Chapter 9 Chapter 7 The Copernican Revolution

Whenever historians write books about the dramatic changes in science, what first leaps to their minds is a fundamental shift in the central question of the universe, a shift away from the view of the earth as the universe. The idea of ​​a stationary center, and the Sun as the center of the universe.This transformation, known as the Copernican Revolution, is often described as a sweeping change in our frame of reference that reverberates on many levels.This shift in cosmology was seen as revolutionary; Copernicus was thus a "rebellious designer of the universe" who brought about a "revolution in the conceptual structure of the universe" (Edward Rowe Sen 1971, pref.).According to Thomas Kuhn (1957), the Copernican Revolution was not a single event (although in terms of is a "singular" noun).It is said that this "epoch-making turning point in the development of Western thought" needs to be considered at different levels of meaning, because, first, it is a "renovation of the basic concepts of astronomy"; second, it is "man's understanding of nature." "a "fundamental" change (which ended with the "unexpected by-product" of "Newton's conception of the universe" "a century and a half later"); Part of "(pp. Vii, 1, 2).Therefore, according to Kuhn's point of view, the so-called Copernican revolution is not just a revolution in science, it is a revolution in the development of human thought and value system.Yet others [e.g., Crombie (1969, 2:176-177)] simply argued that "the Copernican revolution simply attributed the apparent diurnal motion of the celestial bodies to the rotation of the earth about its axis, attribute their annual motion to that revolution of the earth around the sun."

From the point of view of a critical analysis of the concept of a scientific revolution, the Copernican revolution is of special significance, because at that time Copernicus' writings and teachings did not create anything in the accepted basic system of astronomical theory. Immediate fundamental change, it has only slightly affected the practice of experimental astronomers.Those historians and philosophers who admit that there was a Copernican revolution did not pay attention to the principles or details of the Copernican planetary theory, nor did they pay attention to the theory of the moon or the day-to-day work of experimental astronomers—such as The practical work of calculating the positions of the planets and the moon, making ephemeris tables, etc., are all necessary for fortune-telling with astrology.If they first noticed that astronomy is a difficult science, and concentrated their investigations on the question of the possible ways in which, if indeed, Copernican thought had influenced the work of astronomers, these historiography Scientists and philosophers would no longer assert that there had been an astronomical revolution in the sixteenth century, much less a general Copernican revolution.For science, the influence of Copernican astronomy did not begin to appear until some half to three-quarters of a century after the publication of his treatise (1543), when, at the beginning of the 21st century, the physics of the Earth's motion was Thinking about it, some kinematic questions were raised.These problems were not resolved until the advent of a new kind of inertial physics, which was by no means Copernican, and which arose in connection with the work of Galileo, Descartes, Gassendi, and Newton, among others. together.Furthermore, by the 17th century, the Copernican system of astronomy was completely obsolete and it was replaced by Kepler's system.In short, as this chapter will show, the idea that there was a Copernican revolution in science was refuted, and it was a figment of later historians. (The earliest references to the Copernican revolution I found were by J.S. Bailly and J.-E. Montacre, and these accounts will be analyzed in Supplementary Material 7.4.) Obviously, along with the so-called Something similar happened with the English Revolution of the mid-seventeenth century, a so-called revolution as we know it, which was not generally recognized as a revolution until the French Revolution a century and a half later.

Copernican system philosopher.There are simply too many introductions to Copernicus by historians (and historians of science), all of which are confined to the opening pages of Copernicus's treatise, On the Revolutions of the Celestial Spheres.Here, Copernicus describes what is commonly called the "Copernican system," illustrated vividly by an oft-reproduced diagram of concentric circles.The picture looks simple, but its interpretation is far from an easy task.The original manuscript shows a set of eight concentric circles, but does not fully explain what they represent.In the center circle is the word "Sol", which means sun, which is stationary.Looking inward from the outermost circle, the intervals between circles are numbered from 1 to 7: the first ring is marked with stars, and each ring is marked with the name of a planet : 2, Saturn; 3, Jupiter; 4, Mars; 5, Earth; 6, Venus; 7, Mercury.The ring belt of each planet is not only marked with the name of a planet, but also the star period of the planet's revolution.For example, the third ring from the outside is marked: "3Iovis xii annorum revolutio" (3, Jupiter, revolution every 12 years).The circular belt marked with the earth reads: "5. Telluris cu Luna an, re." (Telluris cum Luna annua revolutio: the earth carries the moon around once a year).

