Orbital Period Calculator (Kepler's Third Law)
Calculate orbital period from semi-major axis using Kepler's third law.
Supports the Sun, Earth, Jupiter, or any custom central body.
Kepler’s Third Law states that the square of the orbital period is proportional to the cube of the semi-major axis.
For any central body:
T = 2π √(a³ / GM)
Simplified for the Solar System (a in AU, T in years):
T (years) = a (AU)^(3/2)
This works because it is normalized to Earth’s orbit (1 AU, 1 year, central mass = 1 M☉).
Parameters:
- a = semi-major axis (half the longest diameter of the elliptical orbit)
- G = 6.674 × 10⁻¹¹ N·m²/kg²
- M = mass of the central body
Solar system examples (using T = a^1.5):
- Mercury: a = 0.387 AU → T = 0.241 years (88 days)
- Venus: a = 0.723 AU → T = 0.615 years (225 days)
- Mars: a = 1.524 AU → T = 1.881 years (687 days)
- Jupiter: a = 5.203 AU → T = 11.86 years
- Saturn: a = 9.537 AU → T = 29.46 years
- Halley’s Comet: a = 17.8 AU → T = 75.3 years
Why does mass of the orbiting body not matter? The orbital period depends only on the mass of the central body and the semi-major axis. A satellite and the Space Shuttle orbit at the same speed if at the same altitude. (This assumes M_central » M_orbiting — valid for planets around stars and satellites around planets.)