一哥白尼革命(From Thomas, Kuhn (1957), the Copernican Revolution)

第十一章天文學革命：哥白尼和克卜勒

一、哥白尼革命(from Thomas, Kuhn (1957), The Copernican Revolution)

The criticism of Aristotelian tradition (p.115)
Medieval scholars extended Aristotle’s logic, discovered fallacies in his proofs, and rejected many of his explanations because they failed the test of experience. In the process they forged a number of the concepts and tools that proved essential to the accomplishments of men like Copernicus and Galileo.
Oremse’s brilliant critique has destroyed many of Aristotle’s proofs and suggested important alternatives for a number of Aristotle’s positions. These alternatives were seldom adopted by the scholastics themselves. But medieval scholars continued to discuss them, and that discussion helped to create a climate of opinion in which astronomers could imagines experimenting with the idea of a moving earth.
Oresme was, for example, quite critical of Aristotle’s principal argument for the earth’s uniqueness. Aristotle had said that if there were two earths in space, then they would both fall to the center of the universe and coalesce, because earth moves naturally to the center. This proof, says Oremse, is invalid, because it presupposes a theory of motion that is itself unproved. (He suggests an alternative theory of motion.) On this alternative theory the natural motion of a body is governed, not by its position in an absolute Aristotelian space, but by its position relative to other portion of matter.
Some such theory was prerequisite to the new cosmologies in which the earth was neither unique nor at the center. Similar theories, in various disguises, are common to the work of Copernicus, Galileo, Descartes, and Newton.
(p.118) The tradition of scholastic criticism was a continuous tradition. Key concepts which originated at Paris in the fourteenth century can be traced to Oxford in the same century and to Padua in the fifteenth and sixteenth. Copernicus studied at Padua and Galileo taught there. Though we cannot be sure that from any particular scholastic critic, we cannot doubt that the critics as a group facilitated the production of those arguments. At the very least they created a climate of opinion in which topics like the earth’s motion were legitimate subjects for university discussion.

The impetus theory: Oremse’s refutation of Aristotle’s central argument for the earth’s immobility takes the impetus theory, or something quite like it, for granted.
On the Aristotle’s theory of motion as vertically thrown the stone in the air, the stone cannot accompany it and will therefore not return to its point of departure. But it the earth’s eastward motion endows the stone with an eastward impetus while the stone is still in contact with the projector, that impetus will endure and will cause the stone to pursue the moving earth even after contact is broken. The impetus theory enables the moving earth to endow terrestrial bodies with an internal propellant, and that propellant enables them to follow afterward. |
布里旦說：「當上帝創造世界時，他盡興地移動每個天體，他把衝力加在天體上，以衝力移動天體，如此就不需要再持續地推動它們。他施加在天體上的衝力既不減少，也不會被破壞，因為天體並沒有其它運動傾向。天上也沒有阻抗會抑制或破壞衝力。」Buridan (Oremsme’s teacher) said, “ …when God created the world, moved each of the celestial orbs as He pleased, and in moving them He impressed in them impetus which moved them without His having to move them any more….And these impetuses which He impressed in the celestial bodies were not decreased nor corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.”
歐瑞斯梅則說：「上帝將一定的衝力施加在天體上，正如他把重量施加在地面的每個物體上。….這就好像一個人造了一座鐘，然後使它開始運走。」In Buridan’s writings, perhaps for the first time, the heavens and the earth were at least tentatively subjected to a singled to a single set of laws, and the same suggestion was carried further by Oresme. He suggested that. “when God created …, He impressed them with a certain quality and force of motion, just as He impressed terrestrial things with weight….; it is just the same as a man building a clock and leaving it to run itself….” But to conceive the heavens as a terrestrial mechanism, a piece of clockwork, is to break the absolute dichotomy between the superlunary and sublunary regions.
The possibility of the earth’s motion and the partial unification of terrestrial and celestial law were the impetus theory’s two most direct contribution to the Copernican Revolution.

