It is essentially a geocentric model with the Earth at the center of the universe. The Sun and Moon revolve around the Earth, and the other five planets revolve around the Sun. It can be shown through a geometric argument that the motions of the planets and the Sun relative to the Earth in the Tychonic system are equivalent to the motions in the Copernican system.
Tycho argued that if the Earth orbited the Sun annually, then stars should appear to shift their angular orientations over 6 months as the observer changed their location by the diameter of the Earth's orbit. In fact, this effect of parallax does exist, but it is too small to be observed with the naked eye, and even the telescopes of the next two hundred years could not observe it, because even the nearest stars are far more distant than most astronomers of the time believed possible.
A further consideration for Tycho and his followers was biblical scripture. Some poetic passages seem to assume that the Sun moves or the Earth is stable.
Tycho's system was foreshadowed, in part, by that of Martianus Capella, who described a system in which Mercury and Venus are placed on epicycles around the Sun, which circles the Earth. Copernicus, who cited Capella's theory, even mentioned the possibility of an extension in which the other three of the six known planets would also circle the Sun.
The Tychonic system became a major competitor with the Copernican system as an alternative to the Ptolemaic. After Galileo's observation of the phases of Venus in 1610, most cosmological controversy then settled on variations of the Tychonic and Copernican systems. In a number of ways, the Tychonic system proved philosophically more intuitive than the Copernican system, as it reinforced commonsense notions of how the Sun and the planets are mobile while the Earth is not. Additionally, a Copernican system would suggest the ability to observe stellar parallax, which could not be observed until the 19th century. On the other hand, because of the intersecting deferents of Mars and the Sun (see diagram), it went against the Ptolemaic and Aristotelian notion that the planets were placed within nested spheres. Tycho and his followers revived the ancient Stoic philosophy instead, since it used fluid heavens which could accommodate intersecting circles.
After Tycho's death, Johannes Kepler used the observations of Tycho himself to demonstrate that the orbits of the planets are ellipses and not circles, creating the modified Copernican system that ultimately displaced both the Tychonic and Ptolemaic systems. However, the Tychonic system was very influential in the late 16th and 17th centuries. After the Galileo affair, which transpired early in the 17th century, Copernicanism was officially forbidden to astronomers in the Roman Catholic Church; the Tychonic system was a religiously acceptable alternative that matched available observations. Jesuit astronomers in China used it extensively, as did a number of European scholars.
The discovery of stellar aberration in the early 18th century by James Bradley established that the Earth did in fact move around the Sun, after which Tycho's system fell out of use among scientists. In the modern era, the few who still subscribe to geocentrism use a Tychonic system with elliptical orbits. See modern geocentrism.