Orbital Velocity Calculator Formula

Understand the math behind the orbital velocity calculator. Each variable explained with a worked example.

Use the Orbital Velocity Calculator

Formulas Used

Orbital Velocity

velocity = sqrt(6.674e-11 * central_mass / radius)

Velocity (km/s)

velocity_kmps = sqrt(6.674e-11 * central_mass / radius) / 1000

Variables

VariableDescriptionDefault
radiusOrbital Radius(m)6771000
central_massCentral Body Mass(kg)5.972e+24

How It Works

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.

    Worked Example

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

    radius = 6771000central_mass = 5.972e+24
    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

    Frequently Asked Questions

    Why do lower orbits have higher speeds?

    Closer to the central body gravity is stronger, requiring faster motion to maintain a circular path. Speed scales as 1/√r.

    Does this work for elliptical orbits?

    For an elliptical orbit use the vis-viva equation v = √(G M (2/r - 1/a)). The circular formula is a special case where r = a.

    What is the orbital velocity of the Moon?

    About 1.022 km/s, consistent with its large orbital radius of roughly 384 400 km.

    Ready to run the numbers?

    Open Orbital Velocity Calculator