The intellectual background in the age of Copernicus(p.123-)
Thirteenth-century metaphysics rivals Aristotle’s in profundity; fourteenth-century physics and cosmology exceed Aristotle’s in depth and logical coherence. But Europeans produced no indigenous astronomical tradition to rival Ptolemy’s until the middle of the fifteenth century.
To Europeans of Copernicus’ generation planetary astronomy was, therefore, almost a new field, and it was practiced in an intellectual and social environment quite different from any in which astronomy had been practiced before.
The Renaissance was a period of voyages and explorations. Columbus’ first landfall in America, made when Copernicus was nineteen. Successful voyage demanded improved maps and navigational techniques, and these depended in part on increased knowledge on the heavens. …Each new voyage disclosed new territory, new products, and new people. Men rapidly learned how wrong ancient descriptions of the earth could be. In particular, they learned how wrong Ptolemy could be, for Ptolemy had been the greatest geographer as well as the greatest astronomer and astrologer of antiquity. [Astronomers were aware that Ptolemy might be wrong in astronomy.]
Calendar reform: Agitation for calendar reform had an even more direct and dramatic effect on the practice of Renaissance astronomy, for the study of calendars brought the astronomer face to face with the inadequacy of existing computational techniques. The cumulative errors of the Julian calendar had been recognized much earlier, and proposals for calendar reform date from thirteenth century or before. But these proposals were ineffective until the sixteenth century, when the increasing size of political, economic, and administrative units placed a new premium upon an efficient and uniform means of dating. Then reform became an official Church project….
Copernicus felt that existing astronomical observations and theories did not yet permit the design of a truly adequate calendar. When Copernicus listed the aspects of contemporary astronomy that had led him to consider his radical theory, he began, “For, first, the mathematicians are so unsure of the movements of the Sun and Moon that they cannot even explain or observe the constant length of the seasonal year.” Reform of the calendar demanded, said Copernicus, reform in astronomy. The preface of his De Revolutionibus Orbium Caelestium (On the Revolution of Celestial Bodies；天體運行論) closed with the suggestion that his new theory might make a new calendar possible. The Gregorian calendar, first adopted in 1582, was in fact based upon computations that made use of Copernicus’ work.

The Renaissance Neoplatonism and sunworship (the heliocentric theory:太陽中心論, p.128-)
Neoplatonists such as Proclus, D. M. de Novara, Ficino, may have helped Copernicus to conceive a new system constructed about a central sun. As soon as he had discussed the new position of the sun, Copernicus adverted to the fitness of his new cosmology. His authorities are immediately Neoplatonic: “….So the sun Sits as upon a royal throne ruling his children the planets which circle round him.”
Neoplatonism is explicit in Copernicus’ attitude toward both the sun and mathematical simplicity. It is an essential element in the intellectual climate that gave birth to his vision of the universe. But it is often hard to tell whether any given Neoplatonic attitude is posterior or antecedent to the invention of his new astronomy in Copernicus’ thought.
克卜勒說：「太陽是光的泉源、富含豐饒的熱、最公平、清澈、對視覺最純粹、乃是視覺的來源….我們回到太陽是最正確的，藉著它的尊嚴與權力，它獨自顯現了適合它的責任，它值得變成上帝──第一動者──的家。」No similar ambiguity exists with respect to the later Copernicans. Kepler, for example, the man who made the Copernican system work, is quite explicit about his reasons for preferring Copernicus’ proposal: “[The sun] is a fountain of light, rich in fruitful heat, most fair, limpid, and pure to the sight, the source of vision, …..[Hence] by the highest right we return to the sun, who alone appears, by virtue of his dignity and power, suited for his motive duty and worthy to become the home of God himself, not to say the first mover.”

Copernicus’ Innovation (chapter 5, p.134-)

The beginning of Copernican Revolution:
The publication of Copernicus’ De Revolutionibus Orbium Caelestium in 1543 inaugurates the upheaval in astronomical and cosmological thought that we call the Copernican Revolution.
But, to any reader aware of this outcome, the De Revolutionbus itself must be a constant puzzle and paradox, for, measured from in terms of its consequences, it is a relatively unrevolutionary work. …
(Kuhn’s special comment) The significance of the De Revolutionibus lies, then, less in what it says itself than in what it caused others to say. It is a revolution-making rather than a revolutionary text.
The De Revolutionibus was written to solve the problem of the planets, which, Copernicus felt, Ptolemy and his successors had left unsolved. In Copernicus’ work the revolutionary conception of the earth’s motion is initially an anomalous by-product of a proficient and devoted astronomer’s attempt to reform the techniques employed in computing planetary position.

