๐ช Keplerโs Third Law Calculator
Calculate a solar-orbiting bodyโs orbital period (years) from its semi-major axis (astronomical units, AU), or the reverse, using Keplerโs third law T(years)=a(AU)^1.5. This is an approximation for a Sun-centered two-body system, calibrated to Earthโs orbit (1 AU, 1 year).
How to use
- Choose "axis to period" or "period to axis" mode.
- Enter the semi-major axis (AU) or orbital period (years).
- The corresponding value is calculated automatically.
FAQ
Why does this formula work in these units?
Because Earthโs semi-major axis is defined as 1 AU and its orbital period as 1 year, Keplerโs 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). Itโs 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 Sunโs mass, so it only applies to bodies within the solar system (planets, asteroids, etc. orbiting the Sun).