Orbital mechanics · T = 2π √(a³ / GM)

Orbital Period (Kepler's Third Law)

Kepler's third law: the time to complete one orbit, from the semi-major axis and the central mass. A planet at 1 AU around the Sun takes one year.

Semi-major axis (AU)Central mass (M☉)

Orbital period0.99989yr

Formula: T = 2π √(a³ / GM)

Worked example

With the default inputs, orbital period (kepler's third law) evaluates to 0.99989 yr — 1 AU around 1 M☉ → 1 year. The validator recomputes this against the known value on every build, so the formula is checked, not asserted.

Highlights

›1 AU / 1 M☉ → 1 year

Kepler's Laws of Planetary Motion

Knowledge connections

Associated withKepler's Laws of Planetary Motion

Sources

Facts on this topic will be cited from these primary and reference sources.

NASANational Aeronautics and Space Administration
Mission data, planetary science, space telescopes, and public-domain imagery.
Most NASA-produced imagery is in the public domain; individual items are checked for usage terms before publication.

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Orbital Period (Kepler's Third Law)

Worked example

Highlights

The physics behind it

Knowledge connections

Sources

Orbital Period (Kepler's Third Law)

Worked example

Highlights

The physics behind it

Knowledge connections

Sources