Copernicus’ Physics and Cosmology
Copernicus learned of the earth’s motion by examining the celestial motions, and, because the celestial motions had to him a transcendent importance, he was little concerned about the difficulties that his innovation would present to normal men whose concerns were predominantly terrestrial. …He had at least to make it possible for his contemporaries to conceive the earth’s motion; he had to show the consequences of this motion were not so devastating as they were commonly supposed to be.
Several propositions in Book One:

That the Universe is Spherical.
That the earth also is Spherical.
How Earth, with the water on it, forms one Sphere.
That the motion of the Heavenly bodies is uniform, circular, and perceptual, or composed of circular motion.

(Only a uniform circular motion, or a combination of such motion, can, he thinks, account for the regular recurrence of all celestial phenomena at fixed intervals of time. So far every one of Copernicus’ arguments is Aristotelian or scholastic, and his universe is indistinguishable from that of traditional cosmology.)

Whether circular motion belongs to the earth; and concerning its position: That the earth, besides rotating, wanders with several motion and is indeed a planet.

(Copernicus is here pointing the most immediate advantage for astronomers of the concept of a moving earth. If the earth moves in an orbital around the center as well as spinning on its axis, then, at least qualitatively, the retrograde motions can be explained without the use of epicycles.)

Why the Ancients believed that the Earth is at rest, like a Center, in the Middle of the Universe: Aristotle argue Earth is the heaviest element, and all things of weight move towards it…Another argument is based on the supposed nature of motion.
The insufficient of these arguments, and their refutation: Now if one should say that the Earth moves, that is as much as to say that the motion is natural, not violent [or due to an external push]; and things which occur by violence. Things subjected to any force or impetus, gradual or sudden, must be disintegrated, must be disintegrated, and cannot long exist. But natural processes being adapted to their purpose work smoothly. [That is, if the earth moves at all, it does so because it is of the nature of earth to move, and a natural motion cannot be disruptive.]

7. Copernician astronomy—The moving Earth

（以下論証中文部分是重新整理與簡化後的哥白尼式的理論，而不是De Revolutionibus 中的理論）

7.1從導論中的介紹，我們已知哥白尼讓地球從不動的宇宙中心，變成依其本性不斷運動的天體之一。而地球有三種同時的運動：周日繞地軸旋轉（自轉）、周年軌道運動（公轉）、地軸周年圓錐運動。Copernicus endowed the earth with three simultaneous circular motions: a diurnal axial rotation, an annual orbital motion, and an annual conical motion of the axis.

7.2 如果地球是移動的天體之一，那麼如何說明地球上所觀察到的天球現象？首先是天幕諸星體每天均由東向西運行？首先，讓我們假設地球位於宇宙中心，而且繞著自己的軸而自轉。如此，即可說明天體的每日向西運動（換言之，現在是地球上的觀察者每天轉動）。If the earth is situated at the center of the sphere of the stars, and rotates eastward daily about an axis through its own north and south poles, then all objects that are stationary or nearly stationary with respect to the sphere of the stars will seem to travel westward in circular arcs above the horizon.

