Planet Orbital Period Calculator Formula

Understand the math behind the planet orbital period calculator. Each variable explained with a worked example.

Use the Planet Orbital Period Calculator

Formulas Used

Orbital Period

period_years = sqrt(pow(semi_major_au, 3))

Period (days)

period_days = sqrt(pow(semi_major_au, 3)) * 365.25

Variables

VariableDescriptionDefault
semi_major_auSemi-Major Axis(AU)1

How It Works

Planet Orbital Period from Kepler's Law

When the semi-major axis is given in astronomical units and the central star has approximately one solar mass, the period in years is simply the 3/2 power of the axis.

Formula

T = a^(3/2) years

This is the elegant form of Kepler's third law with the Sun's mass baked in.

Worked Example

Earth at 1 AU from the Sun.

semi_major_au = 1
  1. 01T = a^(3/2)
  2. 02T = 1^(3/2) = 1 year
  3. 03T = 365.25 days

Ready to run the numbers?

Open Planet Orbital Period Calculator