Orbital Period Calculator
Kepler's Third Law, Four Centuries Later
In 1619 Johannes Kepler published the relationship that still governs orbital mechanics today: the square of a body's orbital period is proportional to the cube of its orbit's semi-major axis. No telescope improvement or space mission has changed that math — it falls directly out of Newtonian gravity. This calculator applies it in two forms: a simplified solar-system version using AU and solar masses, and the general form for any two orbiting bodies given in SI units.
The Formula
T = √(a³ ÷ M)
General form (meters, kilograms, seconds):
T = 2π × √(a³ ÷ (G × M))
Here a is the semi-major axis of the orbit, M is the mass of the central body, and G is the gravitational constant (6.674 × 10¹&sup9; m³ kg⁻&sup9; s⁻&sup9;). The solar-system form is a convenient shortcut that works because, in units of AU/solar-masses/years, G effectively drops out of the equation.
Where This Calculation Applies
- Exoplanet characterization — once a planet's orbital semi-major axis is estimated from transit or radial-velocity data, Kepler's third law gives its orbital period without needing to watch a full orbit complete.
- Satellite mission design — choosing an orbital altitude for a satellite directly determines how often it passes over a given point, which is a period calculation.
- Verifying textbook orbits — checking that a planet's known semi-major axis and period are mutually consistent is a standard way to sanity-check astronomical data.
Solar System Orbital Periods
| Planet | Semi-major axis (AU) | Period (years) | Period (days) |
|---|---|---|---|
| Mercury | 0.387 | 0.241 | 87.9 |
| Venus | 0.723 | 0.615 | 224.5 |
| Earth | 1.000 | 1.000 | 365.2 |
| Mars | 1.524 | 1.881 | 687.2 |
| Jupiter | 5.203 | 11.868 | 4,334.8 |
| Saturn | 9.537 | 29.452 | 10,757.4 |
| Uranus | 19.190 | 84.064 | 30,704.5 |
| Neptune | 30.070 | 164.892 | 60,226.9 |
Semi-major axis values are well-established mean figures; periods above are computed directly from them using the calculator's own solar-system formula, so small rounding differences from each planet's official orbital period are expected.
How to Use This Calculator
- Choose a mode: "Solar System (AU / Solar Masses)" for simple planetary calculations, or "General (meters / kg)" for any orbiting bodies in SI units.
- In solar-system mode, enter the Semi-Major Axis in AU, and optionally the Central Mass in solar masses (defaults to 1, the Sun).
- In general mode, enter the Semi-Major Axis in meters and the Central Mass in kilograms.
- Select Calculate to get the orbital period.
Related Calculations
For a quick estimate of where a planet sits along that orbit on a given date, see the Planetary Position Calculator, or compare orbital speeds with the Orbital Velocity Calculator.