Introduction

 

History is replete with revolutions. They have been bloody, bloodless, political, industrial, intellectual, cultural, social, sexual, scientific, and spiritual. The word has been applied to innumerable areas. We may discuss a revolution in music, such as when Jazz or Rock and Roll was introduced, or a revolution in fashion such as when the bikini or mini-skirt first appeared. Revolutions are more than a dramatic change or appearance of a sudden manifestation of a heretofore-unknown idea. A revolution represents a change of values. What we value becomes part of our culture and defines who we are. Who we are today and what we define as our modern world was born of a revolution that took place not on the battlefield, but in the mind. This paper will review the written works of the astronomers, scientists, and mathematicians who participated in what has come to be called the Copernican Revolution.

 

This survey will focus on the contribution of each book to its time and the evolution of scientific thought. On a literary level, these works cannot compare with Chaucer, Dante or Shakespeare. At times the works in question make for very dry reading in that they deal with equations, measurements, theory and conjecture. The value of these works though goes beyond just content and style. These authors demonstrated that the universe was not how the Vatican or the established scientific tradition had defined it. They undermined the almost absolute power political and religious officials held by implying that all the kings and popes in history got wrong one of the basic facts of our universe, that being that the Earth is not the center of it. Coinciding with the Protestant Reformation and the discovery of the New World by European explorers, the literature of the Copernican Revolution contributed to the flowering of intellectual and cultural activity during the Renaissance that shaped the modern world.

 

The Ancient Universe:

Staring up at the night skies and contemplating the nature of the universe must surely rank as one of the humanity's oldest philosophical pursuits. Often, how a particular culture defines the universe tells us more about the culture than the true nature of the universe. The ancient Egyptians, for example, imagined their universe as a sort of an elongated platter, closely resembling the dimensions of the Nile valley.1 Like the Babylonians, the Egyptians imagined the heavens to be a sort of dome over the Earth.2

 

The ancient Greek astronomer and philosopher, Anaximander of Miletus devised the two-sphere system in which to explain the nature of the Earth and Moon and the motion of the stars.3 Despite the common mistaken belief that all ancients thought the Earth was flat, the Greeks did think it was round. Anaximander taught the Sun and Moon were both circles and that the Sun 28 times larger than the Earth, the Moon was 19 times larger, and the entire universe comprised of two spheres; an inner sphere for the Earth and an outer sphere of the heavens.4 A problem arose when early astronomers observed that the planets moved at different speeds. If the heavens were all located on a single sphere then they should all move at the same speed, and they didn't. To make matters worse sometimes the planets even appeared to move backwards (retrograde).

 

Aristotle (384-322 BC) put forth the idea that the universe was comprised of 55 spheres and that the spheres were made up of aether, a material supposed to be crystalline.5 Aether was said to be "transparent and weightless."6 By Copernicus' time in the Sixteenth century the aether was still thought to exist, albeit not quite like Aristotle imagined it. Claudius Ptolemy, a Greek astronomer who lived in Alexandria, Egypt during the Second century AD, simplified things a bit and established a model of the universe with eight spheres.7 Each planet was assigned a sphere of its own and that seemed to solve the problem of retrograde motion for now. A ninth sphere added by later astronomers was an effort to make the theory explain their observations. It is this nine-sphere model of the universe that Copernicus inherited, and ultimately refuted.

We still grope for answers to explain our observations of the night skies. Astronomers once said that aether, an invisible and undetectable substance, held our universe together. Today, astronomers suggest that something called "dark matter," an invisible and undetectable substance, must exist in order keep galaxies from flying apart.8 Have our ideas changed, or just our terminology? One wonders if we are any closer to the truth in our time than Aristotle was in his.

  

Historical Context:

The Crusades opened up to Western Europe ancient Greek knowledge lost to the West. It was the contribution of the conquered Moorish culture in Southern Spain in the Twelfth century that first let loose this flood of knowledge. So great became the deluge that the Archbishop of Toledo (liberated from the Moors in 1085 AD9) established a group of translators to handle, and presumably control, the torrent of information pouring from the captured texts of Arabic translations and commentaries of ancient Greek texts.10 These texts contained information on such subjects as "medicine, astrology, astronomy, pharmacology, psychology, physiology, zoology, biology, botany, mineralogy, optics, chemistry, physics, mathematics, algebra, geometry, trigonometry, music, meteorology, geography, mechanics, hydrostatics, navigation and history."11 For example, zero, as a mathematical concept, is introduced to European scholars while translating works with the assistance of Spanish and Arabic speaking Jewish scholars.12

The Christian re-conquest of Southern Spain was not completed until the end of the Fifteenth century. During Moslem rule some of the most important translations and commentaries of ancient Greco-Roman works are produced, such as those of Ibn Rushd of Cordoba (1126-1198 AD) whose translations of Aristotle with commentary (to explain to the Europeans what they were reading) greatly influenced scholars.13 Rushd, along with Ibn Tufayl of Granada (d. 1185/6 AD), and al-Bitruji and Jabir Ibn Aflah of Seville (both active circa 1200 AD), all attempted to "reformulate" Ptolemaic astronomy.14 Copernicus was aware of the existence of the works of these Arabic scholars and we may infer from that that they had some influence on him. Unfortunately, these works have not been fully edited in both Arabic and Latin, nor completely published and made available for research.15 This makes it difficult to attribute Copernicus' research to specific sources.

 

The end of the Fifteenth century saw the beginning of an era of intellectual awakenings. Guttenberg's printing press debuts in 1455 allowing for the relatively rapid and inexpensive reproduction of the written word.16 The kingdoms of Queen Isabella of Castile and King Ferdinand of Aragon were unified in 1479. This was a precursor to the end of the Moorish domination of Southern Spain in January 1492 when Grenada, the last Moslem city-state, fell.17 This freed up enough money in that war-torn country to allow Christopher Columbus to try out his plan to reach the rich Asian trade markets by sailing west (September-October 1492).18 While certainly this discovery led to the end of many indigenous American cultures, the opening up of new lands to an overcrowded Europe, combined with a flood of new wealth, sparked an economic revival and helped to firmly establish the middle class in our economic system.

