Orbital Velocity Calculator (v = √GM/r)
Orbital velocity is the speed a satellite or spacecraft needs to stay in a stable circular orbit around a planet, moon, or star. The International Space Station travels at about 7,660 m/s (27,600 km/h) at 400 km altitude. This calculator finds that speed for any body and altitude, plus the time to complete one orbit.
The Orbital Velocity Formula
For a circular orbit: v = sqrt(GM / r), where G is the gravitational constant (6.674 x 10 to the negative 11), M is the central body's mass, and r is the orbital radius measured from the body's center.
Altitude vs. Orbital Radius
If you know the altitude above the surface, the calculator adds the body's radius to get the orbital radius: r = R_body + altitude. For the ISS at 400 km altitude above Earth (radius 6,371 km), the orbital radius is 6,771 km.
Orbital Period
Once you have velocity, the period is: T = 2 pi r / v. The ISS completes one orbit in about 92 minutes, seeing 16 sunrises every day.
Key Orbits Around Earth
| Orbit Type | Altitude | Velocity | Period |
|---|---|---|---|
| Low Earth (ISS) | 400 km | 7,670 m/s | 92 min |
| GPS satellites | 20,200 km | 3,870 m/s | 12 hours |
| Geostationary | 35,786 km | 3,070 m/s | 24 hours |
Why Higher Orbits Are Slower
It seems counterintuitive, but satellites farther from Earth orbit more slowly. The gravitational pull weakens with distance, so less speed is needed to balance it. Geostationary satellites at 35,786 km orbit at just 3,070 m/s, compared to 7,670 m/s for the ISS.