Orbital Period Calculator (Kepler)
Kepler’s third law for circular orbits.
Your numbers
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Period (minutes)
Period (minutes)
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Period (hours)
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Orbital speed (km/s)
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Orbital Period Calculator (Kepler) by TheCalcTools
How the Orbital Period Calculator (Kepler) works
Enter the radius from the centre of the central body and its mass.
For a circular orbit, gravity supplies the centripetal force.
The period follows from T = 2π √(r³ ÷ GM).
The formula
T = 2π √(r³ ÷ (G M))v = √(G M ÷ r)
Worked example
Using the default values shown in the calculator:
| Orbital radius from the centre (km) | 6771 |
|---|---|
| Central body mass (× 10²⁴ kg) | 5.972 |
- T = 2π √((6,771,000 m)³ ÷ (G × 5.972×10²⁴ kg)) = 92.4 minutes.
- Orbital speed = 7.672 km/s.
Result:
| Period (minutes) | 92.4 |
|---|---|
| Period (hours) | 1.54 |
| Orbital speed (km/s) | 7.672 |
Frequently asked questions
What is the default example?
A low Earth orbit about 400 km above the surface (Earth’s radius is 6,371 km), similar to the International Space Station.
Does the satellite's mass matter?
Not for a small satellite. Only the central mass and the orbit radius set the period.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.