7.3 但地球不是位於宇宙中心自旋，而是會移離宇宙中心。如果地球移離中心的很遠，我們看到的天幕必定不是對稱的，但觀察結果卻非如此，故地球的移動必定在宇宙中心附近。

7.4 再考慮地球與天球的直徑比例。如果地球的直徑相對於天球是一個不小的比例，則我們看到的天球將不會是二等分，但觀察的結果卻是二等分的天球，故地球的直徑必定非常小，小到相對於天球約只等於一點。(The earth’s central position within the sphere of the stars can apparently be derived from the observation that the horizon of any terrestrial observer bisects the stellar sphere. The vernal equinox and the autumnal equinox are, for example, two diametrically opposite points on the sphere of the stars, for they are defined as the intersections of the two great circles on the sphere, the equator and the ecliptic. P.157)

7.5 進一步，既然地球不是宇宙中心，但又不能偏離中心太遠，所以地球可能環繞太陽旋轉，而太陽才是宇宙的中心[1]。所以，接下來，必須處理地球上觀察到的太陽運動之現象。

8. Copernician astronomy—the sun

8.1我們在地球上觀察到太陽穿越天球的路徑是黃道，太陽約每365天運行黃道一圈，如何說明這種現象呢？過去的解釋是太陽穿過天幕，由西向東轉動，現在如果我們讓地球由西向東繞著太陽旋轉，則由地球上觀察一個靜止不動的太陽，就會把太陽投射到天球上，看起來好像太陽穿過天球運行一般（見圖）。(As the earth has moved eastward from position E1 to position E2 in the diagram, the sun has apparently moved eastward along the ecliptic from position S1 to position S2. Copernicus’ theory therefore predicts just the same eastward annual motion of the sun along the ecliptic as the Ptolemaic theory.)

8.2接著，我們在地球上觀察到的，不同季節時太陽高度之改變，由下圖來說明(p.162)：

8.3地球繞太陽公轉的另一証據，恆星視差(parallax)，但這一直要到十九世紀才能觀察出來。

9. Copernician astronomy—The planets

9.1行星逆行現象的說明（外圍行星(superior planet)）：

9.2內層行星(inferior planets)（金星和水星）：

9.3行星運行所花時間的不規則性之說明。（在托勒密天文學中，以偏心圓來說明）某些行星沿著黃道運行時，在某些時候運行速度較快，某些時候則較慢。換言之，忽快忽慢的現象。哥白尼理論如何說明？

In the above diagram it is assumed that the earth completes 1 and 1/4 eastward trips about its orbit while the planet, in this case a superior planet, travels eastward through its orbit once. 設兩者分別從E1與P點開始，當地球走完1又1/4 圈時（此時在E2點），行星也回到P點，則此時，地球上看行星的位置卻只在2 點處；等於是行星速度變慢了。第二輪，行星回到P點，此時，地球卻在E3點的位置（地球從E2點開始，繞一圈又1/4圈到達E3點），此時看行星則回到3點位置，但和最初的1點重合。接著第三輪，行星又回到P點，地球則達到E4點，此時，看行星卻在4點位置。等於說行星速度變快了。如果E1點時是春天，E2點時是夏天，則有些年間我們會覺得夏天的行星速度變慢了（因為還不到P點）；E4點則是冬天，則有些年間我們會覺得冬天的行星速度變快了（超過P點了）。

10. 哥白尼本人在De Revolutionibus 中的系統，其實不像上述所闡明的那般簡單明確，而是相當複雜繁複；上述的說明，都是在地動論的基礎上簡化精煉後的產物。哥白尼對宇宙結構的觀點，也沒有擺脫古希臘傳統觀點的窠臼（如相信所有的行星都位於最外層的天球。見附圖）哥白尼甚至也沒有完全拋棄托勒密的本輪－均輪系統。但他拋棄了托勒密的均等圓(equant circle)模型。

10.1 從純粹的實行效用上來判斷，哥白尼的新行星系統其實個失敗。它既不比托勒密派更精確，也沒有更簡單。但就歷史來看，這個新系統卻取得很大的成功。《天體運行論》說服了一些後繼者，使他們深信太陽中心天文學乃是行星問題的關鍵。Judged on purely practical grounds, Copernicus’ new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessors. But historically the new system was a great success; the De Revolutionibus did convince a few of Copernicus’ successors that sun-centered astronomy held the key to the problem of the planets, and these men finally provided the simple and accurate solution that Copernicus had sought.

10.2 Copernicus is neither an ancient nor a modern but rather a Renaissance astronomer in whose work the two traditions merge.