Following Columbus' voyages (1492-1504) Copernicus writes his first treatise on planetary dynamics, the Commentariolus (Little Commentary), circa 1507-14.19 In 1517 Martin Luther nails his 95 theses to the door of the Wittenberg church.20 That these events all happened within a single generation indicates that a profound change in Western society was occurring.


 

Copernicus

(1473-1593)

"Of all discoveries and opinions, none may have exerted a greater effort on the human spirit than the doctrine of Copernicus. The world had scarcely become known as round and complete in itself when it was asked to waive the tremendous privilege of being the center of the universe. Never, perhaps, was a greater demand made on mankind-for by this admission so many things vanished in mist and smoke! What became of our Eden, our world of innocence, piety and poetry; the testimony of the senses; the conviction of a poetic-religious faith? No wonder his contemporaries did not wish to let all this go and offered every possible resistance to a doctrine which in its converts authorized and demanded a freedom of view and greatness of thought so far unknown; indeed not even dreamed of."21

Johann Wolfagang von Goethe

Early years:

Fig. 1: Copernicus

Nicholas Copernicus was born February 19, 1473 in Tourn, Poland. Until 1466 Tourn was part of West Prussia so Copernicus would be claimed by both Germans Poles as a native son.22 His native Polish name is Mikolaj Kopernik.23 In German it's Niklas Koppernigk,24 but it is by the latinized version of his name, Nicholas Copernicus, that he is commonly known to history.

After the death of his father in 1483 Copernicus was placed under the guardianship of his maternal Uncle Lucas Watzelrod, who would later become a bishop and Polish senator. Copernicus was educated as a boy probably in the cathedral school of Wloclawek and went to college at the University of Krakow.25 It should be noted with some irony that Copernicus, whose work contributed so much to challenging the Catholic Church's claims of absolute authority, was educated at a cathedral school and had a bishop for his guardian. At the University of Krakow Copernicus studied under the Polish astronomer and mathematician Albert Brudzewski (1445-1495).26 It was under Brudezwski that Copernicus was first formally trained in the science of astronomy.

The Commentariolus:

Copernicus left few written records regarding his research methodology. The Arabic translations of early Greco-Roman works probably came to Copernicus through Brudzeweski, who also passed on the findings of other German and Italian astronomers from the early to middle Fifteenth century.27 Copernicus' first known work on planetary dynamics, the Commentariolus, builds on the research of the scholars who preceded him. A short essay about 18 pages long, it presents a heliocentric (sun-centered) system that would be the basis of his later, more developed work De Revolutionibus.

The Commentariolus was passed from scholar to scholar until it disappeared towards the end of the Sixteenth century, not to reappear until it was found and published in 1878.28 Its main purpose serves to establish Copernicus early thoughts on the heliocentric model. In it he tries to explain the motion and position of planetary bodies, laying the foundation for certain standards he will use in De Revolutionibus. There are some problems in translating the text from Latin. The ancient tongue is not quite able to handle the mathematical expressions. This complicated in some cases by Copernicus himself who, for example, sometimes uses the terms circle and sphere interchangeably.29

Because the Commentariolus was not published, and then temporarily disappeared from the historical record, its impact was limited. While it was passed among Copernicus' colleagues for several decades De Revolutionibus would be his lasting legacy.

The Commentariolus also reveals that Copernicus had not yet completed his calculations of the Sun and the Moon.30 The date of his authorship of the Commentariolus is placed no later than 1514 because he did not begin his observations of the Sun until 1515, and he surely would have referred to such observations had he begun them. Most of Copernicus' significant observations occur after this date.

Table 1: Timetable of Copernicus' Observations

Body Observed

Date of Observation

Earth's Moon

1497-1541

Sun

1515-1516

Mars

1500-1538

Saturn

1500-1538

Jupiter

1520-1529

Venus

1529-1537

 

With his observations of the moon concluding in 1541, Copernicus made the final revisions to a work long in the writing, De Revolutionibus.

 

De Revolutionibus:

"What follows from this demonstration is that the heavens are infinite in relation to the earth. The extent of this immensity we do not know at all."31

Copernicus, De Revolutionibus, chapter one

De Revolutionibus, the Book of Revolutions, is, as its name implies, a study the revolutions of the bodies of the solar system. It was written chiefly between 1515 and 1533, followed by a period of intense revision through 1541.32 The first chapters to be published concerned the mathematical basis Copernicus created for more accurate observations, "his own trigonometry."33 This aspect of De Revolutionibus is an important contribution. Mathematics must evolve in order to express new concepts, as is the case with any language. In this way, Copernicus helped to develop the mathematics arts by devising "his own trigonometry."

By the time De Revolutionibus was published in 1543 (the year of Copernicus' death) most people believed that the Earth was round, however, the thought of whether or not the Earth was in the center of the universe was a far different question. The idea was wrapped up in Western theology and became infallible by association with the church. Copernicus set out to challenge this concept in the first of the five books of De Revolutionibus.


 

 

Left: (Fig. 2) Page from an original copy of De Revolutionibus that belonged to Copernicus. Currently at the Jagiellonian Library at the University of Krakow, Poland.

 

 

 

 

 

 

 

 

 


 

 

Right: (Fig. 3) Diagram of the Copernican model of the universe by Thomas Digges (c. 1545-c.1595) in his book A Perfit Description of the Coelestiall Orbes (1576), which translated part of Book I of De Revolutionibus into English.

 

 

 

 

 

 

 

 

 


In the first book Copernicus describes the universe in general terms, adding as much math as needed to support his work. In comparing the observations of Ptolemy to his own tables and charts Copernicus observes out they do not match up his more accurate findings. He does, however, use some of Ptolemy's proofs, such as that of a departing ship shrinking as it goes over the horizon, to establish the spherical nature of the Earth.34 In the late Fifteenth and Sixteenth centuries, just because people thought the Earth was round that did not necessarily mean they thought it was spherical as well.

Copernicus refers to the work of the ancient scientists such as Heraclides, Ekphantos and Hicetas, who did not believe the Earth stood still, establishing precedence for his ideas.35 Despite this tribute to the ancients, he uses chapter one to disprove Aristotle's and Ptolemy's reasons given in support of the idea that the Earth is at the center of the universe.

