Free Orbital Velocity Calculator

Determine the orbital speed of a body in a circular orbit using v = sqrt(G * M / r).

m
kg

Orbital Velocity

7,672.32 m/s

Velocity (km/s)7.6723 km/s

Orbital Velocity vs Orbital Radius

How Orbital Velocity Is Found

For a circular orbit the gravitational pull provides exactly the centripetal force needed.

Formula

v = √(G M / r)

  • *G* = 6.674e-11 N m² kg⁻²
  • *M* = central body mass
  • *r* = orbital radius (centre-to-centre)
  • Higher orbits are slower; lower orbits are faster.

    Example Calculation

    Find the speed of the ISS at about 400 km altitude (r = 6 771 km).

    1. 01v = √(G M / r)
    2. 02G M = 6.674e-11 × 5.972e24 = 3.986e14
    3. 03v = √(3.986e14 / 6.771e6) = √(5.887e7)
    4. 04v ≈ 7 673 m/s ≈ 7.67 km/s

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