Who finally proved Copernicus theory of a Heliocentric universe?

Answer 1

The modern theory is the one devised by Johannes Kepler. It uses the heliocentric idea, as Copernicus's model did, but Kepler rejected the circles and epicycles used by Copernicus and Ptolemy before him, and used elliptical orbits for the planets instead.

Kepler's model was published in 1609, and it was realised quite quickly that it represented the movements of the planets more accurately than the old models. But the old models were not bad and their inaccuracies were demonstrated only after Tycho Brahe built new, accurate measuring systems in the late 1500s. Kepler used Tycho's observations.

With 3 systems in play that were all reasonably accurate there was no way of deciding the best one, although Kepler's model was slightly better.

But in the late 1600s Isaac newton had built on previous work to produce the law of gravity and the laws of motion. He was able to show that a planet in the Sun's gravity field must move in an elliptical orbit. This was the clincher that made people accept Kepler's model.