What are these circles and rings?To the untrained reader they appear to be circular orbits, but the Copernican scholar Edward Rosen (1971, 11-21) has turned us around to face the fact that these Not the orbits of the planets.They are what physicists call celestial spheres.Copernicus returned to the idea of ​​a celestial sphere embedded with planets, a concept that goes back to the ancient teachings of Eudoxus, Aristotle, Calipus, etc., who believed that (circling the planets in a great revolving sphere, from which it follows that the conception of the celestial sphere (introduced into cosmology by Eudoxus and extended by Aristotle) In a sense, the title of Copernicus's book "On the General Movement" should be changed to "Theory of the Great Sphere".However, we have also noticed that Copernicus has transformed the ancient Greek idea of ​​the celestial sphere centered on the earth into a new celestial sphere thought centered on the sun.The title of the book is hardly revolutionary, but instead suggests that the book is in line with ancient thinking about the universe.Copernicus' use of celestial theory also implies that Copernicus may have considered his work an improvement on ancient astronomy rather than a revolutionary replacement.This is further evidenced by the fact that the order and manner of descriptions used by Copernicus closely followed the guidelines of Ptolemy's Almagest (see below).

The true nature of the Copernican sphere has intensified in recent years.Noel Svedro (1976, 127-129) has compiled some rather convincing evidence that Copernicus may have conceived a series of adjacent celestial spheres.Svedro points out that, in his manuscript, Copernicus gave illustrations to seven circles, while there were eight circles drawn, so it is clear that these illustrations must refer to circles between circles. of seven spaces.He concluded that these spaces probably corresponded to "the large spheres themselves, each representing a certain space layer (the exact extent is not delimited), each corresponding to the celestial sphere above or below Adjacent." The woodblock printed book (Nurimberg, 1543) complicates our problem, and Copernicus neither checked nor corrected the printing problems (cf. Fig. 4(2)]. Here, counting the additional small circles representing the orbit of the Moon around the Earth, there are nine circles in total. The woodcutter may have just foolishly placed the illustration on the wrong side of these circles, but in this way the circles There are too many, for these two unmarked kingdoms lie on either side of the circle marked with the earth and the moon. There is debate about the true nature of these great spheres and the degree of their integrity and continuity. , without a very deep understanding of this debate, we might still think that the drawings in Copernicus's manuscripts are more authoritative than those made by the wood engraver thousands of miles away, and would have It was concluded that the celestial sphere was indeed represented in these pictures, and not the free-circulating orbit in the empty space indicated by the more modern concept.

The outermost celestial sphere is "1. Stellarum fixarum sphaera immobilis (stationary star sphere); here again an old concept is used: the fixed star sphere. However, Copernicus made some changes, because the traditional fixed star sphere must have a daily One rotation. Only in this way can the change of day and night be explained, while in the Copernican format, the celestial sphere is stationary. In the Copernican system, the phenomenon of day and night change is the result of the earth’s daily rotation around the earth’s axis. Say these Stars are "constant" because they have no displacement motion relative to each other in their celestial spheres - planets (or moving stars), in contrast, not only move relative to each other, but Perform motion relative to the stars.

Copernicus assumed that the stars are so distant that their annual parallax is invisible to the human eye.But they can't be infinite either, since the sun is assumed to be their center - which is perfectly true for a celestial sphere, but impossible for an infinite stellar sphere, such stars The sky does not have any geometrical center.Copernicus wrote; "Stellarum fixarum sphaera, seipsam et omniacontinens, ideoque immobilis, nempe universi locus". (Since it is the residence of the universe, the sphere of stars including itself and everything must be stationary.) However, as JT.As Clark (1959, 125) has already pointed out, this is contradicted by a passage he says on the previous pages: "Mobilitsa...sphaerae estin circumlum volvi, ipso actu formam suam exprinmentis" (rotation is a property of the celestial sphere, celestial sphere It is through this rotation that the shape of the object is expressed).

Copernican's celestial diagrams have been misinterpreted (eg by A. Wolf 1935, 16) as a representation of the Copernican astronomical system of the universe, because the circles are marked "II. Orbit of Saturn," respectively III. Orbit of Jupiter," etc.Of course, Copernicus was well aware that no set of simple cyclic motions could accurately describe the world of space.He therefore set about constructing a complex system, first completing a pamphlet entitled "Short Treatise" (written in 154, but not published before the seventeenth century), and later in his "On the General Operation". fully explained in .Anyone familiar with astronomy will probably realize that the diagram in Book 1 of "Theory of General Operations" is at best a diagrammatic, highly simplified model of a system designed to illustrate a wide variety of phenomena. Copernicus introduced not only a certain number of epicycles (which functioned quite differently from those in the Ptolemaic system), but even epicycles of epicycles (or, second order epicycles , that is, epicyclets).As we shall see later, the belief that the Copernican system was extremely simple, as opposed to the Ptolemaic system, was very complex, is doubtful in terms of the number of circles that have been involved in the employment, in fact, This is far from the case.Even Copernicus himself admitted in the Short Treatise that "34 circles" were needed in order to "describe the whole structure of the sky and the coordinated activity of all the planets" (Svedro 1973, 510).

