Orbital Velocity Calculator Formula

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

Formulas Used

Orbital Velocity

orbital_vel = sqrt(6.6743e-11 * mass_body / orbital_radius)

Orbital Period

orbital_period = 2 * pi * orbital_radius / sqrt(6.6743e-11 * mass_body / orbital_radius)

Variables

VariableDescriptionDefault
mass_bodyMass of Central Body(kg)5.972e+24
orbital_radiusOrbital Radius(m)6771000

How It Works

Orbital Velocity

For a circular orbit, gravitational force provides the centripetal force.

Derivation

Setting G*M*m/r² = m*v²/r and solving:

v = sqrt(G * M / r)

The orbital period is T = 2*pi*r / v.

Worked Example

Low Earth orbit at 400 km altitude (r = 6,371 + 400 = 6,771 km).

mass_body = 5.972e+24orbital_radius = 6771000
  1. 01v = sqrt(G * M / r)
  2. 02v = sqrt(6.6743e-11 * 5.972e24 / 6.771e6)
  3. 03v = sqrt(5.888e7)
  4. 04v ≈ 7,674 m/s
  5. 05T = 2*pi*r / v ≈ 5,541 s ≈ 92.3 minutes

Ready to run the numbers?

Open Orbital Velocity Calculator