Orbital Period Calculator
Calculate an orbital period from semi-major axis using Kepler's Third Law.
Assumptions used in this calculation
- Two-body, negligible orbiting mass: Assumes a two-body system where the orbiting object's mass is negligible compared to the central body, and ignores perturbations from other bodies.
About this calculator
Kepler's Third Law elegantly links an orbit's size to its period, but the full relationship involves the gravitational constant and the central body's mass in awkward SI units, which is why astronomers use a simplified version expressed in convenient units instead, astronomical units (AU) for distance, years for time, and solar masses for the central body, letting the constants cancel out entirely. This calculator applies that simplified form, T(years) = √(a(AU)³ ÷ M(solar masses)), to compute how long a body takes to complete one orbit, given its orbit's semi-major axis and the mass of the object it orbits, assuming the orbiting body's own mass is negligible by comparison. It's useful for quickly estimating a planet's, moon's, or satellite's orbital period from its distance, checking a fictional or exoplanet scenario in astronomy coursework, or verifying textbook orbital mechanics problems, without converting through the full Kepler's Third Law formula with the gravitational constant and SI units.
Worked example
Earth's orbit (1 AU around the Sun)
Result: 1.0 years (365.25 days)
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