Kepler's Third Law Calculator

Your details

Choose which quantity you want the calculator to find.
Half the longest diameter of the elliptical orbit. 1 AU is the mean Earth-Sun distance (149,597,870.7 km).
AU
Mass of the object being orbited (star, planet, etc.). 1 solar mass = 1.989 x 10^30 kg.
solar masses
Orbital period
0.9999years

Time for one complete orbit around the central body

Semi-major axis1AU
Central body mass1solar masses
Period in days365.22days
Semi-major axis (km)149,600,000km
Central body mass (kg)1.989e+30 kg
Mean orbital speed29.79km/s
a³ / T²1.000171AU³/yr²
Period (years)0.9999
Semi-major axis (AU)1
Central mass (solar masses)1

The orbital period is 365.2 days.

  • This is very close to Earth's orbit around the Sun.
  • The mean orbital speed is 29.79 km/s (107238 km/h).
  • Kepler's third law assumes the planet mass is negligible compared to the central body. For binary stars or systems where both masses are significant, use the full two-body form: a^3/T^2 = G*(M+m)/(4*pi^2).

Next stepTo find orbital speed at any point in the orbit, pair this with the vis-viva equation: v^2 = G*M*(2/r - 1/a).

 = Powered by OnlyCalculators