Kepler's laws and his analysis of the observations on which they were based, the assertion that the Earth orbited the Sun, proof that the planets ' speeds varied, and use of elliptical orbits rather than circular orbits with epicycles — challenged the long-accepted geocentric models of Aristotle and Ptolemy, and generally supported the heliocentric theory of Nicolaus Copernicus ( although Kepler's ellipses likewise did away with Copernicus's circular orbits and epicycles ).

Alternatively, he may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model, like what Nicolaus Copernicus later did in the 16th century.

That he anticipated in any manner the inductive reasoning of the true scientific method cannot be contended ; his botanical studies did not lead him, like his contemporary Konrad von Gesner, to any idea of a natural system of classification, and he rejected with the utmost arrogance and violence of language the discoveries of Copernicus.

* Pierre Gassendi, Oliver Thill: The Life of Copernicus ( 1473 – 1543 ): the man who did not change the world, 2002, ISBN 1-59160-193-2

In doing so, Copernicus moved heliocentrism from philosophical speculation to predictive geometrical astronomy — in reality it did not predict the planets ' positions any better than the Ptolemaic system.

Copernicus began to write it in 1506 and finished it in 1530, but did not publish it until the year of his death.

Possibly due to this the system of Nicolaus Copernicus did not cause furious resistance, although it was found to be contradicting verses of Tanakh ( Jewish Bible ).

The first to mention the new system was Maharal of Prague, although he did not mention Copernicus, the author of the system.

Osiander also did not sign the preface added to Copernicus ' book, therefore many readers at the time assumed that this is what Copernicus had actually thought himself.

According to Bartel Leendert van der Waerden, Seleucus may have constructed his heliocentric theory by determining the constants of a geometric model and by developing methods to compute planetary positions using this model, as Nicolaus Copernicus later did in the 16th century.

" He used this method to calculate the eccentricity of the Sun's orbit and the annual motion of the apogee, and so did Tycho Brahe and Copernicus shortly afterwards, though Taqi al-Din's values were more accurate, due to his observational clock and other more accurate instruments.

Ibn al-Shatir ( 1304 – 1375 ), in his A Final Inquiry Concerning the Rectification of Planetary Theory, eliminated the need for an equant by introducing an extra epicycle, departing from the Ptolemaic system in a way very similar to what Copernicus later also did.

In the Galileo affair, the acceptance, from 1616 to 1757, of the Greek geocentric model ( Ptolemaic system ) by the Roman Catholic Church, and its consequent opposition to heliocentrism, was first called into question by the Catholic cleric Copernicus, and subsequently disproved conclusively by Galileo, who was persecuted for his minority view.

To Riccioli the question was not between the geocentric world system of Ptolemy and the heliocentric world system of Copernicus, for the telescope had unseated the Ptolemaic system ; it was between the geo-heliocentric world system developed by Tycho Brahe in the 1570s ( in which the sun, moon, and stars circle an immobile Earth, while the planets circle the sun – sometimes called a " geo-heliocentric " or " hybrid " system ) and that of Copernicus.

How Copernicus would have come across al-Shatir's work, exactly, remains an open question, but there are some number of possible routes for first or secondhand transmission.

A clear illustration of the theory in practice is the Copernican revolution where Copernicus ’ idea of a solar system was largely ignored ( not in the rules ) when first introduced, then Galileo was deemed a heretic ( rules called into question ), and after a revolution in cosmology, the solar system is taken as an obvious and foundational part of scientific knowledge ( new rules ).

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

Copernicus, to an extent unachieved by Ptolemy, approximated to Euclid's vision.

Furthermore, Copernicus continued to use as a point of reference the center of the earth's orbit rather than that of the sun, as he says, " as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy.

* c. 1350 – Ibn al-Shatir anticipates Copernicus by abandoning the equant of Ptolemy in his calculations of planetary motion, and he provides the first empirical model of lunar motion which accurately matches observations

" The Eye of Heaven: Ptolemy, Copernicus, Kepler.

