Copernicus received many posthumous accolades after the publication of De Revolutionibus, but the praise was primarily for his success in giving a mathematical description of the motion of the celestial bodies rather than for his sun-centered cosmology.
The first astronomical tables based on the Copernican theory were produced by Erasmus Reinhold (1511-53), a professor of mathematics at the University of Wittenberg at the same time as Rheticus. When Rheti-cus returned to Wittenberg in September 1541 with the manuscript of De Revolutionibus, he probably showed it to Reinhold. The following year Reinhold published his commentary on Peurbach's Theoricae Novae Planetarum, where he wrote of Copernicus in the preface, “I know of a modern scientist who is exceptionally skillful. He has raised a lively expectancy in everybody. One hopes that he will restore astronomy.” Reinhold set out to produce a more extensive version of the planetary tables in De Revolutionibus These were published in 1551 as The Prutenic Tables; in the introduction he praises Copernicus but is silent about his heliocentric theory. Reinhold also wrote a commentary on De Revolutionibus, but it was unfinished when he died of the plague in 1553.
The Prutenic Tables was the first complete compilation of planetary tables prepared in Europe for three centuries. They were demonstrably superior to the older tables, which were now out of date, and so they were used by most astronomers, lending legitimacy to the Copernican theory even when those who used them did not acknowledge the suncentered cosmology of Copernicus. As the English astronomer Thomas Blundeville wrote in the preface to an astronomy text in 1594: “Copernicus … affirmeth that the earth turneth about and that the sun standeth still in the midst of the heavens, by help of which false supposition he hath made truer demonstrations of the motions and revolutions of the celestial spheres, than ever were made before.”
The English mathematician Robert Recorde (1510-58) was one of the first to lend some support to the Copernican theory. He discusses the theory in his Castle of Knowledge (1551), written in the form of a dialogue between a master and a scholar concerning Ptolemy's arguments against the earth's motion. After the scholar sums up these arguments, the master nevertheless presents the Copernican theory in a very positive manner.
That is trulye to be gathered: howe be it, COPERNICUS, a man of greate learning, of much experience, and of wonder-full diligence in observation, hath renewed the opinion of ARISTARCHUS SAMIUS, and affirmith that the earthe not only moveth circularlye about his own centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles.
Five years later the Ephemeris, a set of astronomical tables, was printed in London for the year 1557 by John Feild, based on the work of Copernicus and Reinhold. The introduction was written by John Dee (1527-1608), Queen Elizabeth's astrologer, who noted that he had persuaded Feild to compile the Ephemeris, based on the Copernican theory, since the older tables were no longer satisfactory. Dee praised Copernicus for his “more than Herculean” effort in restoring astronomy, though he said that this was not the place to discuss the heliocentric theory itself.
A second edition of De Revolutionibus was published at Basel in 1566, and copies of it made their way to Italy and England. The English astronomer Thomas Digges (ca. 1546-95), a pupil of Dee's, obtained a copy of De Revolutionibus; it has survived in the library of Geneva University, along with a note he wrote on the title page, “Vulgi opinio Error” (“The common opinion errs”), indicating that he was one of the few sixteenth-century scholars who accepted the Copernican theory.
Digges did a free English translation of Chapters 9 through 11 of the first book of De Revolutionibus, adding it to his father's perpetual almanac, A Prognostication Everlasting, and publishing them together in 1576 as Perfit Description of the Caelestiall Orbes, according to the most ancient doctrines of the Pythagoreans lately revived by Copernicus and by Geometricall Demonstrations approved Digges stated that he had included this excerpt from De Revolutionibus in the almanac “so that Englishmen might not be deprived of so noble a theory.”
The book was accompanied by a large folded map of the sun-centered universe in which the stars were not confined to the outermost celestial sphere but scattered outward indefinitely in all directions. Digges thus burst the bounds of the medieval cosmos, which till then had been limited by the ninth celestial sphere, the one containing the supposedly fixed stars, which in his model extended to infinity.
The geocentric celestial spheres were still very much a part of the general worldview in late-sixteenth-century England, as is evident from Christopher Marlowe's play The Tragical History of Dr. Faustus As soon as Faustus has made his pact with the devil he begins to question Mephistophilis about matters beyond the ken of mortals, beginning with the celestial spheres.
Speak, are there many spheres above the moon?
Are all celestial bodies but one globe,
As is the substance of this centric earth?
The concept of an infinite universe was one of the revolutionary ideas for which the Italian mystic Giordano Bruno (1548-1600) was condemned by the Catholic Church, which had him burned at the stake in Rome on 17 February 1600. At the beginning of his dialogue in The Infinite Universe and the Worlds, published in 1584, Bruno says, through one of his characters, that in this limitless space there are innumerable worlds similar to our earth, each of them revolving around its own star-sun. “There are then innumerable suns, and an infinite number of earths revolve around these suns, just as the seven [the five visible planets plus the earth and its moon] we can observe revolve around this sun which is close to us.”
