Kepler's laws of planetary motion are three mathematical statements, formulated by the German astronomer Johannes Kepler in the early 17th century, that describe the motion of planets around the Sun. The first law states that planetary orbits are ellipses with the Sun at one focus; the second law states that a line segment joining a planet and the Sun sweeps out equal areas in equal time intervals; and the third law states that the square of a planet's orbital period is proportional to the cube of its orbit's semi-major axis. The laws were derived empirically from observational data, primarily that collected by Tycho Brahe, and were later shown by Isaac Newton to follow from the inverse-square law of universal gravitation. Within modern astronomy and physics, the laws are treated as well-established descriptions of orbital motion under Newtonian gravity (and as a close approximation under general relativity for most solar-system purposes); historically, however, their acceptance was bound up with broader disputes over Heliocentrism versus geocentric and geo-heliocentric models, discussed further at Copernican System and Heliocentrism - Scientific Consensus Viewpoint.
Kepler's three laws are part of the standard curriculum in physics and astronomy and are used routinely in celestial mechanics, satellite engineering, and spacecraft navigation. The first and second laws were published in *Astronomia Nova* (1609) 1); the third appeared a decade later in *Harmonices Mundi* (1619) 2). Newton's *Principia* (1687) 3) demonstrated that all three laws follow mathematically from a single force law-gravitation varying as the inverse square of distance-which both validated Kepler's work and subsumed it within a more general theory. Modern refinements, including those arising from general relativity (such as the precession of Mercury's perihelion, which Newtonian mechanics alone does not fully account for), are understood as corrections to Kepler's laws under conditions of strong gravity or high precision, rather than as challenges to their validity within ordinary solar-system contexts. There is no active scientific dispute over the mathematical content of the laws themselves; remaining points of discussion among historians and philosophers of science instead concern Kepler's methodology, the role of his Pythagorean and astrological commitments in arriving at the laws 4), and questions of priority and influence relative to contemporaries 5). See keplers-laws-history for fuller historical background.
There is broad, independent consensus among physicists, astronomers, and historians of science that Kepler's three laws are derivable as a special case (two-body, point-mass) of Newton's law of universal gravitation. See keplers-laws-consensus-newtonian-derivation-consensus.