"It does not follow that the earth is in the center, indeed it would be astonishing if the immense sphere of stars revolved around this little point in twenty-four hours, rather than this little point around itself."36

Copernicus, De Revolutionibus, chapter one

 

The ancients thought the Earth would fly apart if it actually moved through the universe. They had not considered gravity as an effect that would keep the Earth together during such motion. Copernicus considers gravity as a force in this motion, defining it would be left up to Isaac Newton.

"I consider gravity as nothing but a natural striving with which the Creator has endowed the parts in order that they may combine into one whole while they collect into a sphere. The same is probably true of the sun, the moon and the other planets, and yet they are not fixed."37

Copernicus, De Revolutionibus, chapter one

 

Copernicus gives no illustrations of how he thought the motions of the planets to be and complicated the matter further by varying his terms. Perhaps this is a habit he carried over from the Commentariolus, but one that I feel owes much to the limitations of Latin, in which Copernicus wrote De Revolutionibus.

Book II of De Revolutionibus is on spherical astronomy and a catalogue of stars, including corrections of Ptolemy's catalogue. Book III is concerned with the length of the solar year, Earth's orbit, and explaining various computation tables. Book IV details the motion of the moon and its eclipses, once again putting Ptolemy's work under a critical eye. Books V and VI involve Copernicus' notes on planetary motions. Rather than using his observations as a starting point, he focuses on what aspects of the Earth's observable motion modified Ptolemy's data. Again, the refutation of Ptolemy is the overt concern of Copernicus in De Revolutionibus, however he does not abandon Ptolemy entirely. He uses Ptolemy's computations of planetary motions and apogees in his work, accepting the ancient scientist's calculations while rejecting his deductions and theories.38

Reactions:

While Copernicus' observations and calculations from De Revolutionibus soon became accepted within academic circles his theories did not. In 1616 the Catholic Church officially condemned the theory of the movement of the Earth.39 Poland, his homeland, would not introduce his theories into the curriculum of universities until 1722 for protestant schools and 1782 for catholic schools.40 England, owing to its insularity from Europe and its protestant religion, more readily accepted the Copernican heliocentric theory. Thomas Digges, son of English mathematician Leonard Digges, published his analysis of De Revolutionibus in his book, Perfit Description of the Coelestiall Orbes, in 1576.41 His fellow astronomers praised Digges for the accuracy of his observations and calculations, yet it was Digges adoption of the Copernican heliocentric theory that brought him the critical response of one his era's most noted astronomers, Tycho Brahe.42


TYCHO BRAHE

(1546-1601)

Early Years:

Tycho Brahe was born in Skane, then a part of Denmark and now in Sweden. The eldest son of parents with a noble heritage, he was brought up by his paternal uncle, Jörgen Brahe. Jörgen was better off financially then his brother and provided for his nephew by sponsoring his education and providing him an inheritance. Brahe attended the universities of Copenhagen and Leipzig as well as the universities of Wittenberg, Rostock, and Basel. It was during this time that he began his studies in alchemy and astronomy. A quick-tempered young man, Brahe lost his nose in a sword duel with another student in Wittenberg in 1566. Thereafter, he wore a metal nose as a replacement.43

 

De Nova Stella:

Fig. 4: Tycho Brahe

Brahe's first published work is De Nova Stella (The New Star-Copenhagen, 1573), which details his observations of a star that went nova in the constellation of Cassiopeia and was first observed November 11, 1572. The sudden manifestation of what appeared to be a new star demanded explanation. Rumors, inaccurate observations and mistaken deductions were freely tossed about in the search for an answer. Brahe, in an effort to set the record straight, decided to publish his own findings.44

 

Brahe made highly accurate observations and calculations regarding the star's magnitude, position, distance and color. Still under the sway of the Aristotelian/Ptolemic idea that the planets and stars were somehow "fixed" to a crystalline celestial sphere, he put the location of the star on the celestial sphere of fixed stars.45 He was among of the last die-hard adherents of this ancient idea, which slowly phased out of mainstream scientific thought between 1575 and 1625.46 Brahe also spends part of the book discussing the astrological implications of the new star, an illustration that even among the most noted scholars of the Sixteenth century, astronomy and astrology were still linked.

As noted previously, Brahe did not accept the Copernican view of a heliocentric universe. Why then should such an individual be included with our study of the literature of the Copernican Revolution? Brahe's passion was in accurate and detailed observations in a time before the invention of the telescope. Although he never accepted the heliocentric model its proof would be built on detailed, quantifiable facts, some of which Brahe would himself provide through his own observations.

Despite his intellect Brahe was still mired in the pseudo-science of the Catholic Church that then used a literal interpretation of scripture. Brahe could not reconcile a moving Earth with biblical texts.47 In his view, Copernicus had merely used his "trigonometry" to show that it was possible to calculate planetary motions without having the Earth as a fixed center-point.48 In an extraordinary effort involving decades of nightly observations Brahe wrote his greatest work, Introduction to the New Astronomy. Never quite finished, the work can be viewed as a transitional work between the old Ptolemic view of the universe and the Copernican world-view.49

 

A Stare-way to Heaven:

In 1576 Danish king Fredrick II presented Brahe with title to the island of Hveen in recognition of Brahe's work.50 The king made Brahe into a sort of feudal lord of the manor, a role perfectly suited for an astronomer of noble heritage. Here, Brahe constructed an observatory of his own design that would be regarded as the best in Europe. In a time before the telescope, Brahe (like Copernicus) used his eye, astrolabes, sextants and other navigational aides as his tools of observation. He designed his observatory, Uraniberg, in alignment with the paths of the various planets across the night sky to maximize his observations in the time before telescopes. One tribute to Brahe's intelligence and skill is that the accuracy of his observations often exceeded the design limitations of his instruments.51

Fig. 5: Uraniberg

 

 

Brahe's research done at Uraniberg would contribute towards his publications De Mundi Aetherei Recentioribus Phaenomenis (Concerning the New Phenomena in the Ethereal World-Uraniburg, 1588); Astronomiae Instauratae Mechanica (Instruments for the Restored Astronomy-Wandsbeck, 1598); Astronomiae Instauratae Progymnasmata (Introductory Exercises Toward a Restored Astronomy-Prague 1602).52 In Astronomiae Instauratae Mechanica Brahe leaves valuable details regarding his instruments and methods of observation. The quest for ever more reliable observations led him to construct large sextants and quadrants as well as several clocks, whose reliability he was never satisfied with.53 However, it is with his last work, Astronomiae Instauratae Progymnasmata (commonly known as The New Astronomy) that the Copernican Revolution took its next step.

