The Middle Ages ended with the Renaissance, in which classical learning was once again widely studied, and the Reformation, in which the power of the Roman Catholic Church as exercised through the Pope was successfully challenged in many parts of Europe.
In astronomy, the posthumous 1543 printing of On the Revolutions of the World by Nicholas Copernicus [Polish physician and canon lawyer; 1473-1543] marked the revival of the heliocentric theory, although its success was not immediately apparent. Copernicus's model involved circular motions of the planets, including the Earth; so it was hardly the modern heliocentric theory. In agreement with noted Islamic astronomers, Copernicus rejected the equant as a device to save the phenemonena; instead, he adopted small epicycles to explain the residuals in the planetary distances. His solutions tended to be the same: He made use of Ibn al-Shatir's models for lunar and planetary motions, and the Tusi couple (§7.4) to model planetary oscillations in latitude, as well as the variation of the obliquity. Although Copernicus's work was often cited over the following century, his cosmology was rarely advocated in the universities of this period.
Copernicus entrusted the publication of his work to a Wittenberg academic named Georg Rheticus, and it was done (Narratio prima, "First Report" 1540; and De revolutionibus orbium coelestium, "On the Revolutions of the Celestial Orbs" 1543). In the course of the printing, however, an unsigned preface was added by Andreas Osiander, a Lutheran clergyman (and co-signer of the Augsburg Confession, one of the principal Lutheran doctrinal statements). The preface essentially justifies the printing of what was anticipated to be a controversial work, in words that must have been designed to protect it (and Copernicus) from attack:
Since the novelty of the hypotheses of this work has already been widely reported, I have no doubt that some learned men have taken serious offense because the book declares that the Earth moves; these men undoubtedly believe that the long established liberal arts should not be thrown into confusion. But if they examine the matter closely, they will find that the author of this work has done nothing blameworthy . . . For these hypotheses need not be true nor even probable; if they provide a calculus consistent with the observations, that alone is sufficient. . . Now when there are offered for the same motion different hypotheses, the astronomer will accept the one which is the easiest to grasp. ... So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it.. . . (excerpted in Gingerich 1993, pp. 289-290)
The introduction infuriated Rheticus, who knew Coper-nicus's views on the subject, but may have helped to save the book from the censor in many Catholic and Protestant areas (with few exceptions, the book was frequently censored only in Italy; see Gingerich 1993, 281ff). Philipp
Melanchthon [Theologian and classicist, 1497-1560], Luther's principal lieutenant in the Reformation, championed the interpretation of Copernicus's work as a computational improvement. As a consequence of this circumstance (aided by Melanchthon's more general educational reforms of German universities), the Revolutionibus was widely used by astronomers at Protestant universities, beginning at Wittenberg.
The attitude of one of the leading astronomers in the generation following Copernicus is instructive. Erasmus Rheinhold [astronomer, Wittenberg, 16th century] agreed with the spirit of Osiander's introduction, and, with many other astronomers of his day, did not teach the heliocentric cosmology in his classes. He used Copernican methods to construct tables (the Prutenicae tabulae coelestium motuum or "Prutenic Tables," computed for the longitude of Königsberg, were produced in 1551). From the tables, ephemerides of the day-by-day positions of the planets could be generated. Gingerich (1993, pp. 204-251) has computed and compared the planetary positions from the precepts of Copernicus, Reinhold, and Rheticus, with the true positions. He found that Copernicus's method could produce positions within 10 arc-mins for all of the planets except Mercury, for which the error exceeded 20 arc-mins. These errors were dwarfed by those of the Alphonsine tables, based on purely Ptolemaic devices. Thus, progress in prediction was apparent, regardless of the hesitation to accept heliocentrism. In his treatment of precession, however, Copernicus did not represent progress.
In §7.3, we mentioned the "trepidation" or alleged oscillation of the precession. This fictitious notion was accepted throughout the Middle Ages, and up to the time of Copernicus, who provided a theory51 for it (Swerdlow and Neugebauer 1984; Goldstein 1994). Swerdlow and Neugebauer (1984) evaluated Copernicus's model on the basis of data that were available to him and found it to fit them very well. The "trepidation" can be expressed in an equation as follows (from Mercier 1977, cited in Goldstein):
Table 7.15. Basis for Copernicus's trepidation.
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