Kepler's Third Law Calculator

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Calculate the orbital period or distance of a planet or moon based on Kepler's harmonic law.

Orbital Parameters

Solve For

Central Body

Semi-major Axis (a)

Calculation Results

Enter parameters to see the hidden harmony

About this calculator

Quick Reference

TOrbital Period

aSemi-major Axis (avg distance)

GGravitational Constant

MCentral Body Mass

Overview

Kepler's Third Law (The Law of Harmonies) states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This relationship applies to any system of revolving bodies, from planets around stars to moons around planets.

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Pro Tips

In the simplified Earth-Sun system, T² = a³ when using years and AU.
The mass of the orbiting body (m) is usually negligible compared to the central body (M).
Semi-major axis (a) is the average distance from the center of the orbit.

Fun Facts

"Johannes Kepler published this law in 1819 in his work 'Harmonices Mundi'."
"Isaac Newton later proved that this law is a direct consequence of his law of universal gravitation."
"This law allowed astronomers to determine the relative distances of planets from the Sun long before they knew the absolute distances."

Formula: T² ∝ a³