 

 

Fig. 6: Drawing of a large sextant used by Tycho Brahe

 

 

Restoring Astronomy:

In Introductory Exercises Toward a Restored Astronomy Brahe works out a new geocentric model of the universe. In the Ptolemic model the Sun and the planets each orbited the Earth attached to their own celestial sphere. Observations both Copernicus and Brahe made showed problems with that model when accurate calculations of the planets' orbits were made. Copernicus established the theory that all the planets revolved around the sun as his response to this problem. Brahe, who could not accept a heliocentric view of the universe, resolved the problems (in his own mind) by creating the Tychonic model of the universe.54 In this model Brahe compromises between the two competing world-views. In his model the Earth is still the center of the universe, the Sun orbits the Earth, but the planets and comets orbiting the Sun. this way, Brahe could explain the motions of the planets within a geocentric model.

 

 

Fig. 7: The Tychonic Universe

Brahe's contributions as a result of his written works were a greater emphasis on accuracy in the instruments55 and observations of astronomers. He introduced transverse divisions between graduated scales on scientific instruments and improvements to the sighting mechanisms.56 He left a voluminous amount of astronomical observations and calculations that would serve as raw data for generations of astronomers. Tycho Brahe's assistant, Johannes Kepler, would build on this data and make his own contribution to the Copernican Revolution.


JOHANNES KEPLER

(1571-1630)

Early Years:

Johannes Kepler, the son of a mercenary and an innkeeper's daughter, was born in the Holy Roman Empire (now Germany). Unlike the noble upbringing of his contemporary Tycho Brahe, Kepler grew up in a working-middle class atmosphere, often helping out at his grandfather's inn.57 As a Lutheran growing up in the Catholic Holy Roman Empire, Kepler's faith was tolerated under Emperor Rudolf.58 In 1612 Mathias II ascended to the throne of the Holy Roman Empire following the death of his brother, Rudolf. Less tolerant than his brother, this new emperor compelled Kepler to flee to Prague.

Following his exile Kepler was employed as an astrologer for Albrecht von Wallenstein (1583 - 1632), the duke of Friedland, who led his armies to many victories during the Thirty Years War (1618 - 1648).59 Kepler was disdainful of conventional astrology and presented interpretations based on the angles between planets and stars. He died while on route to collect money owed him in relation to his work, The Rudolphine Tables, a collection of observations and calculations made during under the rule of Holy Roman Emperor Rudolf.60

 

 

 

Fig. 8: Johannes Kepler

The Mystery of the Universe:

Kepler's first major work, Mysterium Cosmographicum (The Mystery of the Universe), was published in 1596.61 In it he supports the Copernican system with numerous arguments and in more detail than did Copernicus himself. Kepler applied the full force of mathematics in providing proofs of his positions. His grasp of the mathematics principles behind the theory moves discussion of the Copernican system to another level. Copernicus, while moving the Earth out of the center of the model of the universe, persisted in attributing special qualities to the Earth regarding its orbit and relationship to other heavenly bodies. Kepler rightly proves in Mysterium Cosmographicum that the Earth should be treated as no different than any other planet.62

 

Influences:

Michael Maestlin introduced Kepler to the Copernican system at the University of Tübingen (a theological school). Maestlin was a lecturer who served as an early mentor to Kepler and encouraged him in his studies.63 A series of letters in 1595 from Kepler to Maestlin outlined Kepler's thoughts on proofs regarding the Copernican system. These letters showed Kepler's thoughts on using three-dimensional polyhedrons as mathematical models to be used to figure the orbit and arraignments of the planets instead of the two-dimensional figures that Copernicus and others had been using.64 Maestlin helped Kepler by providing methods for calculating distances of the planets to the Sun and serving as a sounding board for his ideas. Maestlin suggested that Kepler present his information supporting the Copernican system as a mathematical hypothesis so as to avoid a confrontation with the Lutheran Church. Although Kepler suspected his mentor of privately supporting the Copernican system, Maestlin never made an overt declaration in support of it. In 1616, the same year the Vatican condemned the Heliocentric model, Maestlin would reject the idea publicly in a letter, but it did not stop Kepler from pursuing his ideas.65

 

The Church Intercedes:

Kepler required the permission of the Rector and Senate of the University of Tübingen in order to publish Mysterium Cosmographicum (The Mystery of the Universe). A chapter that tried to reconcile the Copernican system with the Bible was removed as a result of the University's review.66 While it was approved to be published the rector who approved it, Matthias Hafenreffer, would later rail against it in a sermon. This was not the first time Kepler encountered the religious intolerance of the time. As a student at Tübingen University a professor rejected an essay he wrote on the Copernican system.67 Later, in 1620 he would successfully defend his mother against charges of witchcraft.68

 

The Noble Dane:

In December 1597 Kepler sent to Tycho Brahe a copy of Mysterium Cosmographicum. Although Brahe disagreed with Kepler regarding the correct model of the universe he asserted (in a letter to Kepler's mentor Maestlin) that progress could not be made through a priori deductions, but only through accurate observations and calculations. Brahe was sufficiently intrigued by Kepler's work to invite him to Uraniberg. Brahe was more interested in Kepler for his mathematical ability than for the theories he espoused.69 Kepler refined the art of observation and data collection under Brahe. Equipped with the Dane's extensive data from a lifetime of obsessive observation Kepler applied the research towards his next published work, Astronomie nova (The New Astronomy).70 Despite religious convictions that prevented Brahe from seeing the logic of a heliocentric model, his dedication to accurate scientific data and mathematical calculations is a lasting tribute to the Danish astronomer and a major contribution to the Copernican Revolution.

