Final answer:
Johannes Kepler was the scientist who discovered that the orbits of planets are ellipses, which was a significant advancement in astronomical science and supported the heliocentric model of the solar system.
Step-by-step explanation:
The person who discovered that the orbits of planets are ellipses was Johannes Kepler. Kepler's work built upon the precise observations made by the astronomer Tycho Brahe, allowing Kepler to formulate his three fundamental laws of planetary motion. His laws provided mathematical support for the heliocentric model envisioned by Nicolaus Copernicus, and established that each planet's orbit is an ellipse, with the Sun at one focus. Kepler's laws significantly advanced our understanding of the cosmos and set the stage for Isaac Newton's work on gravitation. Kepler's discovery was monumental in the transition from the geocentric model, endorsed by Ptolemy, to a heliocentric model that placed the Sun at the center of the solar system.