In this work, Tycho explained two problems posed for Copernicus by the absence of stellar parallax:
- Due to the annual movement of the Earth around the Sun, one would expect to see stars appear to shift in position. This parallax evaded detection, even at Uraniborg.
- Tycho reported precise measurements of the apparent widths of stars, which allowed him to quantify how large they must be as a function of their distance. If stars were mere pinpoints of light, with zero apparent width, there would be no problem for the Copernican system. But if stars show apparent width, then combined with the absence of parallax, there is a problem for Copernicus in that stars that are far enough away to explain the absence of parallax would have to be immense. Indeed, given the observed apparent widths of stars, the diameter of even an ordinary star would have to be no less than twice the distance between the Earth and the Sun. In other words, if the Copernican system were true, then each star must be an incomparably immense body. Indeed, stars would have to be altogether different kinds of bodies than the Sun, far dwarfing the Sun in size, breaking all analogy and proportion with the ordinary course of nature.