Orbital Period Calculator
In solar masses and AU, the constant disappears.
Work out Orbital Period. In solar masses and AU, the constant disappears. Free, with no account and nothing to install.
Orbital period
1 years
365.25 days · orbital speed 29.785 km/s
Kepler's third law says the square of the period is proportional to the cube of the semi-major axis. In solar masses, astronomical units and years the constant disappears entirely and it becomes T² = a³/M — which is exactly why those units were chosen, and why the Earth's year drops out as 1. The 3/2 power is what makes the outer solar system so slow. Four times the distance takes eight times as long, so Neptune at 30 AU needs 165 years for one orbit and has not completed two since it was discovered. Escape velocity is always √2 times the circular orbital speed at the same radius — about 41% more. That fixed ratio is why leaving orbit costs so much less than reaching it did.
How the Orbital Period Calculator works
Orbital period, speed and escape velocity from a semi-major axis and central mass. Worked in solar masses, astronomical units and years, where Kepler's third law reduces to T² = a³/M with no constant at all.
Also known as: how long is a year on another planet · orbital speed at a distance · satellite period calculator · escape velocity from orbit
Frequently asked questions
What is Kepler's third law?
The square of the orbital period is proportional to the cube of the semi-major axis. In solar masses, AU and years the proportionality constant is exactly 1, which is why those units are used.
Why is Neptune's year so long?
The 3/2 power. Neptune sits 30 times further out than Earth, and 30 to the power 1.5 is about 165 — so one Neptunian year is 165 Earth years, and it has not completed two since its discovery in 1846.
How is escape velocity related to orbital speed?
It is always √2 times the circular orbital speed at the same radius — about 41% more. That fixed ratio is why leaving orbit costs so much less than reaching it did.
Does the orbiting body's mass matter?
Only if it is a significant fraction of the central mass. For a satellite around a planet or a planet around a star it is negligible, which is why the law works with the central mass alone.
Why the semi-major axis rather than the radius?
Because orbits are ellipses. The semi-major axis is half the long axis, and the period depends only on it — a comet on a long ellipse and a circular orbit with the same semi-major axis take exactly the same time.
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