10.3 哥白尼其實處理的是老問題，以地球運動而告終。然而哥白尼的後繼者卻以地球運動為起點，他們所面對是一組全新的問題（譬如行星視差(stellar pallax)的問題，宇宙大小的問題：宇宙要比古人認知的大得多，所以才觀察不到視差[2]）。Those whom Copernicus converted to the concept of a moving earth began their research from the point at which Copernicus had stopped. Their starting point was the earth’s motion, which was all they devoted themselves were not the problems of the old astronomy, which had occupied Copernicus, but the problems of the sun-centered astronomy, which they discovered in the De Revolutionibus.

10.4 哥白尼所提出的太陽中心論的問題，乃是一組他和他的先驅者都不曾面對過的新問題。哥白尼本人並沒有完成革命，而是其後繼者在解答這些問題時，才完成了「哥白尼式的革命」。（其實，我們可以說，這個「哥白尼式的革命」一直要到牛頓才真正完成）。Copernicus presented the problems of the sun-centered theory with a new set of problems neither he nor his predecessors had had to face. In pursuit of those problems the Copernican Revolution was completed, and a new astronomical tradition, deriving from the De Revolutionibus, was founded.

10.5 (R. A. Hall, p.143, Fig6)哥白尼的宇宙系統（其中superior planets 仍然要依賴本輪來說明。而太陽也不是真正位於軌道運行的中心。）

11. 無限宇宙(infinite universe)的觀念：

11.1 行星視差可以說是哥白尼系統的最大挑戰之一。對堅持哥白尼學說的人而言，這個問題的一個可能解答就是放大宇宙的尺度：宇宙一定比古人所想的還大得多。恆星層距離太陽系太遙遠了，所以才觀測不到視差。後來的科學家進一步取消了恆星都位於同一球體的觀念。

11.2 布魯諾已經有一個無限擴張的宇宙之觀念。英國的狄吉斯(Thomas Digges, 1543-1595)改寫《天體運行論》的第一冊，取消恆星固定在最外圍球體的觀念。恆星存在於在天球體外，四面八方無限伸展的空間裏。（見附圖）

11.3 同樣是英國人的吉伯特(William Gilbet, 1540-1603)，取消外圍球體，恆星散佈於宇宙的無限空間中。吉伯特的宇宙中，地球不是位在某個天球殼上，但其它行星仍在於天球殼層上（見附圖）。

二、哥白尼之後：第谷(Tycho Brache, 1546-1601)、克卜勒(Johannes Kepler, 1571-1630)、伽利略(Galileo Galilei)

1. 哥白尼讓地球轉動之觀念，很多人不能接受，特別在當時的觀念中，如果地球自轉的話，地球早就變成碎片四散紛飛了。十六世紀後半最具權威性的天文學家第谷（他是當時最好的觀察天文學家），即是不同意哥白尼的地動說。他以為物理意義與聖經都不支持地動的觀念，而且第谷一直觀察不到視差，所以哥白尼必定是錯的。第谷自己提出了一個宇宙系統，主張其它行星繞太陽旋轉，而太陽則帶著其它行星繞地球轉。地球仍是保持不動，且做為宇宙的中心。

2. 克卜勒是個旗幟鮮明的新柏拉圖主義者，太陽中心的信仰者。他的研究包含了新柏拉圖主義與物理思辨的奇怪組合。He desired to find in the architecture of the heavens both an obvious mathematical harmony, and a physical explanation of why this exist harmony exists. Thus Kepler was both the last in the line of pure geometrical astronomer who sought to define the celestial motions by lines and curves, and the first to conceive of a celestial mechanics that was not a mere hypostatization of geometry.