Bruno's universe was not only infinite but dynamic, in contrast to the finite cosmos of Aristotle, for whom the celestial region was immutable. Here he took his inspiration from the atomic theory of Democritus as expressed by Lucretius in his De Rerum Natura,which had been rediscovered in 1417. According to Bruno, the living universe is limited neither in its extent nor in its constantly changing multiplicity:
A model of the Copernican system from Thomas Digges's A Prognostication Everlasting, 1576.
There are no ends, boundaries, limits or walls which can defraud or deprive us of the infinite multitude of things Thus Democritus and Epicurus, who maintained that everything throughout infinity suffered renewal and restoration, understood these matters more truly than those who at all costs maintain a belief in the immutability of the Universe, alleging a constant and unchanging number of particles of identical material that perpetually undergo transformation, one into another.
The concept of an infinite universe appears also in the work of the English scientist William Gilbert (1544-1603), who may have been influenced by Thomas Digges and Giordano Bruno. Gilbert's De Magnete, published in 1600, was the first work on magnetism since that of Petrus Peregrinus in the thirteenth century. The sixth and final book of this work was devoted to Gilbert's cosmological theories, in which he rejected the crystalline celestial spheres of Aristotle and said that the apparent diurnal rotation of the stars was actually due to the axial rotation of the earth, which he believed to be a huge magnet. His rejection of diurnal stellar motion was due to his belief that the stars were limitless in number and extended to infinity, so that it was ridiculous to think that they rotated nightly around the celestial pole.
Meanwhile, astronomy was being revolutionized by the Danish astronomer Tycho Brahe (1546-1601), who in the last quarter of the seventeenth century made systematic observations of significantly greater accuracy than any ever done in the past, all just before the invention of the telescope.
Tycho, born to a noble Danish family, became passionately interested in astronomy while still a young boy and spent his nights observing the heavens. He enrolled at the University of Copenhagen at the age of thirteen and subsequently continued his studies at the universities of Leipzig, Basel, and Rostock. The astronomy books he studied included Sacrobosco's De sphaera, which had been in use since the thirteenth century, and other texts based on the homocentric spheres of Aristotle and the epicycles and eccentrics of Ptolemy. He was keenly interested in the new theory of Copernicus, whom he called “a second Ptolemy.”
Tycho made his first important observation in August 1563, when he noted a conjunction of Saturn and Jupiter. He found that the Alfonsine Tables were a month off in predicting the date of the conjunction, and that the Prutenic Tables were several days in error. This convinced Tycho that new tables were needed, and that they should be based on more accurate, precise, and systematic observations, which he would make with instruments of his own design in his own observatory.
The first of Tycho's observatories was at Augsburg, Germany, where he lived in the years 1569-71. The instruments that he designed and built for his observatory included a great quadrant with a radius of some nineteen feet for measuring the altitude of celestial bodies. He also constructed a huge sextant with a radius of fourteen feet for measuring angular separations, as well as a celestial globe ten feet in diameter on which to mark the positions of the stars in the celestial map that he began to create.
Tycho returned to Denmark in 1571, and on 11 November of the following year he began observing a nova, or new star, that suddenly appeared in the constellation Cassiopeia, exceeding even the planet Venus in its brilliance. (It is now known that a nova is a star that is exploding at the end of its evolutionary cycle, releasing an enormous amount of energy for a few months.) Tycho's measurements indicated that the nova was well beyond the sphere of Saturn, and the fact that its position did not change showed that it was not a comet. This was clear evidence of a change taking place in the celestial region, where, according to Aristotle's doctrine, everything was perfect and immutable.
The nova eventually began to fade, its color changing from white to yellow and then red, finally disappearing from view in March 1574. By then Tycho had written a brief tract entitled De Nova Stella (The New Star), which was published at Copenhagen in May 1573. After presenting the measurements that had led him to conclude that the new star was in the heavens beyond the planetary spheres, Tycho expressed his amazement at what he had observed. “I doubted no longer,” he wrote. “In truth, it was the greatest wonder that has ever shown itself in the whole of nature since the beginning of the world, or in any case as great as [when the] Sun was stopped by Joshua's prayers.”
