Calculator Inputs
Choose a body preset or select Custom for manual values.
Orbital Velocity Plot
The curve shows how circular orbital velocity changes as orbital radius increases.
Example Data Table
| Body | Altitude (km) | Orbital Radius (km) | Velocity (km/s) | Period (min) | Escape Velocity (km/s) |
|---|---|---|---|---|---|
| Earth | 400 | 6771.0 | 7.6726 | 92.4141 | 10.8507 |
| Earth | 35786 | 42157.0 | 3.0749 | 1435.6993 | 4.3486 |
| Mars | 250 | 3639.5 | 3.4305 | 111.1012 | 4.8514 |
| Moon | 100 | 1837.4 | 1.6331 | 117.8214 | 2.3095 |
Formula Used
Circular orbital velocity
v = √(GM / r)
Orbital period
T = 2πr / v
Escape velocity at the same radius
ve = √(2GM / r)
Gravity at orbit
g = GM / r²
Where:
- G is the gravitational constant, 6.67430 × 10-11 N·m²/kg².
- M is the central body mass in kilograms.
- r is the orbital radius from the body center in meters.
- v is circular orbital velocity.
- T is orbital period.
How to Use This Calculator
- Select a preset body or choose Custom.
- Pick altitude mode or orbital radius mode.
- Enter the body mass and radius if needed.
- Enter altitude above the surface or total orbital radius.
- Press the calculate button.
- Review velocity, period, gravity, and energy outputs.
- Inspect the Plotly graph for radius versus velocity behavior.
- Download the result summary as CSV or PDF.
Frequently Asked Questions
1. What does circular orbital velocity mean?
It is the exact sideways speed needed for a stable circular orbit at a given radius. Below that speed, the spacecraft falls inward. Above it, the orbit becomes larger or noncircular.
2. Why does orbital velocity decrease farther away?
Gravity weakens with distance from the central body. A weaker inward pull means less sideways speed is required to keep a circular path, so orbital velocity drops as radius increases.
3. Is altitude the same as orbital radius?
No. Altitude is measured from the body surface. Orbital radius is measured from the body center. The calculator converts altitude to orbital radius by adding the body radius.
4. Why is escape velocity larger than orbital velocity?
Escape velocity must remove the object from the body's gravitational influence without further propulsion. Circular orbital velocity only balances gravity for a closed orbit, so it is always lower at the same radius.
5. Can I use this calculator for any planet or moon?
Yes. Choose a preset for common bodies or use Custom mode. Enter the correct mass and radius, then the calculator applies the same gravitational relations to produce the orbital results.
6. Does this calculator include atmospheric drag?
No. It assumes an ideal circular orbit in vacuum. Real low-altitude orbits can lose energy through atmospheric drag, causing decay unless propulsion or altitude adjustments are used.
7. Can this tool handle elliptical orbits?
Not directly. This page is for circular orbits only. Elliptical analysis needs the vis-viva equation, periapsis and apoapsis distances, and different speeds at different orbital positions.
8. What units does the calculator use?
Mass uses kilograms. Radius and altitude use kilometers. Velocity is shown in meters per second and kilometers per second. Period is shown in seconds, minutes, and hours.