Kepler found that the square of a planet’s orbital period is proportional to the cube of its distance from the Sun.
How to use the Orbital Period Calculator
- Central body mass
- Semi-major axis (from centre)
- Want to work backwards? Type a value into Orbital period and Semi-major axis (from centre) is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Cube the semi-major axis, divide by G times the central mass, take the square root and multiply by 2π.
Inputs explained
| Field | What to enter |
|---|---|
| Central body mass | In kg |
| Semi-major axis (from centre) | Units: m, km, AU |
What each result means
- Orbital period = 2×pi×sqrt([Semi-major axis (from centre)]^3 ÷ (6.6743e-11 × [Central body mass]))
- Mean orbital speed = 2×pi×[Semi-major axis (from centre)] ÷ [Orbital period]
Example values
How the main result changes when Semi-major axis changes and everything else stays at the example values above:
| Semi-major axis (from centre) (m) | Orbital period (min) |
|---|---|
| 3,385,500 | 32.67 |
| 5,078,250 | 60.03 |
| 6,771,000 | 92.42 |
| 8,463,750 | 129.15 |
| 10,156,500 | 169.78 |
| 13,542,000 | 261.39 |
Formula
T = 2π √(a³ ÷ GM)Worked example
Inputs — Central body mass: 5.972e+24 kg; Semi-major axis (from centre): 6,771,000 m.
Results — Orbital period = 92.42 min; Mean orbital speed = 7.67 km/s.
Frequently asked questions
Why use distance from the centre?
Kepler’s law uses the distance from the centre of the central body, not altitude.
How long does the ISS take to orbit?
About 92 minutes at roughly 400 km altitude.
What formula does the Orbital Period Calculator use?
T = 2π √(a³ ÷ GM).
Can I work backwards from the result?
Yes. Type the result you want into Orbital period and the calculator finds the matching semi-major axis (from centre).