 

The New Astronomy:

Astronomie nova, published in 1609, introduces Kepler's first two laws of motion. Ptolemy, Copernicus and Brahe all explained the apparent retrograde orbit of the planets as the result of a series of epicycles that take place within a planet's orbit, both of which were assumed to be perfect circles.71 This was in accordance with the belief that the heavens were divine in origin. Since anything divine was assumed to be perfect, the orbits must therefore be perfect 360-degree circles. Kepler's observations proved this doubtful and he used Brahe's data to establish the first two of three laws that would serve as the foundation of Isaac Newton's Principia Mathematica.72

 

Kepler's Laws of Motion:

Kepler's first law: Planets move in simple elliptical orbits around a focal point, the Sun.73

This is the equation for an ellipse:

 

 

 

Kepler's second law: The speed of the orbit of each planet varies in proportion to its distance. The closer to the focal point, the Sun, the faster the speed.74

This means that a planet will cover the same distance in one hour, for example, whether moving quickly close to the Sun, or slowly further away from it.75 Ironically, even though Kepler's Second Law was proven true, Isaac Newton showed Kepler's mathematical methodology and premise regarding velocity were fallacious.76

 

 

Fig. 9: Each slice represents a unit of time.

 

 

 

The Harmony of the World:

Ten years after Astronomie nova Kepler publishes Harmonices Mundi (The Harmony of the World). In it he establishes his third law regarding the motion of the planets.

 

Kepler's third law: The squares of the periods of the planets are proportional to the cubes of their semi-major axes. In other words, as a planet moves away from the Sun its orbital speed decreases.77

T= The orbits of two planets

R= Mean distance between planets and sun

Ta2 / Tb2 = Ra3 / Rb3

Based on the second law it may be logically assumed that the further away from the Sun a planet got the slower it would go, but Kepler had insufficient data to support a third law to be published in Astronomie nova. By 1619 he had sufficient data to back a third law and presented it in Harmonices Mundi. It is this third law, and the data that supports it, that inspired Newton's law of gravitation. An idea that Kepler himself touched upon via his "theory of heaviness" he briefly mentions in his introduction to Astronomie nova.78


Galileo Galilei

(1564-1642)

While Copernicus, Brahe and Kepler avoided major confrontations with the church, Galileo found himself in a serious struggle with the Vatican as a result of his research. By the year 1609 when Galileo published his first work based upon his observations with the telescope, Europe had enjoyed nearly 100 years of Protestantism. Perhaps enjoy isn't quite the right word for it for in reaction to Protestantism came the Inquisition. It is with that force that Galileo, unlike his predecessors, had to contend with.

 

Early Years:

Fig. 10: Galileo Galilei

Born in 1564 in Pisa, Italy, Galileo's father was a musician and his mother quite educated for a woman of her time and class. Galileo's father, in addition to a talent for math, was mistrustful of authority, two characteristics he passed on to his son.79 Galileo received his early education from local monks; however, when his father learned that his son was considering joining the local monastery he immediately withdrew Galileo and sent him off to the University of Pisa school of medicine. Here, Galileo conducted experiments with a pendulum that helped him form ideas that eventually led to his law of falling bodies.80

Galileo's works that come under consideration here are Sildereus Nuncius (The Starry Messenger-1610), the Discourse on Floating Bodies (1612), Dialogue Concerning the Two Chief World Systems (1629-32), and The Two New Sciences (1638). In the early years of his career in Pisa Galileo lectured and wrote on mathematics and mechanics while criticizing Aristotle's science.81 Galileo also imprudently criticized an engineering proposal by one of the members of the ruling family, the de' Medicis, which led to his departure to Padua in 1592. There he served as chair of the mathematics department at the University of Padua until 1610 and it was here that Galileo became acquainted with an instrument that would literally open the eyes of astronomers everywhere, the telescope.82

Galileo had long been aware of the inaccuracies of Aristotelian science. He could not help noticing that large and small hailstones hit the ground at the same time, contradicting Aristotle's teaching that heavy objects fall faster than light objects.83 Galileo's famous "experiment" from the top of the Leaning Tower of Pisa (circa 1590) did not take place as reported.84 He instead demonstrated his point by rolling balls down an incline. Similar experiments though had been previously documented. Benedetti Giambattista in published his results in 1553, and the test had also been made and published by the Flemish engineer Simon Stevin in 1586.85 Galileo may have been challenged by the conservative academic climate of Pisa to conduct his own experiments.

 

The Starry Messenger:

In 1604 a nova appeared that gave Galileo an opportunity to show that Aristotle was wrong, yet again, in suggesting the heavens are unchanging (a belief endorsed by the Catholic Church). Tycho Brahe's studies of the nova of 1574 gave credence to what Galileo's was saying and in 1609 Galileo constructed his first telescope which allowed him to support his propositions with evidence. The original Dutch patent for the telescope indicates that it was intended for land observation, not the night sky. Hearing about the device from a clergyman friend, Galileo made one of his own with the ability to magnify a distant object nine times, far exceeding the original Dutch design.86 The following year, in 1610, Galileo would publish Sidereus nuncius (Starry messenger) which detailed his observations of the mountains of the Moon, four moons of Jupiter, and "innumerable" stars unseen by the naked eye.87 All first seen and documented by Galileo.

Fig. 11: Galileo's Telescope

 

 

Left: (Fig. 12) Galileo's drawing of the Moon's surface from his 1609 observations.

 Right: A photograph of the Moon from the same angle.

 

Kepler read Sidereus nuncius and endorsed its findings before ever seeing a telescope.88 That he accepted Galileo's observations, even though he lacked the instrumentation to duplicate them, is a testament to the influence of Sidereus nuncius. Kepler wrote a long letter to Galileo discussing his impressions and even wrote the duke of Tuscany, Giuliano de'Medici, to praise his most noted resident's work.89 This letter was published in Prague in 1610 and lent crucial support to Galileo's findings in the secular world. The religious world though would have a different opinion on the matter.

