Kepler's Third Law Calculator

Kepler's Third Law says that for any two bodies orbiting the same central mass, the square of their periods divided by the cube of their semi-major axes is the same constant.

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What Is a Kepler's Third Law Comparison Calculator?

Kepler's Third Law says that for any two bodies orbiting the same central mass, the square of their periods divided by the cube of their semi-major axes is the same constant. That lets you compare two orbits — like two planets around the Sun — without even knowing the central mass.

How to Use This Kepler's Third Law Comparison Calculator

  1. Enter the known period (T1) and semi-major axis (a1) of the first orbit, in any consistent units.
  2. Enter either the period or semi-major axis of the second orbit, leaving the other blank.
  3. Click Calculate to find the missing value for the second orbit.

Formula

Worked Example

Earth orbits the Sun with T1 = 1 year at a1 = 1 AU. Mars orbits at a2 = 1.524 AU. Leaving T2 blank: T2 = 1 × (1.524/1)^1.5 ≈ 1.88 years — matching Mars's real orbital period.

Frequently Asked Questions

What does Kepler's Third Law state?

The square of a planet's orbital period is proportional to the cube of its orbital semi-major axis: T² ∝ a³.

How is this calculator used?

Given either orbital period or distance, it solves for the other using the proportional relationship, often calibrated to Earth's orbit as a reference.

Why does this matter for exoplanet discovery?

Once astronomers measure a planet's orbital period, this law lets them calculate its distance from its star without directly measuring it.

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