Johannes Kepler ( 27 December 1571 – 15 November 1630 ) was the first to closely integrate the predictive geometrical astronomy, which had been dominant from Ptolemy to Copernicus, with physical concepts to produce a New Astronomy, Based upon Causes, or Celestial Physics .... His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe.

Various 16th-century books based on Ptolemy and Copernicus use about equal numbers of epicycles.

As a measure of complexity, the number of circles is given as 80 for Ptolemy, versus a mere 34 for Copernicus.

Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt, it is one of the most influential scientific texts of all time, with its geocentric model accepted for more than twelve hundred years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus.

In 1632, shortly after the publication of Galileo's Dialogues of the New Science, Torricelli wrote to Galileo of reading it " with the delight [...] of one who, having already practiced all of geometry most diligently [...] and having studied Ptolemy and seen almost everything of Tycho Brahe, Kepler and Longomontanus, finally, forced by the many congruences, came to adhere to Copernicus, and was a Galileian in profession and sect ".

In this respect it differed from the epicyclic and eccentric models with multiple centers, which were used by Ptolemy and other mathematical astronomers until the time of Copernicus.

He described objectively three systems: Ptolemy, Copernicus and of Tycho Brahe without taking sides.

The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others.

* Copernicus, Nicolaus On the Revolutions of the Heavenly Spheres, in Great Books of the Western World: 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952

* Kepler Epitome of Copernican Astronomy ( Bks 4 & 5 ) published in Great Books of the Western World: 16 Ptolemy Copernicus Kepler Encyclopædia Britannica Inc 1952

Two anthologies of his essays have been released, The Great Copernicus Chase and Other Adventures in Astronomical History from Cambridge University Press and The Eye of Heaven: Ptolemy, Copernicus, Kepler in the American Institute of Physics.

* Owen Gingerich: The Eye of Heaven: Ptolemy, Copernicus, Kepler.

As Copernicus ( following Ptolemy ) wrote,

** Celestial spheres, fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others

Galileo, however, felt that the descriptive content of the technical disciplines warranted philosophical interest, particularly because mathematical analysis of astronomical observations — notably the radical analysis offered by astronomer Nicolaus Copernicus concerning the relative motions of the Sun, Earth, Moon, and planets — indicated that philosophers ' statements about the nature of the universe could be shown to be in error.

You could call any century from the twelfth to the twentieth a revolution in science " and that the concept " does nothing more than reinforce the error that before Copernicus nothing of any significance to science took place ".

The Aristotelian model was accepted in the Western world for roughly two millennia, until Copernicus revived Aristarchus ' theory that the astronomical data could be explained more plausibly if the earth rotated on its axis and if the sun were placed at the center of the universe.

As he worked through the mathematics, however, Copernicus discovered that his models could be combined in a unified system.

He concluded that since he could see stellar disks, the stars could not be as distant as was required in the Copernican world system, and he said that the appearance of the stars as seen through a telescope actually argued against Copernicus.

Among the astronomers who were asked to work on the problem of how the calendar could be reformed was Nicolaus Copernicus, a canon at Frombork ( Frauenburg ).

It has been argued that, given some differences between the two models, it is more likely that Copernicus could have taken the ideas found in the Tusi couple from Proclus's Commentary on the First Book of Euclid.

Thus while Tycho acknowledged that the daily rising and setting of the sun and stars could be explained by the Earth's rotation, as Copernicus had said, still such a fast motion could not belong to the earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.

At this time, Copernicus anticipated that he could reconcile the motion of the Earth with the perceived motions of the planets easily, with fewer motions than were necessary in the Alfonsine Tables, the version of the Ptolemaic system current at the time.

An example of this type of claim can be seen in the Catholic Encyclopedia, which states " Fortunately for him dying Copernicus, he could not see what Osiander had done.