Final answer:
Kepler's work advanced Copernicus's heliocentric theory by demonstrating that planets move in elliptical orbits.
Step-by-step explanation:
Johannes Kepler's work improved upon and supported Copernicus’s heliocentric theory by introducing the concept of elliptical orbits. Kepler showed that the motion of each planet is an ellipse, which is the first of his three laws of planetary motion, effectively explaining the motions of the planets in the heliocentric, or sun-centered, model of the universe previously proposed by Nicolaus Copernicus. Through the utilization of Tycho Brahe's precise astronomical observations, Kepler was able to formulate these laws, providing mathematical backing to the Copernican theory which replaced the previously accepted Ptolemaic system with its complex system of epicycles.