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All four were major players in a massive controversy that lasted at least 164 years about the nature of what we now call the Solar System.
Copernicus kicked it off in 1543, the year he died, with a book called 'De Revolutionibus' in which he described an alternative model for the movements of the planets among the fixed stars. By placing the Sun at the centre he realised that the paths of the planets could be made simpler in their geometry than in the standard Ptolemaic model that had the Earth at the centre and had ruled for 1400 years.

Galileo took this new theory up and promoted it aggressively to the point that he was eventually convicted of heresy by the Catholic church for trying to reinterpret The Bible. That put a wedge between scientists and the church.

Meanwhile Johannes Kepler got hold of some new very accurate measurements of the planets' positions and realised that it could all be very much simplified by assuming elliptical orbits for all the planets. That was published in 1609.

Up to then the models were purely phenomological, in other words they modelled the observed positions, and all three model predicted the planets' positions pretty accurately.

But Newton published the 'Principa' in 1687 and in it he described new theoretical discoveries. He showed by mathematical analysis that a planet moving under the Sun's gravity must follow an elliptical orbit.

After that Kepler's theory gradually became accepted everywhere, and it still is generally accepted.
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