The tract impressed King Frederick II of Denmark, who gave Tycho an annuity along with the small offshore island of Hveen, in the Øre-sund Strait, north of Copenhagen, the revenues of which would enable him to build and equip an observatory. Tycho settled on Hveen in 1576, calling the observatory Uraniborg, meaning “City of the Heavens.” The astronomical instruments and other equipment of what came to be a large research center were so numerous that Tycho was forced to build an annex called Stjernborg, “City of the Stars,” with subterranean chambers to shield the apparatus and researchers from the elements. That same year Tycho and his assistants began a series of observations of unprecedented accuracy and precision that would continue for the next two decades, laying the foundations for what would prove to be the new astronomy.
A spectacular comet appeared in 1577 and Tycho made detailed observations that led him to conclude that it was farther away than the moon, in fact even beyond the sphere of Mercury, and that it was in orbit around the sun among the outer planets. This contradicted the Aristotelian doctrine that comets were meteorological phenomena occurring below the sphere of the moon. He was thus led to reject Aristotle's concept of the homocentric crystalline spheres, and he concluded that the planets were moving independently through space.
Tycho's star catalog was based on systematic measurements of the coordinates of twenty-one principal stars, with a mean error, compared to modern values, of less than 40 seconds of arc, far less than that of any of his predecessors. Comparing the coordinates of the twenty-one principal stars in his catalog with those measured from antiquity until to his own time, Tycho computed a value for the rate of precession of the equinoxes equal to 51 seconds of arc per year, as compared to the modern value of 50.23 seconds. He correctly assumed the precession to be uniform, making no mention of the erroneous Islamic trepidation theory, which had caused unnecessary problems for Copernicus.
Despite his admiration for Copernicus, Tycho rejected the heliocentric theory, both on physical grounds and on the absence of stellar parallax; in the latter case he did not take into account the argument made by Archimedes and Copernicus that the stars were too far away to show any parallactic shift. Tycho rejected both the diurnal rotation of the earth as well as its annual orbital motion, retaining the Aristotelian belief that the stars rotated nightly around the celestial pole.
Faced with the growing debate between the Copernican and Ptolemaic theories, Tycho was led to propose his own planetary model, in which Mercury and Venus revolved around the sun, which together with the other planets and the moon orbited around the stationary earth. Tycho believed that his model combined the best features of both the Ptolemaic and the Copernican theories, since it kept the earth stationary and explained why Mercury and Venus were never very far from the sun.
Tycho's patron Frederick II died in 1588 and was succeeded by his son Christian IV, who was then eleven years old. When Christian came of age, in 1596, he informed Tycho that he would no longer support his astronomical research. Tycho was thus forced to abandon Uraniborg, taking with him all of his astronomical instruments and records, hoping to find a new royal patron.
Tycho moved first to Copenhagen and then in turn to Rostock and Wandsburg Castle, outside Hamburg. He remained for two years at Wandsburg Castle, where in 1598 he published his Astronomiae Instauratae Mechanica, a description of all of his astronomical instruments. He sent copies of his treatise to all of the wealthy and powerful people who might be interested in supporting his further researches. He appended his star catalog to the copy he presented to the emperor Rudolph II, who agreed to support Tycho's work, appointing him as the court astronomer.
Thus in 1600 Tycho moved to Prague, where he set up his instruments and created a new observatory at Benatky Castle, several miles northeast of the city. Soon afterward he hired an assistant named Johannes Kepler (1571-1630), a young German mathematician who had sent him an interesting treatise on astronomy, the Mysterium Cosmo-graphicum.
The Tychonic system, showing Mercury and Venus in orbit around the sun, which orbits the earth along with other planets and the moon, with the stars in the outermost sphere.
Kepler was born on 27 December 1571 in Weil der Stadt in southwestern Germany. His father was an itinerant mercenary soldier, his mother a fortune-teller who at one point was accused of being a witch and almost burned at the stake. The family moved to the nearby town of Lemberg, where Kepler was enrolled in one of the excellent Latin schools founded by the Duke of Württemberg. His youthful interest in astronomy had been stimulated by seeing the comet of 1577 and a lunar eclipse in 1580.
In 1589 Kepler entered the University of Tübingen, where, in addition to his studies in mathematics, physics, and astronomy, he was influenced by Platonism, Pythagoreanism, and the cosmological ideas of Nicholas of Cusa. His mathematics lectures were based on the works of Euclid, Archimedes, and Apollonius of Perge. (As Kepler later said, “How many mathematicians are there, who would toil through the Conks of Apollonius of Perge?”)
Kepler was particularly influenced by his professor of astronomy, Michael Maestlin, from whom he first learned of the heliocentric theory. In the introduction to his first book, the Mysterium Cosmographicum, Kepler wrote of his excitement on discovering the work of Copernicus, which he described as “a still unexhausted treasure of truly divine insight into the magnificent order of the whole world and of all bodies.”