In considering the possible revolutionary impact of the Revolutions of the Celestial Spheres, we must pay attention to the differences that exist between the first book, which opens, and the remaining five books.For this difference, E. J．Already clearly outlined by Diexter Hughes (1961, 289), he reminds us that "The Revolutions of the Celestial Spheres consist of two parts which are quite different in purpose, nature and importance. of." The whole book is divided into 6 volumes, and the first volume of the book alone constitutes the first part of the book.It . . . gives an extremely concise and understandable account of this new world-system.

The second part consists of volumes 2-6, which give a complex and detailed account of this system...in a strictly scientific way..., thus constituting a textbook with the same level of difficulty as Almagest.The third volume of the book presents the discovered evidence that the earth is in motion and the sun is stationary. Difference Between Copernicus and Ptolemy In two works, The Revolutions of the Celestial Spheres and the Short Treatise, Copernicus attacked Ptolemaic astronomy.Copernicus did this not because in Ptolemaic astronomy, the sun is moving while the earth is stationary, but because Ptolemy did not strictly adhere to the rule that all celestial bodies must move at a constant speed. Circular motion or a combination of circular motions to explain.Ptolemy realized that in order to make an accurate description of the motion of the planets, he must abandon the idea of ​​uniform circular motion, and he boldly introduced the so-called "equal point" in the future, so that the motion along a certain arc Non-uniform motion looks like uniform motion relative to this point.From an accuracy point of view, this is a huge step forward (see Figure 5), and it is indeed Kepler's most complete previous explanation of planetary motion.Copernicus, however, believed that the use of equal points violated fundamental principles, and he focused his initial research on designing a system consisting of the sun, planets, moon, and stars, in which the planets and The moon slides along a circle in uniform motion, or some combination of such motions.

Copernicus had two goals for his astronomy.He wanted to be consistent with those motions shown (not actually observed) by the known Ptolemaic model; at the same time he insisted on the physical principle that the motion of all celestial bodies must be uniform circular motion.Both Copernicus mentioned and endorsed the doctrine recognized by the ancient Callipus and Eudoxus in the "Short Treatise" and "On the Revolutions of the Celestial Spheres", in which the combination of circular motions (or rotation) has been used to explain various phenomena; however, Copernicus recognized that this particular system had several shortcomings.In terms of the numerical results involved, Copernicus wrote a considerable portion of the Petit Tracts on the planetary theories of Ptolemy and "most other" astronomers, which used epicycles (See Fig. 6); however, as Copernicus laments (in the introduction to the Petit Essays), the fact of introducing "equal points" means that "any planet, In the celestial sphere to which it is attached, or with respect to a particular circle to it. So far, there has never been uniform motion." As Noel Svedro (1973, 434) has already pointed out, Copernicus Ney "in his comments on the Ptolemaic model ... admits that this description of the motion of the planets is computationally accurate," but he "rejects on principle the violation of the idea of ​​uniform circular motion approach." It is generally accepted that Copernicus' insistence on uniform circular motion was an integral part of philosophical or metaphysical dogma regressing back to Plato, yet Svedro (p. 435) defends Copernican's position ( at least for his position in the Short Essay) and he concludes that "for speculation on such things as [philosophical or metaphysical principles concerning the peculiar motions of celestial bodies], does not belong to the field of mathematical astronomy." Copernicus apparently thought that one of his great achievements in astronomy was to restore the principle of