Orbital Velocity Calculator
Circular orbit speed and period from altitude for Earth, Moon, and Mars.
What it does
Staying in orbit means falling around the planet exactly as fast as gravity bends the path: too slow spirals in, too fast escapes out. One radius sets both the speed and the lap time.
The tool above takes the body with altitude. It returns circular velocity with period and orbital radius.
The default 420 km above Earth needs 7.66 km/s with 92.8 min laps, the ISS regime. The same height math on the Moon gives 1.63 km/s.
Formulas follow OpenStax gravitation with NASA Glenn flight dynamics and Goddard fact sheets behind them. All three agree on v = root(GM/r) used here.
How to use
- Pick Earth, Moon, or Mars.
- Enter altitude in km.
- Read circular speed first.
- Read period beside it.
- Check the radius line.
- Compare with the ISS example.
Formula
- GM
- Body gravity parameter, m^3/s^2.
- r
- Center distance: radius + altitude.
- altitude
- Height above the surface.
Inputs stay in km while math runs SI meters with GM. Period prints minutes with seconds in the note. Altitudes cap at 1,000,000 km; practical low orbits need roughly 150 km or more.
Worked example
Example: 420 km above Earth
Defaults: Earth, 420 km altitude (ISS zone).
- Body Earth: GM = 3.986004418e14, radius 6,371 km.
- Radius: 6,371 + 420 = 6,791 km = 6,791,000 m.
- GM/r = 3.986004418e14 / 6.791e6 = 5.8699e7.
- Speed: root = 7,661.5 m/s = 7.66 km/s.
- r cubed / GM = 785,690 s squared, root 886.4 s.
- Period: 2 x pi x 886.4 = 5,569 s = 92.8 min.
- Tool shows 7.66 km/s, 92.8 min, 6,791 km radius.
Reference table
| Body | GM (m3/s2) | Radius (km) |
|---|---|---|
| Earth | 3.986004418e14 | 6,371 |
| Moon | 4.9048695e12 | 1,737.4 |
| Mars | 4.282837e13 | 3,389.5 |
Limits
- Circular orbits only.
- Single body gravity, no drag or thrust.
- Below ~150 km needs reboost logic.
- Relativity ignored at these speeds.
Common mistakes
- Using surface g at altitude.
- Mixing km with SI GM.
- Forgetting radius plus altitude.
- Applying circular math to ellipses.
- Reading period in seconds as minutes.
Try it yourself
Quick checks. Answers sit tucked under each question.
400 km above Earth?
Radius 6,771 km: 7.67 km/s, 92.4 min.
100 km above the Moon?
Radius 1,837 km: 1.63 km/s, 117.8 min.
Zero altitude on Earth?
Surface skimming: 7.91 km/s near 84 min, drag forbids it.
Questions
What is the orbit formula?
v = root(GM / r) with r in meters from the body center. Period T = 2 x pi x root(r^3 / GM).
How fast is the ISS?
About 7.66 km/s with a 92.8 min period at 420 km.
Can I orbit at 50 km?
Below about 150 km drag decays orbits fast. Formulas still compute; physics still wins.
Does the Moon work too?
Yes: same formulas with the Moon or Mars GM and radius built in.
Do elliptical orbits fit?
No. Elliptical orbits use semi major axis for period; speed varies around the loop.
Why GM instead of G times M?
Use GM directly: 3.986004418e14 for Earth avoids Earth mass spread entirely.