OrbitLab

Orbital Period Calculator

How long is a year on this orbit?

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.

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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.

A clean relationship between distance and time

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.