keplerian

Keplerian is an adjective relating to the German astronomer Johannes Kepler or to his laws of planetary motion. In astronomy and spaceflight, the term is commonly used to describe motion or orbits governed by Kepler's laws or by the two-body gravitational problem.

Kepler's laws: 1) The orbit of a planet is an ellipse with the Sun at one focus. 2) A line joining a planet and the Sun sweeps out equal areas in equal times. 3) The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.

In the context of celestial mechanics, a Keplerian orbit is a conic section—ellipse (bound), circle, parabola, or hyperbola—with a focus at the attracting body, arising when gravitational force acts as a central inverse-square force in the two-body problem.

Keplerian elements are six orbital parameters used to specify an orbit: the semi-major axis a, eccentricity e, inclination i, longitude of ascending node Ω, argument of periapsis ω, and either the true anomaly ν or the mean anomaly M at a given epoch. These elements determine the size, shape, and orientation of the orbit as well as the position of the orbiting body along its path.

Applications of the concept are widespread in celestial navigation, satellite tracking, and space mission design, where a Keplerian orbit often serves as a baseline model before perturbations are accounted for. In astrophysics, the term also appears in descriptions of Keplerian rotation, where orbital velocity around a central mass follows v ∝ 1/√r in disks such as accretion disks and some planetary systems.