Kepler's Laws of Planetary Motion: Structures & Vocabulary

Kepler's three laws describe the geometry and timing of planetary orbits: planets move on ellipses with the Sun at one focus, sweep out equal areas in equal times, and obey a relationship between orbital period and orbital size. The laws were empirical discoveries later explained by Newtonian gravitation.

Newtonian gravity supplies the inward acceleration that continuously bends inertial motion into an orbit. Conservation of angular momentum explains the equal-area law, causing an orbiting body to move faster near periapsis and slower near apoapsis. Combining gravity with circular-orbit scaling leads directly to the period-size relation and generalizes to elliptical orbits.

Tycho Brahe's precise planetary positions allowed Kepler to reject circular models and fit Mars with an ellipse. Modern radar ranging, spacecraft tracking, binary-star observations, and exoplanet orbits all confirm Keplerian relationships within the regimes where perturbations and relativity are small.

An ellipse is described by semimajor axis and eccentricity. Periapsis and apoapsis mark minimum and maximum distance. The equal-area law means areal velocity stays constant, while the third law connects orbital period to semimajor axis for bodies dominated by the same central mass.