第谷系统1588

It is conceptually a geocentric model, or more precisely geoheliocentric: the Earth is at the centre of the universe, the Sun and Moon and the stars revolve around the Earth, and the other five planets revolve around the Sun. At the same time, the motions of the planets are mathematically equivalent to the motions in Copernicus' heliocentric system under a simple coordinate transformation, so that, as long as no force law is postulated to explain why the planets move as described, there is no mathematical reason to prefer either the Tychonic or the Copernican system.

Motivation for the Tychonic system

Tycho admired aspects of Copernicus's heliocentric model, but felt that it had problems as concerned physics, astronomical observations of stars, and religion. Regarding the Copernican system, Tycho wrote,

This innovation expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principle of mathematics. Yet it ascribes to the Earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches, and a triple motion at that.

(The "triple motion" refers to its daily rotation, yearly revolution, and axial precession.)

In regard to physics, Tycho held that the Earth was just too sluggish and heavy 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" or "Quintessence"; this substance, not found on Earth, was light, strong, and unchanging, and its natural state was circular motion. By contrast, the Earth (where objects seem to have motion only when moved) and things on it were composed of substances that were heavy and whose natural state was rest. Consequently, the Earth was considered to be a "lazy" body that was not readily moved. Thus while Tycho acknowledged that the daily rising and setting of the Sun and stars could be explained by the Earth's rotation, 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.

In regards to the stars, Tycho also believed that if the Earth orbited the Sun annually there should be an observable stellar parallax over any period of six months, during which the angular orientation of a given star would change thanks to Earth's changing position (this parallax does exist, but is so small it was not detected until 1838, when Friedrich Bessel discovered a parallax of 0.314 arcseconds of the star 61 Cygni). The Copernican explanation for this lack of parallax was that the stars were such a great distance from Earth that Earth's orbit was almost insignificant by comparison. However, Tycho noted that this explanation introduced another problem: Stars as seen by the naked eye appear small, but of some size, with more prominent stars such as Vega appearing larger than lesser stars such as Polaris, which in turn appear larger than many others. Tycho had determined that a typical star measured approximately a minute of arc in size, with more prominent ones being two or three times as large.

History and development

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. This was foreshadowed by the Irish Carolingian scholar Johannes Scotus Eriugena in the 9th century, who went a step further than Capella by suggesting both Mars and Jupiter orbited the sun as well. In 1501 CE, Nilakantha Somayaji, an Indian astronomer of the Kerala school of astronomy and mathematics presented a comprehensive geoheliocentric model in his treatise Tantrasamgraha (and later elaborated in his Aryabhatiyabhasya). In Nilkantha's computational system, the five planets—Mercury, Venus, Mars, Jupiter and Saturn—orbit the Sun, while the Sun in turn revolves around a central, rotating Earth. According to George G Joseph his equation of the centre for the interior planets(Mercury and Venus) remained the most accurate until the time of Johannes Kepler in the 17th century.

The Tychonic system, which was announced in 1588, 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.

Legacy

After Tycho's death, Johannes Kepler used Tycho's observations 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. In 1616, during the Galileo affair, the papal Congregation of the Index banned all books advocating the Copernican system, including works by Copernicus, Galileo, Kepler and other authors until 1758. The Tychonic system was an acceptable alternative as it explained the observed phases of Venus with a static Earth. Jesuit astronomers in China used it, as did a number of European scholars.