Orbital Period Calculator
Enter the orbit's semi-major axis and the central body's mass to find the orbital period using Kepler's third law, returned in seconds, days and years.
How to use the orbital period calculator
- Enter the semi-major axis of the orbit in metres.
- Enter the mass of the central body in kilograms.
- Read the orbital period in seconds, days and years.
Examples
Earth around the Sun
a = 1.496e11 m, central mass = 1.989e30 kg
T = 3.156e7 s, about 365 days
Low Earth orbit satellite
a = 6.771e6 m, central mass = 5.972e24 kg
T = 5545 s, about 92 minutes
Frequently asked questions
What is Kepler's third law?
For a body orbiting a much larger mass, the period T satisfies T = 2 x pi x sqrt(a^3 / (G x M)), where a is the semi-major axis and M is the central mass.
What is the semi-major axis?
It is half the longest diameter of the elliptical orbit. For a circular orbit it equals the orbit radius, the centre-to-centre distance.
Does the orbiting body's mass matter?
For a small body around a large one it is negligible and drops out. The simple form assumes the central mass dominates, as with a satellite around Earth.
What units does this calculator use?
Metres for the semi-major axis and kilograms for the central mass. The period comes back in seconds, then converted to days and Julian years.
Why is Earth's year close to one year in the result?
Using Earth's orbital radius and the Sun's mass, the formula returns about 3.156 x 10^7 seconds, which is roughly 365.3 days or one year, as expected.
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