The famous mathematician and astronomer known for their laws of planetary motion is Johannes Kepler. He lived during the 17th century and is best known for formulating three fundamental laws that describe the motion of planets in the solar system. Kepler's first law states that planets move in elliptical orbits with the Sun at one focus, challenging the traditional circular orbit theory. His subsequent laws further explained the relationship between a planet's distance from the Sun and its orbital period. Kepler's work laid foundational principles for modern astronomy and helped pave the way for future scientists, including Isaac Newton, in understanding gravitational forces.