OrbitLab

Orbital Period Calculator

How long is a year on this orbit?

Semi-major axis (AU)

Central mass (solar masses)

Orbital period

1 years

Kepler's third law, T = √(a³/M)

What you entered

Semi-major axis (AU): 1Central mass (solar masses): 1

1
a³ (semi-major axis cubed, AU)
1³= 1
2
T = √(a³ ÷ M)
√(1 ÷ 1)= 1 years

Result

Orbital period: 1 years

An orbit with a semi-major axis of 1 AU takes about 1 years to complete.

Orbital period of each planet from its distance

Kepler's third law: the period in years is the square root of the semi-major axis in AU cubed, divided by the central mass in solar masses. Nothing about the orbiting body matters.

Planet	Semi-major axis	Calculated period	Actual period
Mercury	0.387 AU	0.2408 years	0.2408 years
Venus	0.723 AU	0.6148 years	0.6152 years
Earth	1 AU	1.0000 years	1.0000 years
Mars	1.524 AU	1.8814 years	1.8808 years
Jupiter	5.203 AU	11.8681 years	11.862 years
Saturn	9.537 AU	29.4522 years	29.457 years
Uranus	19.19 AU	84.0645 years	84.011 years
Neptune	30.07 AU	164.8922 years	164.79 years

The calculated column matches observation to within a fraction of a percent across a 78-fold range of distance, which is why Kepler's law was such convincing evidence for gravity. Doubling the central mass shortens the period by a factor of the square root of 2.

A clean relationship between distance and time

Kepler's third law (in solar-system units) says the orbital period squared is proportional to the semi-major axis cubed, divided by the central mass — Earth's own 1 AU, 1 solar mass orbit gives exactly 1 year, which is why the units work out so simply.

Why it works for any orbiting body

This same law predicted the existence and location of undiscovered planets, and today lets astronomers infer a star's mass just from timing how long a planet takes to orbit it.

Frequently asked questions

An exoplanet orbits at 2.5 AU from a star with 1.2 solar masses — what is its orbital period?

T² = a³/M = 2.5³/1.2 = 15.625/1.2 = 13.02. T = sqrt(13.02) = 3.61 years.

How is the orbital period calculator different from the planetary distance calculator?

The orbital period calculator uses Kepler's third law to find how long one orbit takes from the distance and central mass. The planetary distance calculator converts AU to kilometers and light travel time. Use both together for a complete orbital picture.

Does Kepler's third law work for the Moon orbiting Earth?

Yes, but you must use Earth's mass instead of solar masses and convert units accordingly. The Moon at 384,400 km with Earth's mass gives T ≈ 27.3 days, matching its actual sidereal period.

Why do outer planets have such long orbital periods?

Period scales with the 3/2 power of distance. Neptune at 30 AU has T ≈ 30^1.5 ≈ 164 years. The relationship is steeper than linear — doubling the distance more than doubles the period.