uniform circular motion.His follower, Erasmus Reinhold, asserted that, in Copernican's view, the equivalence point was excluded compared with the removal of the earth from its throne at the center of the universe and the setting of the sun at the center of the universe And a return to the idea of ​​pure uniform circular motion is a more meaningful contribution (Owen Gingerich 1973, 515).Erasmus Reinhold, who completed the compilation of the Prussian Tablets (1551), wrote (in Latin) on the title page of a copy of the Revolutions of the Celestial Spheres in his own collection: " Astronomical axiom: The motion of celestial bodies is uniform circular motion, or motion composed of parts of uniform circular motion" (Gingerich 1973, 515). If the restoration of the Greek canon of uniform circular motion is considered a revolution, then it can be said that there was a Copernican revolution in the sense of retro-thinking, a ritual of cleansing, in which the later Any innovations that arise will be eliminated; this is not a revolution in the new sense of smashing the old, and it is precisely in the new sense that the term "Copernican revolution" usually refers to. .Copernicus's treatise can be seen as a farewell to uniform motion, or at least, he hoped to be understood that way.If so, then, just like O.As Nugebauer pointed out, this was more successful in philosophy than in astronomy because, as Galileo proved less than a century later, the motion of the planets is not uniform, but simply The synthesis of circular motion does not describe the motion of planets very accurately. Copernicus' impact on astronomy When Copernicus wrote "On the Movement of Celestial Spheres", he first wanted to write a monograph on astronomy, rather than conducting a philosophical discussion on the motion of the earth. It was the task of the Deconvolutions, as Ptolemy did, to show the "mathematical structure" of the universe, as the title of his great treatise suggests.Copernicus emphasized the mathematical content of the book in the preface to his treatise, where he pointed out that "mathematics is exclusively for the needs of the mathematician"; Plato's dictum, which warns the reader, stands out: "A man who does not know geometry stops here." When the first edition of The Revolutions of the Celestial Spheres totaled 391 pages, only 14 pages were devoted to general rules, physical principles of science, his philosophy, and his reasons for thinking that the earth, not the sun, moves.Here are included Copernicus' arguments that the apparent motion of the planets is due to their motion in their respective orbits about the sun, and that this apparent motion is due to changes in the position of observation caused by the annual orbital motion of the earth. weakened.The vast majority of this monograph is devoted to "tough" mathematical astronomy.Copernicus showed how to determine the latitude and longitude of planets and moons, and how to deal with problems in the whole field of planetary and lunar phenomena.Copernicus designed a set of orbits for the motion of the outer planets, namely Mars, Jupiter, Saturn, etc., and the motion of the inner planet Venus; Mercury itself needs a special and completely different orbit.The question of the moon is left aside for the time being, and will be discussed later (see below).Copernicus, unlike Ptolemy, was contemptuous of the use of equal points, and because of this he had to introduce a cumbersome system of orbits within orbits: the center of an epicycle is on a deferent, and The center of another small epicycle is on this epicycle again.Since Copernicus' model evolved directly from Ptolemy's model, in order to be suitable for the treatment of the heliocentric theory, Copernicus fixed the center of the planet's celestial sphere on a void point in space—that is, the earth The center of the celestial sphere or a kind of "flat sun"—rather than centering the planetary universe on the sun itself.So in fact, the theory of Copernicus' "On the Movement of Celestial Spheres" is not really a heliocentric (or sun-centered) theory as people usually describe, but just a theory of the sun at rest (that is, the sun does not move. )theory.The true