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
Frequently Asked Questions
How is orbital velocity related to escape velocity?
Escape velocity is sqrt(2) times orbital velocity at the same radius: v_escape = sqrt(2) * v_orbital.
Does a satellite in orbit need fuel to stay in orbit?
In an ideal vacuum, no. In low Earth orbit, atmospheric drag gradually slows the satellite, requiring periodic boosts.
What happens if an orbiting object speeds up?
It moves to a higher orbit. If it reaches escape velocity, it leaves the gravitational field entirely.
Ready to run the numbers?
Open Orbital Velocity Calculator