Calculate orbital periods, distances, and central masses using Kepler's Third Law with solar system verification and unit conversions.
Kepler's Third Law of Planetary Motion, published by Johannes Kepler in 1619, states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. Refined by Newton with the inclusion of the central body's mass, this relationship is one of the most powerful tools in astronomy: T² = (4π²/GM) × a³.
In convenient units where distance is in AU, period in years, and mass in solar masses, the law simplifies beautifully to T² = a³/M. This means that for any object orbiting the Sun, the ratio T²/a³ equals exactly 1. For objects orbiting other bodies, the ratio equals the inverse of the central mass in solar masses.
This calculator lets you solve for any one of the three variables—orbital period, orbital distance, or central mass—given the other two. It includes a verification table showing Kepler's Third Law holds precisely for all eight planets of our solar system, complete with eccentricity data and predicted periods.
This calculator brings one of astronomy's most fundamental laws to life. It's invaluable for students studying orbital mechanics, for verifying astronomical data, and for quickly computing orbital parameters for any two-body gravitational system. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Kepler's Third Law: T² = a³/M (in AU-year-solar mass units). General form: T² = (4π²a³)/(GM). Orbital velocity: v = 2πa/T. Where T is orbital period, a is semi-major axis, M is central body mass, G is gravitational constant.
Result: T ≈ 11.862 years
Jupiter orbits at 5.203 AU from the Sun. Kepler's Third Law predicts T = √(5.203³) ≈ 11.862 years, matching the observed orbital period almost exactly.
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It states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. For solar orbits: T² = a³ (in AU and years).
Yes. Newton's generalized version includes the central mass: T² = a³/M. It works for moons orbiting planets, exoplanets orbiting other stars, and even binary star systems.
For objects orbiting the Sun, T²/a³ = 1 (in AU-year units). For other central bodies, it equals the inverse of the central mass in solar masses.
Kepler spent years analyzing detailed observational data compiled by Tycho Brahe. He published the Third Law in 1619 in his work Harmonices Mundi.
Newton showed the proportionality constant depends on the central mass. Kepler's original form implicitly assumed a solar-mass central body.
No. Kepler's Third Law depends only on the semi-major axis, not the eccentricity. A highly elliptical orbit and a circular orbit with the same semi-major axis have the same period.