How did Kepler’s laws replace Ptolemy’s circular planetary motions?

Johannes Kepler’s laws of planetary motion replaced the Ptolemaic system by abandoning the ancient requirement of uniform circular motion, which had long been considered the most perfect path for heavenly bodies.12

While Ptolemy used complex combinations of circles—including epicycles, deferents, and the equant—to account for observed irregularities from a stationary Earth, these models grew increasingly cumbersome. Kepler, working with the highly accurate observational data of Tycho Brahe, found that he could not reconcile the motion of Mars with circular orbits.134

Kepler’s transition to a new model involved:
* Elliptical Orbits: Replacing circular paths with ellipses, placing the Sun at one focus.35
* Variable Speed: Replacing the equant with the "area law," where a planet moves at varying speeds, sweeping out equal areas in equal times.54
* Physical Basis: Moving beyond mere mathematical modeling to propose a physical, Sun-centered system where the Sun actively influences planetary motion.62

These laws provided a simpler, more accurate description of the universe, eventually allowing Isaac Newton to derive them from his own laws of motion and gravitation.36