 

On Floating Bodies and Sunspots:

In 1612 Galileo was once again on the attack against Aristotelian science. His Discourses on Floating Bodies discussed what causes an object to float as well as the physical nature of ice. In the book Galileo also provides a number of simple experiments that contradict the Aristotelian position on the nature of buoyancy.90 Galileo would defend this work against numerous academic attacks.91

Also in 1612 a German Jesuit priest published observations of sunspots and explained them as small planets orbiting the sun. Although this is in keeping with the church's view that the sun was perfect, and therefore free of such imperfections as a blemish on its surface, the Jesuit was nonetheless compelled to publish under a pseudonym in order to protect himself from prosecution.92 Galileo, who had observed sunspots sometime prior to 1612, published his own conclusions in a series of letters in 1613. Not only did Galileo correctly assert that sunspots were an ever-changing manifestation of the sun itself, but he also signed his name. In 1614 he was denounced from the pulpit in Florence and the Inquisition soon took up the matter on referral from a Dominican priest.93

 

Inquisition:

In 1615 the Church begins its counterattack against the Copernican Revolution. Pope Paul V declared the Sun and Earth did not move and Galileo was ordered to cease espousing views to the contrary.94 In addition, the pope effectively banned Copernicus' De Revolutionibus by suspending it "pending correction."95 Galileo, in Rome to answer his accusers, defended his views only to be commanded by the pope to remain silent. Recalled to Florence, Galileo entered a period of scientific inactivity for the next two years.96

 

The Dialogue:

It was not until Pope Urban VIII succeeded Pope Paul V in 1624 that was Galileo able to resume public discourse of his ideas on cosmology.97 The new pope gave Galileo permission to discuss his ideas in a hypothetical context. The result was Dialogue Concerning the Two Chief World Systems (1632).98 Rather than a text of observations, calculations, diagrams and maps, Galileo presents the discussion of the difference between the two competing world systems as a discourse between three "interlocutors," Salviatus, Sagredus and Simplicius. Salviatus is a proponent of the Copernican system. Sagredus and Simplicius argue for the Aristotelian view. Over the course of four days various issues with both systems are discussed. Salviatus is imbued with Galileo's persuasive prowess. Sagredus has a mind open to civilized conjecture while Simplicius, on the other hand, is obnoxious and rude.99 Although the book ends with affirmations of the glory of God it led to a serious encounter with the Inquisition. Naming the defender of the Aristotelian world-view "Simple" probably didn't earn Galileo any favor with the Inquisitors.

 

Later Years:

In 1633, almost seventy, Galileo went to Rome to stand trial. The case centered around the injunction originally filed against Galileo in 1616 after his last trial. The inquisitors had an unsigned memorandum from the Church's records suggesting that Galileo did indeed exceed the injunction's commands.100 Galileo, however, produced a signed letter from the original trial that his prosecutors did not know existed. This letter from the Cardinal in charge of the 1616 trial left room for doubt regarding Galileo's guilt.101 Sentenced to life in prison and prohibited from writing about Copernicanism Galileo was allowed to return to his home near Florence to remain under the close scrutiny of the Inquisition. All of Galileo's works, published and unpublished, were banned. To their credit, it should be noted that three of the ten cardinal-judges conducting the trial refused to sign the decree of sentence.102

 

The Two New Sciences:

Despite the ban on the publication of his works Dialogue Concerning the Two Chief World Systems was published in Strasbourg in 1635 out of reach of the Vatican's control.103 Galileo did not cease writing in the face of the Inquisition. Using the same characters from Dialogue Concerning the Two Chief World Systems, Galileo finished work on The Two New Sciences in 1636. In it he establishes laws of accelerated motion and of falling bodies as well as basic theorems regarding projectile motion (ballistics).104 Similar in format to the Dialogue of 1632, it also uses the same interlocutors Salviatus, Sagredus and Simplicius. He presents his theory regarding ballistics, which discussed resistance, cohesion, and acceleration in bodies in motion as well as proof of parabolic trajectories in projectiles (Aristotelian science taught projectiles went straight out, then straight down).105

Galileo's sight fails until finally going blind in 1637, just after finishing The Two New Sciences. The following year, in 1638, The Two New Sciences is published in Leyden, Holland.106 Galileo got around the ban on publication by reporting that the book was published without his permission. He spent his final years dictating new chapters for The Two New Sciences and occasionally teaching and lecturing until passing away in 1642, the same year Isaac Newton was born.107

The Church, by the way, never got around to officially forgiving Galileo until 1981.108

 

 


Isaac Newton

(1643-1727)

 

Nature and Nature's laws lay hid in night;
God said, Let Newton be! and all was light

Alexander Pope (1727)109

 

Isaac Newton's work is the culmination of the Copernican Revolution. He confirmed the validity of the Copernican model of the universe (with Kepler's modifications) and in doing so put the last nail into the coffin of Aristotelian science. His major work, Principia Mathematica, also known as Principles of Natural Philosophy, is a cornerstone of modern science. In it Newton introduces the basic laws of physics, provides a mathematical analysis of force and motion, is first to use vectors to describe the direction and size of forces, and describes his law of universal gravitation.110

Fig. 13: Isaac Newton

Early Years:

Born January 4, 1643 Isaac Newton in the farm country of Lincolnshire, England. His father was an wealthy, illiterate farmer who owned much land and livestock but was unable to sign his own name. After his father's death his mother remarried when little Isaac was only two. Newton did not get along with his stepfather and accounts of his childhood are not happy ones. Idle and inattentive in school, Newton shows little of his genius early on. It is only later when an uncle and the schoolmaster take an interest in him that Newton begins to shine academically. He attended his uncle's alma mater, Trinity College, Cambridge in order to become a lawyer, yet was attracted by the works of Copernicus, Kepler and Galileo.111

 

Influences:

"What Des-Cartes did was a good step. You have added much several ways, and especially in taking the colors of thin plates into philosophical consideration. If I have seen further it is by standing on the shoulders of giants."