heliocentric system in modern astronomy was not introduced by Copernicus but by Kepler in his 1609 work on Mars. For astronomers, however, the important question is not whether the evidence for a stationary sun and a moving earth is more convincing than the evidence for a stationary earth and a moving sun (as in the opening paragraphs of volume 1 of the book as stated).Instead, what the astronomer must do is to decide whether the mathematical theory of the motion of the planets, of the Earth (equivalent to the apparent motion of the sun), and of the moon is superior to that which was described in Ptolemy's Almagest and those mathematical theories seen in later catalogs.There are two aspects to this question; (1) Does Copernicus' calculation method give results that are more consistent with observations than Ptolemy's method? (As we shall see in a moment, the answer is: no.) (2) Is Copernicus' method of calculation easier (ie, more convenient) to use than Ptolemy's method? (There is no evidence yet that this question was discussed in the late 16th century.) These two questions can be posed as questions that have nothing to do with philosophical debates (whether uniform circular motion is a necessary condition) or cosmological debates (whether it is the earth or the sun that is "really" moving).It seems impossible to us to evaluate methods of calculation without knowing either the philosophical or the cosmological discussions about the motion of the Earth, but in the 17th century the two subjects were considered separately.That is, Copernicus' mathematical astronomy was independent of his cosmology, which was considered a kind of hypothetical basis for doing calculations.To be precise, there was actually a preface written by Copernicus himself when "On the Revolutions of the Celestial Spheres" was published, which is in favor of this view.By the 17th century, people began to realize that this passage saying that the Copernican system can only be regarded as a preface to a calculation hypothesis, and its author was not Copernicus.However, until the early 19th century, the learned astronomer-historian J. B．Derambre still believes that this statement about the hypothesis was written by Copernicus himself. In considering possible Copernican revolutions in astronomy (rather than in the cosmology or philosophy of circular motion), we must consider Copernicus' system of calculating the motion of the earth (or the apparent motion of the sun), the planets, and the moon Compare and contrast with Ptolemy's system.Did Copernicus' method provide astronomers with more accurate results?Irving Gingerich used a computer to find out where the planets actually were in the 16th century and compared the results with those of the 16th-century Ptolemaic catalog makers.He found that the error of the celestial longitude of Mars is 5. .But he pointed out: "As Kepler complained in his Rudolphian Tables, Copernicus' Martian error was close to 5 in 1625." (Gingerich 1975, 86).In short, Copernicus' results were not numerically more complete than those of Ptolemy (which they were supposed to replace).Had Copernicus used Bernhard Walter's observations rather than his own (see R. Kremer 1981), he might have reduced these errors considerably. To what extent did Copernicus himself think his planetary astronomy could be accurate?According to Rheticus ("Nova List"... MDLl, p. 6; cf. Angus Armitage 1957, 153), Copernicus once said that if his planetary theory could be compared with the observed (that is, to within 10 minutes of arc), he himself would have been as excited as Pythagoras had been when he discovered the famous theorem that bears his name.In reality, however, Copernicus never achieved this level of accuracy.To appreciate the magnitude of this exact value, it may be necessary to point out that the observer's naked eye can, on average, only distinguish two pairs of stars 4 arcminutes apart.According to Neugebauer (1968, 90), before Tycho Brahe at the end of the 16th century, people would think that the observations and theories were completely consistent with the accuracy of 10 arc minutes.It didn't take long for 10 arc minutes to be considered too imprecise, and a