The astronomical theory formulated by Copernicus that referred to the heliocentric cosmology negated earlier, time-honoured astronomical geocentric theories. This caused a strong reaction within astronomy (mathematics), physics (natural philosophy) and cosmology, which had already appeared during the lifetime of Copernicus in the 16th century, and stopped as late as in our times.
The disputes concerned matters of the methodological and ontological issues (including the status of scientific hypotheses) on the one hand, and the empirical, mathematical and physical-cosmological on the other.
In the initial period (from 1530 to the second half of the 16th century) astronomers were very favourably disposed towards Copernicus’ theory in the empirical-mathematical sphere as a theory, where the hypothetical models of astronomic phenomena agreed with the observations of the Ptolemaic theories and corresponded with the propositions of astronomy at that time that the motions of celestial bodies must be a collection of uniform circular motions with respect to the physical centre. For these reasons Copernicus was known as "the divine thinker", "the second Ptolemy" or "the renovator of astronomy". Scholars, however, repudiated the cosmological sphere of this theory and considered it as contrary to Aristotle’s physics and the Bible.
As a consequence a research program was decided upon, the result of which was formulation of geocentric and geostatic models which were equivalent to those of Copernicus. Such an approach towards Copernicus’ theories was propagated by the representatives of the famous Wittenberg school, founded in the second half of the 16th century around Philipp Melanchthon (1497–1560), including: Caspar Peucer (1525–1602), Erasmus Reinhold (1511–1553), Johannes Praetorius (1537–1616), as well as by Tycho Brache (1546–1601) who was also associated with this school. It was commonly acccepted by Catholic scholars, such as the Jesuit Christoph Clavius (1537–1612) and Giovanni Maggini (1557–1617).
However later, in the early 17th century, Tycho Brahe denied the existence of the slow astronomical phenomena described in the theory of Copernicus, which he recognised in accordance with the traditional formulation of various versions of geo-heliocentric models (consistent with the geocentric cosmology of medieval science). In the first half of the 17th century the Bible, as well as part of Copernicus’ theories, prevailed. Such theories were at that time more valued than the theories of Ptolemy or Copernicus; astronomers led disputes concerning the importance of the discovery of this new system. Besides Brahe such people were engaged in these disputes as Paul Wittich (c. 1546–1586), Helisaeus Röslin (1548–1616), Nicolaus Reimers Bär (Ursus) (1551–1600), Duncan Liddel (1561–1613), and Simon Marius (1573–1624).
The interest in astronomical observations that was caused by the presentation of Copernicus’ theory resulted in the fact that, in Europe, astronomical phenomena became regarded as inconsistent with the scientific paradigm of permanence and perfection of celestial bodies, which had existed since ancient times. New stars were then discovered and it was proved that comets move in the area situated over the Moon (Michael Maestlin (1550–1631)). Thanks to the use of the telescope various imperfections of the Moon’s surface, a satellite of Jupiter, and numerous stars that were yet unknown could be observed (these phenomena were described in 1610 by Galileo in his Sidereus Nuncius) as well as sunspots and phases of Venus observed by Christoph Scheiner (1573–1650) and Galileo.
This criticism of the empirical sphere of Copernicus’ theory by Brahe had a great input on the supporters of the astronomer from Frombork in the first half of the 17th century (there were only ten of them at that time!). They reduced the original version of this theory basically to its Pythagorean-Aristotelian core (i.e. to the daily and annual motion of the Earth, but without the so-called declination motion of the Earth). This was made by William Gilbert (1544–1603), among others, in the context of the magnetic philosophy that he was then formulating, and also by Galileo.
The empirical data gathered by Brahe had a crucial influence on Johann Kepler (1571–1630) who in his four works: Astronomia nova (1609), Epitome astronomiae Copernicanae (1618–1621), Harmonice mundi (1619) and Tabulae Rudolphinae (1627) formulated a new heliocentric theory. He based it on Copernicus’ basic hypotheses (daily rotation of the Earth, the Earth’s annual motion around the Sun, a motionless sphere of fixed stars), on Brahe’s observations, and on the magnetic philosophy of Gilbert. The most important of Kepler’s achievements in this sphere was the discovery that planets move in ellipses. Thus he discarded the dogma sanctioned since the ancient times that orbits of celestial bodies should be described with the use of a combination of uniform circular motions.
From the dialectic with Copernicus’ theory a modern physics was being formed – kinematics, dynamics, theory of gravitation (Giovanni B. Benedetti (c. 1530–c. 1590), Gilbert, Galileo, Descartes (1596–1650), Giovanni A. Borreli (1608–1679), Christiaan Huyghens (1629–1695), Robert Hooke (1635–1703), Isaac Newton (1642–1727)). It was Newton in particular who, by following the searches of Galileo and Kepler, in his Philosophiae naturalis principia mathematica (1687) formulated a great synthesis of terrestrial and celestial mechanics. For many scholars it then became obvious that he had achieved a goal that had been sought by Aristarchus of Samos, Copernicus, Galileo, and Kepler: he had formulated a unified theory of terrestrial and celestial phenomena that coherently explains these phenomena and corresponds with the observations and, at the same time, allows for the existence of the motions of the Earth. The culmination point of these achievements in the 17th, 18th, and 19th centuries was the presentation of direct evidence for the existence of these motions by Jean Richer (1672), James Bradley (1729), Giovanni B. Guglielmini (1791), Friedrich W. Bessel (1838), Friedrich G.W. von Struve (1840), Thomas Henderson (1840) and Jean B.L. Foucault (1851) among others.
Copernicus’ achievements were temporarily less popular among scholars between 1870–1945 in the context of the development of the theory of relativity, when it was originally assumed (by physicists Ernst Mach (1872), Max Born (1922), Willem de Sitter (1932), Albert Einstein, and Leopold Infeld (1938); as well as philosophers Hans Reichenbach (1942) and Bertrand Russell (1945)) that because of the relativity of motion, all the reference systems, including Ptolemy’s and Copernicus’ systems, were physically (kinetically and dynamically) equivalent. However later, in the fifties and sixties of the 20th century this approach became more precise and it was assumed that all the systems of reference are equivalent kinetically, but not dynamically. Thus it was eventually acknowledged that the Copernican system was superior to Ptolemy’s, for it would be impossible to formulate Newtonian physics in the geocentric system.