Isaac Newton to Robert Hooke 1676112

 

During his university years Newton was exposed to works that would greatly influence his thinking. One of these works was Rene Decartes' (1596-1650) Principles of Philosophy, first published in 1644. In it, Decartes dealt with the nature of aether and how it influenced motion in an evolving theory of the time called of corpuscularism, which maintained the aether was comprised of minute particles called corpuscles that influenced motion.113 Decartes believed that all change in the universe occurred as a result of the free movement and occasional collisions of these corpuscles. He engaged in a series of logical deductions as a way to comprehend the structure of the Copernican universe. His deductions are intuitive, but not supported by quantifiable physical evidence. Indeed, many of his deductions can now be proven wrong. Of the seven laws of collision Decartes introduced only one was retained by his successors. Although his theories regarding the laws of collision were largely disproved, his idea regarding the collision process itself was retained.114

The solutions required to address the problems introduced by corpuscularism led to the law of the conservation of momentum and the development of the relationship between force and the change in momentum it creates.115 That many of Decartes' conclusions can be proven wrong doesn't lessen the importance of the contribution of Principles of Philosophy. Tycho Brahe never accepted the Copernican universe, yet his observations provided valuable evidence leading to its eventual acceptance. Similarly, while Decartes' conclusions may miss the mark, Principles of Philosophy does lead to Newton's Principia Mathematica.

Corpuscularism was only one of two explanations for the motion of the planets that evolved from Copernicus' work. Kepler advanced the theory of the mechanical solar system to explain the orbits of the planets. The mechanical solar system model relied on recent research regarding magnets to explain the eccentric orbits of the planets.116 In 1600 English physician William Gilbert published On the Magnet, in which he recognizes that the Earth itself is one large magnet.117 Kepler took this one step further and suggested that the Sun and other planets were also magnets and it was this force that drove the orbits of the planets (Kepler named this force the anima motrix).118

In 1666 English physician Robert Hooke took this idea to the next level by suggesting the solar system actually moved as a sort of celestial equivalent to a terrestrial mechanism.119 Hooke got rid of the idea of the anima motrix and used a pendulum to explain his hypothesis. Imagine a simple pendulum, such as a weight attached to a string hung on a hook in the ceiling. The weight at the end of a pendulum has the tendency to move in a straight line, yet due to the resistance of the string the pendulum's tendency to move in a straight line is modified. Observing the movement of the pendulum, Hooke noticed that the weight would settle into circular movements. He rationalized that this must be similar to the movements of the planets.120 The irregularities of the orbits of the planets could be explained as the planets' tendency to move in a straight line, modified by the action of some unknown force. Newton would identify and explain that force as gravity.

While this section is titled Influences, Isaac Newton would probably take exception to his colleague Dr. Robert Hooke being listed as an influence. Newton could document that he arrived at similar conclusions to the questions Hooke dealt with prior to any of Hooke's publications.121 Furthermore, Hooke, along with Dutch physicist Christaan Huygens, was a critic of Newton's work.122 To make matters worse, Hooke also claimed that Newton's Law of Universal Gravitation was stolen from him, which was easily shown not to be true.123 Despite these events, Hooke's work though does show the evolution towards Principia Matematica and presents problems that it would have to address.

 

De Motu:

Early on in his life Newton was a proponent of the corpuscular philosophy, for without any physical evidence to support that's all it ever was. Yet, Newton was aware of the limitations of corpuscularism and the attempt to resolve them led to Principia Mathematica.124 The idea of some kind of gravity, or theory of heaviness as Kepler referred to it, was acknowledged by his predecessors. Newton did not invent gravity but he did quantify and define the attractive force that was driving the orbit of the planets. A visit in 1684 with Edmond Halley (who predicted the time interval for the orbit of the comet that bears his name) resulted in a short treatise called De Motu (On Motion).125 De Motu gives Newton the opportunity to work out his ideas on centrifugal and centripetal force and how they relate to an object's trajectory.

De Motu considers four theorems and four problems in about ten pages of text. A much smaller book than the Principia, which has almost 200 propositions and over 500 pages.126 Halley proposed a question, which in effect said Given the law of force, how do you determine an object's trajectory? Newton responded, but the question he responded to in De Motu was Given the trajectory, how do you find the law of force? This is the "inverse problem" of De Motu.127 Newton presents an innovative idea in response to what he thinks is the question. He introduces and defines centripetal force as "a body which is attracted or impelled towards some point viewed as a center."128 What that force is, however, is left undefined and little is known about the center point as well. Despite this Newton does manage to answer Halley's question by addressing its inverse, if doing so in a roundabout manner; however, an important question is left. If centripetal force is responsible for the obit of an object (a planet) can it be demonstrated that this force diminishes as the square of the distance from the focal point (the Sun)?129 Principia Mathematica extends the study of force by examining other areas such as "simple machines, impact, pendular motions, optics, motion in resisting media and fluid dynamics."130

 

Principia Mathematica:

Newton began writing Principia Mathematica after his visit with Halley in 1684. It was the intended follow up to De Motu and its purpose was to "demonstrate the frame of the System of the World."131 It was initially published in Latin in 1687 and the first English translations appeared just a few years after Newton's death in 1727.132 Comparing the translations it is evident that translators may miss references, or translate a passage so poorly that interpreting its meaning can be a challenge. Considering the difficulty of the material that can make ascertaining Newton's intention nearly impossible depending on the translation.133 This also underscores the necessity to go back to primary sources periodically, particularly with translated texts.

Newton's law of universal gravitation is the power that drives the Copernican heliocentric world system. In the Principia Newton expresses it as;

"Any two bodies in the universe are attracted to each other with a force that is proportional to the masses of the two bodies and inversely proportional to the square of the distance between them."134

In other words,

 

The Laws of Motion:

The Principia sets down Newton's laws of motion, the core of the fundamental physics behind the heliocentric model of the universe. These laws explain the basis of how universal gravitation works.

Table 2: Newton's Laws of Motion

Law 1

A body at rest tends to stay at rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it.

Law 2

The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Law 3

To every action there is an equal and opposite reaction.

Newton attributes the first two laws to Galileo.

