Kepler's Third Law Calculator Formula

Understand the math behind the kepler's third law calculator. Each variable explained with a worked example.

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Formulas Used

Semi-Major Axis

semi_major_au = pow(pow(period_years, 2), 1/3)

Semi-Major Axis (km)

semi_major_km = pow(pow(period_years, 2), 1/3) * 149597870.7

Variables

VariableDescriptionDefault
period_yearsOrbital Period(yr)1

How It Works

Kepler's Third Law

For bodies orbiting the same central mass, the square of the period is proportional to the cube of the semi-major axis.

Simplified Form (Solar System)

T² = a³ when T is in Earth years and a is in AU.

Rearranging: a = T^(2/3)

Worked Example

Mars has an orbital period of 1.881 years. Find its semi-major axis.

period_years = 1.881
  1. 01a = T^(2/3)
  2. 02T² = 1.881² = 3.538
  3. 03a = 3.538^(1/3) = 1.524 AU
  4. 04In km: 1.524 × 149 597 870.7 ≈ 228 million km

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