2.1 克卜勒在1596年的Mysterium cosmographicum 一書中，提出了一個宇宙結構，每個行星位在於一個天球殼層上，殼層與殼層之間由五個規則固體撐住，由內而外依序為：（水星）八面體（金星）十二面體（地球）二十面體（火星）四面體（木星）立方體（土星）。

2.2 然而，由於慧星的研究，發現慧星的軌道是穿行在各行星之間，如此天空必定不能存在球殼，否則會干擾慧星運行。克卜勒在十七世紀初放棄原先的宇宙結構之觀念。既然放棄球殼宇宙的觀念，則行星在虛空中能維持在軌道上的原因是什麼？就成為下個階段最重要的課題。

3. 克卜勒三大行星定律：（他從第谷那兒獲得大量的觀察資料，而歸納出三大定律）。第一第二定律在1609年的Astronomia nova(Celestial Physics)中提出；第三定律在1619年的Harmonices Mundi(Harmony of the World) 中提出）。

第一定律：行星軌道是橢圓的，而太陽位於其中一焦點。
第二定律：行星在相等的時間內，掃過軌道平面的面積相等。（因此行星在遠離太陽時速度變慢；在靠近太陽時速度變快。）

第三定律：行星軌道直徑的立方和它們的周期時間平方成正比。

3.1 克卜勒在《世界的和諧》一書中，致力於研究行星所發出的四種聲音（女高音域(soprano)、女低音域(contralto)、男高音域(tenor)、男低音域(bass)）。這表明了他的新柏拉圖主義之影響。

4 接著克卜勒試圖回答：為什麼非圓形（橢圓的）軌道的天體仍能保持和諧？它們運行的力量又來自何處？他想像行星被旋轉太陽的輻射力所驅動，當距離越增加時，外圍行星就被驅動得較慢。為了說明橢圓軌道，克卜勒也假設了太陽與每一行星之間存在一種兩極的磁力，在遠日點(aphelion)那一半時，行星被磁力推動，在近日點(perihelion)，行星則被反向磁力往裏拉。但這只是想像，無法以數學來說明。

5 哥白尼系統的天體動力學要一直到牛頓才完全奠定。其中伽利略也扮演革命科學家的角色。(以下出自Kuhn , Copernican Revolution, pp. 222-223)

5.1 伽利略的貢獻在兩方面：一方面，運用望遠鏡的觀察，提供了哥白尼系統旁證。另方面，處理哥白尼系統所面對的「地球在動」之後產生的種種問題。如自由落體為什麼不會被拋在後頭問題。

6 伽利略有望遠鏡這種新工具，他聽說荷蘭磨鏡工人組合兩片透鏡後，可以放大遠距離的物體，他自己嘗試各種組合，而製作出自己的低倍率望遠鏡。

7 伽利略首先發現許多新星星，銀河在肉眼看來只是一條稀薄雲帶，現在則有許多星星擁擠在一塊兒。宇宙一下子膨脹許多。這給哥白尼系統的放大宇宙一個旁証。他又發現月亮表面佈滿坑洞山谷，不是平面如鏡，這衝擊了天體與地面物體區分之觀念。後來，發現了木星的衛星──木星有自己的「月亮」對十七紀人來說是一巨大衝擊。也確立了月球乃是地球衛星的觀念。古代天文學中的恆星、行星範疇開始加入衛星這個新範疇。

8 木星衛的發現降底了對哥白尼系統的反對。而且它為哥白尼的太陽系統提供了一個視覺上的模型。The discovery of Jupiter’s moons therefore reduced the force of one more objection to the Copernican system. The old astronomy, as well as the new, would have to admit the existence of satellites, governed by planets. In addition, and perhaps most consequential of all, the observations of Jupiter provided a visible model of the Copernican solar system itself.

9 伽利略的望遠鏡所提供的證據，對哥白尼來說是有力的，但也很奇怪。因為主要的證據──如太陽位於宇宙中心，而地球在運動（如視差現象）都無法觀察到。望遠鏡並不能完全證明哥白尼的架構有效，但它提供了理論戰鬥上的有效武器。The evidence for Copernicanism provided by Galileo’s telescope is forceful, but it is also strange. None of the observations discussed tenets of Copernicus’ theory—the central position of the sun or the motion of the planets about it. The telescope did not prove the validity of Copernicus’ conceptual scheme. But it did provide an immensely effective weapon for the battle.

