structural:scholar_edition, quality:correction
Publications, correspondence and scientific disputes

In 1588, Tycho's royal benefactor died, and a volume of Tycho's great two-volume work Astronomiae Instauratae Progymnasmata (Introduction to the New Astronomy) was published. The first volume, devoted to the new star of 1572, was not ready, because the reduction of the observations of 1572–73 involved much research to correct the stars' positions for refraction, precession, the motion of the Sun etc., and was not completed in Tycho's lifetime. It was published in Prague in 1602–1603.

The second volume, titled De Mundi Aetherei Recentioribus Phaenomenis Liber Secundus (Second Book About Recent Phenomena in the Celestial World) and devoted to the comet of 1577, was printed at Uraniborg and some copies were issued in 1588. Besides the comet observations, it included an account of Tycho's system of the world. The third volume was intended to treat the comets of 1580 and following years in a similar manner. It was never published, or written, though a great deal of material about the comet of 1585 was put together and published in 1845 with the observations of this comet.

While at Uraniborg, Tycho maintained correspondence with scientists and astronomers across Europe. He inquired about other astronomers' observations and shared his own technological advances to help them achieve more accurate observations. Thus, his correspondence was crucial to his research. Often, correspondence was not just private communication between scholars, but also a way to disseminate results and arguments and to build progress and scientific consensus. Through correspondence, Tycho was involved in several personal disputes with critics of his theories. Prominent among them were John Craig, a Scottish physician who was a strong believer in the authority of the Aristotelian worldview, and Nicolaus Reimers Baer, known as Ursus, an astronomer at the Imperial court in Prague, whom Tycho accused of having plagiarized his cosmological model.

Craig refused to accept Tycho's conclusion, that the comet of 1577 had to be located within the aetherial sphere, rather than within the atmosphere of Earth. Craig tried to contradict Tycho by using his own observations of the comet, and by questioning his methodology. Tycho published an apologia (a defense) of his conclusions, in which he provided additional arguments, as well as condemning Craig's ideas in strong language for being incompetent. Another dispute concerned the mathematician Paul Wittich, who, after staying on Hven in 1580, taught Count Wilhelm of Kassel and his astronomer Christoph Rothmann to build copies of Tycho's instruments without permission from Tycho. Craig, who had studied with Wittich, accused Tycho of minimizing Wittich's role in developing some of the trigonometric methods used by Tycho. In his dealings with these disputes, Tycho made sure to leverage his support in the scientific community, by publishing and disseminating his own answers and arguments.