How did Johannes Kepler improve the Copernican model of planetary motion?

Johannes Kepler significantly improved the Nicolaus Copernicus model by transforming it from a system based on circular orbits into a dynamic, physical universe. While Copernicus correctly placed the Sun at the center of the solar system, he still relied on circular paths to describe planetary motion.123

By analyzing the precise observational data of Tycho Brahe, Kepler discovered that the circular model could not accurately account for the observed positions of planets, particularly Mars. Kepler’s improvements were formalized in his three laws of planetary motion:23

• Elliptical Orbits: Planets move in elliptical paths with the Sun at one focus, rather than in perfect circles.41
• Equal Areas in Equal Times: A planet sweeps out equal areas in equal intervals of time, meaning its speed varies depending on its distance from the Sun.42
• Harmonic Law: There is a precise mathematical relationship between a planet's orbital period ($T$) and its mean distance from the Sun ($a$), expressed as $T^2\propto a^3$.42

These discoveries replaced the rigid geometry of the Copernican system with a physical framework where the Sun actively influences planetary motion.1