(1 + e)