theory that differed close to this value from the observed position of Mars as determined by Tycho Brahe could be considered invalid. valuable and should be discarded.For Kepler, an error of even 8 arc minutes in Tycho's observations of the planets was inconceivable.The positions of some of the elementary stars ascertained by Tycho generally differ from their true positions by within 1 arcminute (A. Berry 1898, 142), and it is conceivable that, with a few exceptions, the positions of the planets he ascertained The error in position has not exceeded 1 or 2 arc minutes.In New Astronomy (1609), Kepler, following on from Tycho Brahe's observations, wrote (Berry's translation 1898, 184): Since the gods have graciously blessed us with one of the most careful observers, Tycho Brahe, whose observations revealed... calculations with an error of 8 arc minutes, we should be grateful.in the mood to recognize and apply this gift of God...because if I think that the 8 arc minutes of longitude are negligible, then I should completely correct the...hypothesis presented in Chapter 16.Since these errors are not negligible, however, these 8 arcminutes alone have shown the way to a revolution in astronomy; these 8 sections have become the basis material for much of this book. Those historians who believe that there was a Copernican revolution in astronomy are fond of citing as proof Lazmus Reinhold's ("Prussian Tables" or "Prussian Tables"), which The title of the book is in honor of two "Prussians": Copernicus and Reinhold's patron, Duke Albrecht of Prussia.Published in 1551, just eight years after The Revolutions of the Celestial Spheres, it is generally accepted to be a work of the Copernican system, although star tables are accurate to the lone second" whereas Copernicus was only accurate to the lone second. points" (Dreyer 1906, 345), but the overall arrangement of the book still follows the pattern of "On the Revolutions of the Celestial Spheres".The real success of these catalogs undoubtedly "enhanced the reputation of Copernicus" (Gingerich 1975a, 366), but he made "some minor changes to the planetary parameters in order to make them more accurately correspond to the The observations recorded by Copernicus agree with each other", but it is "a futile exercise, because there are some errors in the positions of the planets determined by Copernicus" (p. 366).Dreyer (1906, 345) concluded that "Reinhold's catalogs" were no better than those they superseded because of "the extreme poverty of recent observations... Moreover, Tycho and Nothing could have been better before Kepler's work came to fruition." One thing (Irving Gingerich reminded me of this and it is crucial to mention it) is that, at the end of the 16th century, no one had in fact calculated the positions of the planets according to the Copernican epicycle system (in Copernicus In this system of Pernicus, the center of the small epicycle or the small circle is on the epicycle, and the center of the epicycle is on the deferent wheel or the reference circle). or Reinhold's "Prue Saturn Catalog" listed in the content of the star catalog. Moreover, Copernicus used the terminal position rather than the mean position, so there is never a question whether to add or subtract The ambiguity of a certain correction value, which is a feature of older (mean position based) catalogs, is a serious problem and a source of error. Thus It seems that the star tables in the "On the Motions of the Celestial Spheres" had a real (and beneficial) impact on computational astronomy, although the fundamental features of Copernican's fixed-sun astronomy did not. However, it is believed that what constituted the Copernican revolution was precisely the set of concepts of Copernican astronomy and its cosmic system, rather than the star tables he calculated. Although the Copernican system did not lead to more accurate results, it is often considered "simpler and more refined than the Ptolemaic system" (S.F. Mason 1953, 102), and, "according to the Copernican system, because the number of circles required in the calculation is much smaller." There is a biography of Copernicus subtitled "Father of Modern Astronomy," which would