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
| Variable | Description | Default |
|---|---|---|
mass_body | Mass of Central Body(kg) | 5.972e+24 |
orbital_radius | Orbital 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
- 01v = sqrt(G * M / r)
- 02v = sqrt(6.6743e-11 * 5.972e24 / 6.771e6)
- 03v = sqrt(5.888e7)
- 04v ≈ 7,674 m/s
- 05T = 2*pi*r / v ≈ 5,541 s ≈ 92.3 minutes
Ready to run the numbers?
Open Orbital Velocity Calculator