Kepler's third law

Kepler's third law states that an orbiting body's orbital period squared is proportional to the cube of its orbit's semimajor axis. For bodies orbiting the same central mass, the ratio is constant.

Newton's law of universal gravitation: The law that every pair of masses attracts with force proportional to their masses and inversely proportional to their separation squared. Combining gravity with orbital motion derives the period–semimajor-axis relation.
Johannes Kepler: A German astronomer and mathematician who formulated three laws describing planetary motion. He stated the period–distance relation in 1619, after analyzing planetary observations.
Exoplanet: A planet that orbits a star other than the Sun. A planet's period and its star's mass constrain its orbital scale.
Kepler's first law: The law stating that each planet's orbit is an ellipse with the Sun at one focus. It specifies orbital shape, while the third law relates orbital size to period.
Newton's Principia: Isaac Newton's 1687 work presenting the laws of motion and universal gravitation. Newton showed that Kepler's orbital laws follow approximately from universal gravitation.
Two-body problem: The problem of predicting the motion of two objects interacting through their mutual gravitational attraction. Its exact solution explains how the law applies when both orbiting bodies have significant mass.
Tycho Brahe: A Danish astronomer whose precise pre-telescopic observations recorded planetary positions. His measurements of Mars gave Kepler the data needed to discover the law.
Radial velocity method: A technique for detecting orbiting planets by measuring periodic shifts in a star's spectral lines. The measured period helps infer the planet's orbit and, with stellar mass, its semimajor axis.
Kepler's second law: The law stating that a line from a planet to the Sun sweeps out equal areas in equal times. It describes changing orbital speed, unlike the third law's period–size relation.
Orbital mechanics: The study of the motion of objects under gravitational forces, especially artificial satellites and spacecraft. The period–size relation is a basic constraint in designing and analyzing orbits.

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