probably lead us to believe, " By establishing that the earth rotates on its axis and revolves in an orbit, Copernicus reduced by more than half the amount of circular motion that Ptolemy considered necessary to carry out the hypothesis" (Armitage 1957, 159).Many accounts of this problem exhibit what Robert Palt (1970, 114) called the "80-34 set," a tenet that goes back at least as far as Arthur Berry's 1898 Astronomical Brief. According to this book, the Copernican universe only needs 34 circles, while Ptolemy or his followers need 80 circles.In fact, it is difficult to say exactly how many circles are needed for each system; the number of circles depends on the computational model and the state of development of the system.We have already seen that Copernicus said at the end of his "Short Essays" that he only needed 34 circles, while Ernst Zinner (1943, 186), a German expert on the history of astronomy, said that , Copernicus actually needed 38 circles.Arthur Koestler (1959, 572-573) calculated that the number of circles needed in The Revolutions of the Celestial Spheres was 48.Nugebauer (1975, 926) showed that the number of circles required by Ptolemy was 43 - 5 less than the number required in the Desperation.Irving Gingerich found that "comparisons of the Copernican system with the classical Ptolemaic system" are "possibly" more accurate, as long as we restrict the circle counts to the longitude structures of the (Sun), Moon, and planets that K: Thus, Copernicus needed 18 circles, and Ptolemy needed 15." He thus concluded that "the Copernican system is a little more complicated than the original Ptolemaic system" (Gingerich 1975 , 87). Obviously, there was no Copernican revolution in simplifying the system of astronomy.In any case, determining which of the two astronomical systems is more compact is not simply the total number of circles required.Regardless of how many circles Copernicus actually probably needed to go through (or assumed he needed to go through), the fact is that all it takes is a quick flip through of The Revolutions of the Celestial Spheres (in any one of three English either of the two facsimiles, either of the first printed or manuscript copies, or any of the later Latin texts), one can get the impression that Copernicus used epicycles extensively.Even a novice can see that there is a certain kinship in geometrical method and composition between the Discourses and the diagrams in the Almagest, which is different from any naive work that considers Copernican The idea that in any obvious sense more modern and more succinct than Ptolemy's writings does not fit. Copernicus was able to explain (or, rather, explain) certain features of the accepted Ptolemaic system.For example, to explain why Venus was never seen from far from the sun, Ptolemy postulated that the center of the epicycle of Venus always lay on a straight line from the Earth to the sun (see Figure 7).Mercury has the same characteristics, although some of its situations are more complicated.Copernicus, however, explained the same phenomenon by referring to the simple fact that the orbits of Venus and Mercury around the sun are smaller than the orbit of the earth around the sun.For the three planets, or exoplanets, whose orbits lie outside the orbit of the Earth, the Ptolemaic theory contains the premise that the radius of the epicycle of each of the three planets is always the same as (average ) parallel to a straight line of the sun.In Copernicus' explanation, these two straight lines seem to converge, or—in other words—"the direction of the radius of the epicycle pointing to the planet is always parallel to the direction of the straight line from the earth to the sun, which is no longer An unexplained coincidence, it is a manifestation of the physical phenomenon of the earth's orbit around the sun" (Rosen 1971a, 408). It is often said that one of the main features of the Copernican system, as compared with the Ptolemaic system, is this "natural" interpretation of planetary motion.In the Ptolemaic system, the sun moves around the earth, which is just another planet or "wandering star", why the motions of Mercury, Venus, Mars, and Jupiter and Saturn, etc., show