I think Copernicus and his contemporaries were modeling based on some data.
What data was Copernicus using and who created it?
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There's a notable problem of shortage of historical evidence for the way in which Copernicus came to his theories.
His earliest work that described his heliocentric concept is known as the 'Commentariolus', and in it he "says next to nothing about how he arrived at his new theories" -- see N M Swerdlow's (1973) paper "The Derivation and First Draft of Copernicus's Planetary Theory: A Translation of the Commentariolus with Commentary". The 1973 paper is available from Jstor and is still a good source along with the 1984 book "Mathematical Astronomy in Copernicus’s De Revolutionibus" by N M Swerdlow and O Neugebauer (publ. Springer).
Copernicus was trying to improve the Ptolemy system. I will use modernized language to describe this.
In Ptolemy system, the longitude of a planet is given by a function $\lambda(t)=mt+$(other smaller terms), where $m$ is the "mean motion" related to the period, $T=2\pi/m$. He noticed that the second largest term depends on the elongation of the planet from the Sun. So the motion of the Sun is somehow incorporated to motion of all planets. Ptolemy's system does not explain this. To explain this dependence he conjectured that the planets really rotate around the Sun, and thus obtained a simpler description of their motion. This still leaves the choice whether Sun rotates about Earth (Brahe system) or vise versa (Copernicus). Observations known at that time cannot distinguish one possibility from another. So this was a guess, based on "physical reasons'': it was already known that the Sun must be much larger than the planets, including Earth. This was his principal innovation. But he made many other changes to Ptolemy system, some of them were improvements (from the modern point of view), others not.
Speaking of the data used for determining parameters of the system, he used the same data that Ptolemy used, mainly observations of conjunctions and oppositions, besides the periods.