Method / assumptions / examples
How this calculation works
The result is deterministic: the same measurements always return the same estimate. Here is the relationship and where real-world results can differ.
Formula
T = 2π × √(a³ ÷ GM)
Newton's form of Kepler's third law relates period T to semi-major axis a and the central body's standard gravitational parameter GM. This implementation treats the orbiting object as negligible in mass compared with the selected central body, so it is appropriate for ordinary satellite, moon, planet, and test-particle estimates.
Worked example
Examples
Using a 6,771 km semi-major axis—about Earth's 6,371 km mean radius plus 400 km—the ideal period is approximately 92.4 minutes.
Using the Sun and a semi-major axis of 149,597,870.7 km gives approximately 365.26 days.
Common mistakes
What to check before using the result
- Enter semi-major axis from the central body's center. For a circular Earth orbit, add Earth radius to altitude before calculating.
- For an elliptical orbit, semi-major axis is half the long axis—not the current distance, periapsis, or apoapsis alone.
- The negligible-orbiting-mass assumption breaks down for binary systems whose two objects have comparable mass. Those require G multiplied by the sum of both masses.
- The result is an ideal two-body period. Perturbations, oblateness, atmospheric drag, and relativistic effects are outside this model.
FAQ
Frequently asked questions
Is semi-major axis the same as orbital altitude?
No. Semi-major axis is measured from the central body's center. In a circular orbit it equals body radius plus altitude.
Does eccentricity change the period?
Not when semi-major axis and central mass stay fixed in the ideal two-body model. Eccentricity changes speed and distance around the path, but not the full orbital period.
Can I calculate an exoplanet's year?
Yes. Select Custom mass for the host star and enter the planet's orbital semi-major axis in kilometres. Include both masses when they are comparable.
Why is a low Earth orbit about 90 minutes?
A low orbit has a much smaller semi-major axis than the Moon's orbit or Earth's solar orbit. Kepler's third law makes period grow with semi-major axis to the three-halves power.
Primary references