Orbital Velocity Calculator
Calculate orbital velocities for circular and elliptical orbits using the vis-viva equation
Calculate Orbital Velocity
Solar System Planets:
Vis-viva Equation
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