"By the first two Laws and the first two Corollaries, Galileo discovered that the decent of bodies varied as the square of the time and that the motion of projectiles was in the curve of the parabola…"136

Isaac Newton

Newtonian Mechanics:

Principia Mathematica also defines the principles of the mechanics behind the Newton's laws of motion. Over 300 years after their first publication these principles are the among the first concepts studied by physics students today. Due to the necessity to accurately restate these laws I am reprinting them as defined by Dr. Joseph S. Tenn of the Department of Physics and Astronomy, Sonoma State University, Rohnert Park, CA);

 

  1. The position of a body is a function of the time. It can be expressed in terms of three coordinates, for example, how far East, North, and Up it is from an arbitrarily chosen origin (a distance South is just a negative distance North).
  2. The rate of change of the position is called the velocity. It includes both magnitude (speed) and direction.
  3. The rate of change of the velocity is called the acceleration. It also includes both magnitude and direction.
  4. If you know where a body is at some instant and you also know its velocity, you can calculate where it will be a very short time later.
  5. If you know the velocity of a body at some instant and you also know its acceleration, you can calculate its velocity a very short time later.
  6. Acceleration of a body is the net force acting on it divided by its mass.  
  7. The net force acting on a body is the vector sum of all of the forces acting on the body. For two forces it is the diagonal of the parallelogram formed by representing them as arrows.137

 

Isaac Newton demonstrated in the Principia that any motion in the sky could be explained by using the above laws plus gravity, a universal force. This gravitational force is proportional to the mass of the objects in question (be they planets, moons or comets) and inversely proportional to the square of the distance between the objects. The same laws apply to the motion of the Earth as well with the inclusion of friction in addition to gravity.138

 

The World According to Newton:

Copernicus, Kepler, Brahe, Decartes, even Galileo to a degree, consider a divine force to be at least partially responsible for the motion of the planets and stars. Newtonian mechanics showed that a set of physical laws, not divine intercession, was responsible for motion. To the people of the time this seemed as though the universe was a giant clockwork mechanism with the Earth as just another cog. Perhaps God winded the mechanism up, but it is not an act of the divine that moves the planets and the stars, rather a force of nature that is the result of the interaction of two bodies on one another.

Newtonian science influenced other scientific areas as well. Consider Newton's Third Law of Motion, for every action there is an equal and opposite reaction. It has been used to illustrate innumerable cause and effect situations completely unrelated to physics. Among all of the laws and principles of physics covered in this paper it is probably the one law most people can identify.

Chemistry, biology, psychology and the social sciences applied the principles of Newtonian science to their own disciplines by reducing the objects of their study into events and "objective entities" whose actions are observed, documented and evaluated. A set of rules or core principles are formulated then applied to determine the reaction of any subject or object under their study.139 In the sciences of human behavior the effect of this is to remove the moral question from consideration. Behavior becomes an observable, quantifiable event to be documented and evaluated, not judged.140 Homosexuality, for example, was once considered by the American Psychiatric Association to be a disorder. In the 1970s they changed their diagnosis from disorder to normal behavior.141

By the time of the publication of Principia Mathematica in 1687 the Protestant Reformation was already well under way. What Newton contributes to the Reformation, and the evolution of philosophical thought itself, is to move discussion of morality from a debate about standards of absolute right and wrong to a more subjective perspective.142 Behavior that is wrong for one culture then may be seen as perfectly acceptable to another. This further weakened the Catholic Church's influence by implying that what the Vatican held to be true just might not be relevant to everyone.


Conclusion

Truth:

At one time the Western mind conceived the universe to be a series of crystalline spheres that carried the stars, planets, sun and Earth's moon in an orbit around the Earth. The Earth was the exact center of the universe and God was the force behind the motion. Then we moved to model of the universe where Earth was not at the center, there were no crystalline spheres, the force behind the motion was gravity and not an act of God. We went from being at the center of a divine universe to just another cog in the universal machine.

When Galileo turned his telescope up to the night sky he saw countless stars where the naked eye only saw the blackness of the void. In 1755 Emmanuel Kant speculated that the fuzzy patches of light he saw through his telescope were other galaxies, perhaps "just [island] universes,"143 to use his own words. Mainstream astronomy rejected the idea of other galaxies and the idea remained quite controversial until confirmation came in 1924 when our technology was sufficiently advanced. Until then most people thought the universe to be limited to just our own galaxy.144

Today, our picture of the universe is quite complicated. There are exotic inhabitants such as quasars and black holes. Numerous other solar systems and planets have been catalogued. We can recreate the conditions of the universe down to a split second after its creation. NASA publicly came forward to support evidence that "strongly suggests" a Martian rock that fell to Earth contains fossilized microbacterial life from the red planet.145 Our universe is becoming larger and our place in it becomes less unique.

 

Consequences:

To explain the universe we once used imagined, unobservable phenomena such as crystalline spheres and corpuscles. We attempt to do the same today with superstrings and dark matter, equally unobservable phenomena and perhaps equally imagined. We are eternally at that point where Galileo turned his telescope up to revel what was always present, but never proven. The next step in the evolution of our conception of the universe may be the embrace of the concept of the "multi-verse," where our universe is only one of many universes created in a multi-dimensional big bang.146 Many cosmologists, such as Sir Martin Rees, former director of Cambridge University's Institute of Astronomy and England's Astronomer Royal, concede this possibility after looking at the body of modern cosmological research.147 How possible this theory may turn out to be is up to history to determine. Since it has turned out that we are not the center of the universe, we are neither the only solar system nor the only galaxy and life may not be unique to Earth, the trend doesn't look good for the single universe model. Still, we must keep in mind the lessons given to us by the Copernican scientists. What we believe is only as valid as what we can prove.

The literature of the Copernican Revolution is the literature of possibility. It succeeded because the authors backed up what they believed with quantifiable proof. It's hard, after all, to argue with the numbers. It also teaches us not to dismiss the value of someone's work because his or her conclusions may be wrong. Copernicus set out to prove Ptolemy's conclusions wrong, yet utilized the ancient astronomer's computations of planetary motions and apogees in his own work. Brahe never accepted the heliocentric model of the universe, yet the decades of astronomical observations he collected are invaluable to the Copernican Revolution. Likewise, Descartes' conclusions may miss the mark, yet Newton acknowledged the French mathematician's contributions to the evolving theory of motion.

The effects of the Copernican Revolution ripple out to many areas. The math that was created to solve the questions of motion advanced the arts, architecture and ballistics. The quest for more accurate instrumentation benefited navigation and surveying. The struggle for truth to overcome superstition, to stand up for what is right when everyone says you are wrong, is a legacy all cultures can appreciate regardless of their view of the universe.


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