一、哥白尼革命的思想背景：

1. 對亞氏物理學的批判：

1.1 十四世紀巴黎和牛津學派對亞氏物理學的批判，為哥白尼和伽利略等人提供了必要的概念和工具。

1.2 士林學者很少採納他們的觀點，但持續討論，創造一種思想氣候──可以想像一個移動的地球。

1.3 歐瑞斯梅(Oresme)批判亞氏地球唯一性的論證：如果有兩個地球，則兩個必定都落在宇宙中心而合併，因為地（土(earth)）自然地會移向中心。歐瑞斯梅認為這個論証無效，因為它預設了一個有待證明的運動理論──即運動是由其絕對所在(place)來決定。但歐瑞斯梅建議另種運動理論──運動由相對所在來決定。

1.4 經院傳統對亞氏的批判，由巴黎、牛津到巴都亞，而哥白尼曾在巴都亞唸書，伽利略則曾在巴都亞教書。

2. 衝力理論：

2.1 按亞氏的運動理論，如果地球在動，那麼垂直向上丟石頭，石頭不會掉回原處，如此與經驗不符。然而歐瑞斯梅的衝力理論則可以容許地球運動。因為地球的向東運動提供石頭一個向東的衝力，當物體向上丟時，物體因為有衝力，還是可以保持和地球的運動方向平行，所以掉落原處。

2.2 布里旦和歐瑞斯梅的作品中，天體運動和地面運動首度可以統一起來。因此，地球運動的可能性和天與地的局部統一，乃是他們哥白尼革命的最大貢獻。

3. 社會背景：

3.1 對托勒密天文傳統的質疑一直要到十五世紀中以後──與歲差問題有關。即由於托勒密系統的年曆不準確，春分點的日期不斷前移。

3.2 航海冒險帶來地圖與航海技術的需求，航海也擴展歐洲人的視野，使他們開始質疑古人的權威。

3.3 年曆改革的壓力：十三世紀的羅傑．培根已發現朱里安曆的問題，但一直到十六世紀，教會才開始正視。

3.4 哥白尼感到托勒密天文學無法容許更精確的年曆計算。1582年的格利哥曆(Gregorian calendar)即是建立在哥白尼作品的計算上。

4. 文藝復興時的新柏拉圖主義與太陽崇拜：

4.1 新柏拉圖主義幫助哥白尼認知到一個建立在太陽中心上的新系統。

4.2 很難辨識新柏拉圖主義究竟先於或後於哥白尼的天文學。

4.3 克卜勒則是旗幟鮮明的新柏拉圖主義者和太陽崇拜信仰者。

5. 哥白尼革命的開端：

5.1 1543年《天體運行論》出版。

5.2 哥白尼的著作本身並不那麼地具有革命性。

5.3 因此哥白尼革命的意義在於，《運行論》讓其它人說了革命性的東西，而不是它自己有什麼革命性。

5.4 《運行論》的目的在於解決托勒密學派不能解決的行星問題，地動說只是這個目標的副產品。

6. 哥白尼的物理學和宇宙論（很多地方仍殘留亞氏的觀點）：

6.1 第一冊的幾個命題：

a. 宇宙是球體的

b. 地球是球體的

c. 地球如何形成一個球體？

d. 天體的運動是等速、圓周且永恆的運動。（只有圓周運動或其組合，才能說明天體的周而復始。）

e. 地球是顆行星。有自轉和公轉（繞太陽轉）。

f. 為什麼古人相信地球靜止？

g. 亞氏的論證不充分：地球的移動是自然的(natural)，不是受力的(violent)。如果地球移動的話，運動就是地球的本性(nature)，它的自然運動不能被打斷。

[1]更精確地說，哥白尼的系統不是太陽中心系統(heliocentric system)，而是太陽靜止系統(heliostatic system)。

[2]被教會送上火刑台的Giordano Bruno, 1548-1600，正是如此主張。布魯諾說：「上帝的卓越，顯現在祂的王國之偉大上；祂並不是由於一個、而是由於無數個太陽（指恆星）而受到尊崇；不是由於一個地球，而是由於在這個無限宇宙中的幾千個地球而受到尊崇。」布魯諾認為：不只我們的地球環繞太陽；有很多地球環繞著它們的太陽。