Earth-centered models of the universe, geocentric, and sun-centered models of the universe, heliocentric, equally predicted the position and movement of the planets. Given that the competing systems produced identical planetary predictions, astronomers searched for other kinds of observations that might decide between them. Comets seemed to cross through multiple spheres. The spheres of Mars and the Sun seemed likely to intersect. Several systems predicted that Venus might show phases. The Copernican system predicted stellar parallax, that stars should appear to slightly shift in position, which was not observed. Definitive evidence that could decide the true system of the universe proved elusive.

Since antiquity, comets had posed an enigma. They appear without warning. They do not stay within the Zodiac like the planets. They come from different directions. Their speed and brightness change radically. Their tails always point away from the Sun. Parallax was observed for the Moon but not for comets, which implied that comets are farther away than the Moon, contrary to Aristotle’s argument that comets are fiery vapors in the upper atmosphere.

While mathematicians defied the attempts of physicists and theologians to discount their conclusions, mathematical methods alone were not able to explain the appearance of comets, parallax, and diverse systems of the world. Galileo advocated for the Copernican theory of the universe, while disregarding the system of Tycho Brahe.