some characteristics related to the sun. The system does not explain.It is said that this strange phenomenon becomes plausible or understandable when the center of reference of the system is turned from the earth to the sun.In this connection, however, it must be noted that in the Copernican system the motions of the same five planets are characterized in relation to the Earth, although for Copernicus the Earth was a planet like them (cf. Neugebauer 1968, 102-103). Copernicus was very proud of his own theory of the motion of the moon.Ptolemy's explanation of the motion of the moon not only violated the principle of uniform motion.而且对于月球的位置，只有在极大地夸张月球距离的变差的条件下，这种解释的准确性才能达到可以容忍的程度，尽管月球的表现尺寸与视差并没有什么相应的变化。在《天体运行论》中，哥白尼（罗森1971，72）毫不含糊地批评了托勒密的月球理论，因为它预言说："当月球处在上弦情况下并且位于本轮的最下方时，它…将新月和满月时看上去几乎大四倍。"同样，"在上弦和下弦时，月球的视差也应大大增加。"然而，哥白尼断定，任何一位进行细心观测的人"都将会发现，就这两方面而言，上弦月和下弦月的差别是微不足道的。"在《天体运行论》第4册第3章中，哥白尼充分地阐述了他自己的月球理论，该理论长期以来一直被认为可能是这一论著中最有独创性的部分；该理论运用了第二个本轮，即小本轮，它是其中心位于本轮之上的一个小圆。设想月球是在小本轮上运行，这样就排除了非匀速运动以及明显错误的、人们并未观察到的所谓表现尺寸的巨大变化。近年来已有学者指出，早在此理论大约一个半世纪以前，大马士革的天文学家伊本·阿沙特就阐述过这类月球理论（参见E．S．肯尼迪、V．罗伯茨、F．阿布德以及W．哈特内等人的系列论文），但是我们没有任何证据可以说明哥白尼是怎样受到他的穆斯林前辈的影响的。 （参见哥白尼1978，pp．358，385；Derev，bk．3，ch．4） 《天体运行论》与托勒密的《天文学大成》是密切相关的，它并没有真正构成什么人们可以察觉到的、焕然一新的离经叛道行为，此外，事实上，在这两部书中，就像在中世纪的阿尔-巴塔尼的《天文学》中那样，"章与章之间、定理与定理之间、星表与星表之间"（纽格鲍尔，1957，Zbo）都有着一种对应的关系。只是到了开普勒时代（在第谷·布拉赫时代也是如此），"这种传统的魔力才被破除"；我们可以同意纽格鲍尔的这一观点："在开普勒论火星的著作《新天文学》出版以前，没有哪部天文学著作的标题像它那样意味深长。" J． L． E．德雷尔通常总是赞美哥白尼的成就，但他也不得不得出这样的结论：哥白尼的著作有"一个严重的缺陷"（1909，342）。不仅哥白尼本人几乎没有进行过什么实际的观测，而且，由于"对新的观测无所需求"，他的著作因此受损。更确切地讲，这一缺陷的产生部分是由于哥白尼"过分相信了托勒密所进行的观测的准确性"，部分是由于"哥白尼在许多方面寸步不离他的伟大前辈。"开普勒显然是第一位作出这样批评的天文学家，在他的《新天文学》中，他批评了哥白尼试图"更多地去解释托勒密而不是去解释自然。"几乎所有的评论者都指出，哥白尼和托勒密使用的是同样的资料。纽格鲍尔（1957，202－206）曾把"托勒密的水星运动的模型与哥白尼理论"加以对比，他得出这样的结论，即"除了哥白尼坚持用圆周表示每一部分的运动而托勒密则已更为自由地进行探讨以外，这两种模型就在像投影中显示出的那样，几乎没有什么差别。 是否曾有过哥白尼革命？ 那么，对于所谓与哥白尼及其《天体运行论》有关的革命，我们能得出什么结论呢？无论就实用天文学还是计算天文学而言，哥白尼所进行的改革很难说是革命性的，在某些方面甚至可以说是倒退。不过，在提倡用实在论哲学取代流行的工具主义方面（参见补充材料7．1），哥白尼或许可以说是富有革命精神的。我们已经看到，有人声称，所需圆周数目的锐减意味着更进一步的简明性，但是经过严格的考察证明，这类主张是错误的。推广匀速圆周运动是哥白尼体系的一个特点，从某种特定的物理学观点或哲学观点考虑，匀速圆周运动的推广比托勒密的等分点更能令人满意，然而这并没有证明天文观测是件轻而易举的事。开普勒放弃了这种推广。在成功地以本轮轨道为基础构造一个新的天文学体系时，开普勒首先恢复了托勒密的等分点结构。 在16世纪下半叶，人们就地球运动问题对哥白尼体系曾有过一番争论（关于这一点，请参见J．E．L．德雷尔、T．S．库恩、多罗西·斯廷森以及恩斯特·律纳等人的著作）。我认为，这一点也是很有意义的，即莱因霍尔德制作《普鲁土星表》，是16世纪行星天文学的发展依赖哥白尼的唯一重要的例子。就这些星表而言，是哥白尼提供了观测、模型、计算方式以及原始推导和数据，而莱因霍尔德不过是再加工了一下。然而，这些星表的制作——正如我们看到的那样——"并没有为莱因霍尔德提供机会，以表明其信仰，而且他也没有暗示，哥白尼体系在物理学方面是否是正确的"（德雷尔1906，346）。简而言之，尽管有人使用了哥白尼的星表以及他的某些计算方法，但1543-1600年的天文学文献并未表明有什么革命的迹象。按照第3章所提出的检验来看，我们必定会得出这样的结论：如果曾有过哥白尼革命，那么这场革命是发生在17世纪而不是16世纪，而且它是一场与开普勒、伽利略、笛卡尔以及牛顿等人的伟名联系在一起的革命。这些科学家们所进行的改革使天文学体系发生了如此大的变化，以致于它已经不再是严格意义上的哥白尼体系了，尽管开普勒出于对哥白尼的尊敬把他的一部巨著取名为《哥白尼天文学概要》，但这部书是对他自己的革新所作的终极陈述。17世纪许多论述科学问题的作者并不怎么重视哥白尼（参见补充材料7．2），这也暗示了，在天文学中不曾发生过哥白尼革命。 从严格的天文学观点而不是宇宙学（形而上学）观点出发，我们这个时代的早期天文学研究领域中的杰出学者0．纽格鲍尔（1968，103）就会得出这样的结论： 现代史学家充分利用事后认识的有利条件，他们强调日心体系和它所导致的简明性的革命意义。事实上，行星位置的计算完全遵循的是古代的模式，而且所得出的结果也是同样的。哥白尼的太阳理论肯定是与实际的计算、与根本的投影式观念背道而驰的。对月球理论而言，应该有第二个本轮并以此代替等分点——我们现在知道，这是些与伊斯兰天文学的某一学派相似的方法——这种投影式的美妙想法，并不能使人们更容易地想象行星现象。若不是第谷·布拉赫和开普勒，哥白尼体系只会有助于使托勒密体系以更复杂但能令哲学家满意的形式永久存在下去。 按照纽格鲍尔的观点（1957），哥白尼为天文学作出了三项重要贡献。他澄清了从观测到确定参照值的各个步骤，这是方法论上的一项重要改进。他富有洞察力，发现无需附加的和任意的假定而凭借简单的计算便可得知行星与太阳的距离。另外，他那所有行星的轨道有一个统一的中心的假设，为行星纬度的问题找到了答案。 考虑一下例如1600年的情况，或许除了第谷·布拉赫正在进行的革命外，那时的天文学中大概没有什么可以觉察得到的革命。当时，第谷·布拉赫正在用他的新方法对天文学进行全面的改造。这些新的方法包括：使用设计巧妙、制造精良的天文仪器〔规模很大，并备有"小水平板"系统（asystemof"pinnules"），以便能指示出细微的弧的标度的确切的读数〕，使用新的大气折射表、新的观测体系，以及——也许最重要的是——从事这样一种新的，实践，即夜复一夜地在某个行星可见的全部时间内对它进行连续的观测。第谷的那些革新像伽利略用望远镜对月球表面所做的观测一样，其本身并没有在科学中构成一场革命，但它们确确实实地为将会逐渐导致牛顿革命的新的开普勒天文学提供了新的和准确的数据。 1616年，哥白尼的学说因其革命的内容而名扬天下，当时，《天体运行论》被列入了《禁书索引》之中；类似地，伽利略的《关于两大世界体系的对话》在1633年也被禁止出版了。不过，据说《天体运行论》只是"doneccorrigatur"（在修改前）被禁止，而伽利略的《对话》却被无条件地列入了《索引》之中；而且，大概直到19世纪，情况始终如此。在1600年的索引中，《天体运行论》被列入了圣徒会众命令修改的图书的目录之中，此书的非革命的性质和特点由此昭然若揭。几乎要求进行的所有修改，都不过是把对实在的陈述或确定的陈述改为对种种前提条件或假说的陈述。例如，第1册第11章的标题《地球三相运动的证明》被一笔改为《论地球三项运动假说及其证明》。 以牛顿的《原理》（1687）为顶峰的17世纪物理学所取得的伟大进展，并非起源于哥白尼那一个圆套一个圆的复杂体系，而是起源于新的开普勒体系（该体系以太阳为中心，而且每一行星的轨道都是一种统一的简单的曲线即椭圆曲线），起源于显然决非哥白尼主义者的伽利略和笛卡尔等人的物理学思想。正如我们将在第8章中看到的那样，开普勒体系差不多在每一基本原理上都与哥白尼相矛盾。在17世纪的大半个世纪中以及以后的时间里，每当科学家讨论哥白尼体系时，他们几乎总是在指开普勒体系。德雷尔（1909，344）曾直率而大胆地指出："哥白尼并没有创造出当今人们所说的哥白尼体系。"如果说天文学中有过一场革命的话，那么，这是一场开普勒和牛顿的革命，而决不是什么不折不扣或确凿无疑的哥白尼革命。