No, Copernicus did not prove that Earth moves around the Sun in the modern scientific sense. He lacked the instruments to detect stellar parallax or directly measure Earth’s motion. What he offered instead was a mathematical model that reorganized the solar system in a way that made planetary motion simpler, more consistent, and more predictable.
Under the geocentric system, astronomers were forced to pile epicycles upon epicycles to explain what they observed—especially retrograde motion. Copernicus’s heliocentric model didn’t immediately improve observational accuracy, but it dramatically improved coherence. The strange motions of the planets became natural consequences of Earth itself being in motion.
This distinction matters. Science does not always begin with proof; it often begins with better explanations. Copernicus showed that a model could be superior even before it was empirically confirmed. Later observations—by Galileo, Kepler, and eventually Newton—would supply the proof Copernicus lacked. But without his model, those confirmations might never have been recognized for what they were.