๐Ÿช Keplerโ€™s Third Law Calculator

Orbital period (years)1.8808 years

Calculate a solar-orbiting bodyโ€™s orbital period (years) from its semi-major axis (astronomical units, AU), or the reverse, using Keplerโ€™s third law T(years)=a(AU)^1.5. This is an approximation for a Sun-centered two-body system, calibrated to Earthโ€™s orbit (1 AU, 1 year).

How to use

  1. Choose "axis to period" or "period to axis" mode.
  2. Enter the semi-major axis (AU) or orbital period (years).
  3. The corresponding value is calculated automatically.

FAQ

Why does this formula work in these units?

Because Earthโ€™s semi-major axis is defined as 1 AU and its orbital period as 1 year, Keplerโ€™s third law simplifies to T=a^1.5 in this unit system.

Is this accurate for other planets?

It closely matches observed values for the major planets (e.g. Mars, at 1.524 AU, gives about 1.881 years, matching the actual measured period). Itโ€™s still an approximation that ignores gravitational perturbations from other planets.

Can this be used for bodies orbiting other stars?

No, this simplified formula is calibrated to the Sunโ€™s mass, so it only applies to bodies within the solar system (planets, asteroids, etc. orbiting the Sun).