Tycho Brahe
The Tychonic cosmological model

Although Tycho admired Copernicus and was the first to teach his theory in Denmark, he was unable to reconcile Copernican theory with the basic laws of Aristotelian physics, which he believed to be foundational. He was critical of the observational data that Copernicus built his theory on, which he correctly considered to be inaccurate. Instead, Tycho proposed a "geo-heliocentric" system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun. His system had many of the observational and computational advantages of Copernicus' system. It provided a safe position for those astronomers who were dissatisfied with older models, but reluctant to accept heliocentrism.

It gained a following after 1616, when the Catholic Church declared the heliocentric model to be contrary to philosophy and Christian scripture, and only able to be discussed as a computational convenience. Tycho's system offered a major innovation in that it eliminated the idea of transparent rotating crystalline spheres to carry the planets in their orbits. Kepler and other Copernican astronomers, tried unsuccessfully to persuade Tycho to adopt the heliocentric model of the Solar System. To Tycho, the idea of a moving Earth was "in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount."

Tycho held that the Earth was too sluggish and massive to be continuously in motion. According to the accepted Aristotelian physics of the time, the heavens, whose motions and cycles were continuous and unending, were made of aether, a substance not found on Earth, that caused objects to move in a circle. By contrast, objects on Earth seem to have motion only when moved, and the natural state of objects on its surface was rest. Tycho said the Earth was an inert body, not readily moved. He acknowledged that the rising and setting of the Sun and stars could be explained by a rotating Earth, 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.

Tycho believed that, if the Earth did orbit the Sun, there should be an observable stellar parallax every six months (the stars' positions would change thanks to Earth's changing position). The lack of any stellar parallax was explained by the Copernican theory as being due to the stars' enormous distances from Earth. Tycho noted and attempted to measure the apparent relative sizes of the stars in the sky. He used geometry to show that the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the Sun to Saturn and to be seen at these distances the stars would have to be gigantic, at least as big as the orbit of the Earth, and of course vastly larger than the Sun. Tycho said:

Deduce these things geometrically if you like, and you will see how many absurdities (not to mention others) accompany this assumption by inference.

Copernicans offered a religious response to Tycho's geometry: titanic, distant stars might seem unreasonable, but they were not, for the Creator could make his creations that large if He wanted. In fact, Rothmann responded to this argument of Tycho's by saying:

hat is so absurd about having size equal to the whole ? What of this is contrary to divine will, or is impossible by divine Nature, or is inadmissible by infinite Nature? These things must be entirely demonstrated by you, if you will wish to infer from here anything of the absurd. These things that vulgar sorts see as absurd at first glance are not easily charged with absurdity, for in fact divine Sapience and Majesty is far greater than they understand. Grant the vastness of the Universe and the sizes of the stars to be as great as you like – these will still bear no proportion to the infinite Creator. It reckons that the greater the king, so much greater and larger the palace befitting his majesty. So how great a palace do you reckon is fitting to GOD?

Religion played a role in Tycho's geocentrism – he cited the authority of scripture in portraying the Earth as being at rest. He rarely used Biblical arguments alone. To him they were a secondary objection to the idea of Earth's motion, and over time he came to focus on scientific arguments, but he did take Biblical arguments seriously.

Tycho's 1587 geo-heliocentric model differed from those of other geo-heliocentric astronomers, such as Wittich, Reimarus Ursus, Helisaeus Roeslin and David Origanus, in that the orbits of Mars and the Sun intersected. This was because Tycho had come to believe the distance of Mars from the Earth at opposition (that is, when Mars is on the opposite side of the sky from the Sun) was less than that of the Sun from the Earth. Tycho believed this because he came to believe Mars had a greater daily parallax than the Sun. In 1584, in a letter to a fellow astronomer, Brucaeus, he had claimed that Mars had been further than the Sun at the opposition of 1582, because he had observed that Mars had little or no daily parallax. He said he had therefore rejected Copernicus's model because it predicted Mars would be at only two-thirds the distance of the Sun.

He apparently later changed his mind to the opinion that Mars at opposition was indeed nearer the Earth than the Sun was, but apparently without any valid observational evidence in any discernible Martian parallax. Such intersecting Martian and solar orbits meant that there could be no solid rotating celestial spheres, because they could not possibly interpenetrate. Arguably, this conclusion was independently supported by the conclusion that the comet of 1577 was superlunary, because it showed less daily parallax than the Moon and thus must pass through any celestial spheres in its transit. While Tycho Brahe and his contemporaries lacked a fully developed alternative to Aristotelian physics, Brahe's comet observations cast significant doubt on its validity.
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