The fact that the planets move around the Sun, not in circles but in ellipses, was first demonstrated by

Johannes Kepler was the first to demonstrate that planets move around the Sun in elliptical orbits rather than perfect circles. While Nicolaus Copernicus introduced the heliocentric model, he incorrectly maintained that planets moved in circular paths modified by epicycles [1]. Kepler, utilizing the precise observational data of Tycho Brahe, realized that uniform circular motion did not fit the observed positions of planets like Mars [1]. In his seminal work 'Astronomia nova' (1609), he proposed his first two laws of planetary motion, explicitly stating that planetary orbits are elliptical with the Sun at one focus [1]. This discovery corrected the Copernican model and provided the mathematical foundation for modern astronomy [2]. Galileo Galilei supported the heliocentric theory through telescopic observations but did not formulate the elliptical law.

Sources

1. [1] https://en.wikipedia.org/wiki/Copernican_heliocentrism
2. [2] https://www.britannica.com/biography/Johannes-Kepler