Kepler received his master's degree at Tübingen in 1591, after which he studied theology there until 1594, when he was appointed a teacher of mathematics at the Protestant seminary in the Austrian town of Graz. A year after his arrival in Graz, Kepler came up with an idea that he thought explained the arrangement and order of the heliocentric planetary system. He had learned from his reading of Euclid that there are five and only five regular polyhedra, the so-called Platonic solids, in which all of the faces are equal as well as equilateral—the cube, tetrahedron, dodecahedron, icosahedron, and octahedron—and it occurred to him that they were related to the orbits of the earth and the five other planets. He explained the scheme in his treatise the Mysterium Cosmographicum,published in 1596, in which his values for the relative radii of the planetary orbits agree reasonably well with those determined by Copernicus, though there was no physical basis for his theory.
The earth's orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing it will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets.
Kepler sent copies of his treatise to a number of scientists, including Galileo Galilei (1564-1642). In his letter of acknowledgment, dated 4 August 1597, Galileo congratulated Kepler for having had the courage, which he himself lacked, to publish a work supporting the Copernican theory.
Kepler wrote back to Galileo on 13 October 1597, encouraging him to continue supporting the Copernican theory. “Have faith, Galilii, and come forward!” he wrote. “If my guess is right, there are but few of the prominent mathematicians of Europe who would wish to secede from us: such is the power of truth.”
Galileo was born in Pisa on 15 February 1564 to a Florentine family; they moved back to Florence in 1574. He enrolled in the school of medicine at the University of Pisa in 1581, studying physics and astronomy under Francesco Buonamici, who based his teachings on Aristotle. Galileo left Pisa without a degree in 1585 and returned to Florence, where he began an independent study of Euclid and Archimedes under Ostilio Ricci.
In 1583 Galileo made his first scientific discovery, that the period of a pendulum is independent of the angle through which it swings, at least for small angles. Three years later he invented a hydraulic balance, which he described in his first scientific publication,La Balancetta (The Little Balance), based on Archimedes’ principle, which he also used in determining the centers of gravity of solid bodies.
Galileo was appointed professor of mathematics in 1589 at the University of Pisa, where he remained for only three years. During this period he wrote an untitled treatise on motion now referred to as De Motu (On Motion), which remained unpublished during his lifetime. The treatise was an attack on Aristotelian physics, such as the notion that heavy bodies fall more rapidly than light ones, which Galileo is supposed to have refuted by dropping weights from the leaning tower of Pisa. Through his study of balls rolling down an inclined plane, he found that the distance traveled was proportional to the square of the elapsed time, one of the basic laws of kinematics. He also concluded that a ball rolling on a frictionless horizontal surface would continue to roll with constant velocity, while one at rest would remain motionless, thus stating the law of inertia.
In 1592 Galileo was appointed to the chair of mathematics at the University of Padua, where he remained for eighteen years. During that period he wrote several treatises for the use of his students, including one that was first published in a French translation in 1634 under the title Le Meccaniche, a study of motion and equilibrium on inclined planes that further developed the ideas he had presented in De Motu
In May 1597 Galileo wrote to a former colleague at Pisa defending the Copernican theory. Three months later he received a copy of Mysterium Cosmographicum, which led to his first correspondence with Kepler.
Kepler had also sent a copy of the Mysterium Cosmographicum to Tycho Brahe, who received it after he had left Denmark for Germany. Tycho responded warmly, calling the treatise “a brilliant speculation,” beginning a correspondence that eventually led Kepler to accept Tycho's invitation to join him at his new observatory outside of Prague. As Tycho wrote in response to Kepler's letter of acceptance: “You will come not so much as a guest but as a very welcome friend and highly desirable participant and companion in our observations of the heavens.”
Kepler finally arrived in Prague with his family early in 1600, beginning a brief but extraordinarily fruitful collaboration with Tycho. When Kepler began work at Prague he had hopes that he could take Tycho's data and use it directly to check his own planetary theory. But he was disappointed to find that most of Tycho's data was still in the form of raw observations, which first had to be subjected to mathematical analysis. Moreover, Tycho was extremely possessive of his data and would not reveal any more of it than Kepler needed for his work.
These and other disagreements with Tycho led Kepler to leave Prague in April of that year, though he returned in October after considerable negotiation concerning the terms of his employment. Tycho then assigned Kepler the task of analyzing the orbit of Mars, which until that time had been the responsibility of his assistant Longomontanus, who had just resigned. Kepler later wrote, “I consider it a divine decree that I came at exactly the time when Longomontanus was busy with Mars. Because assuredly either through it we arrive at the knowledge of the secrets of astronomy or else they remain forever concealed from us.”
Mars and Mercury are the only visible planets with eccentricities large enough to make their orbits significantly different from perfect circles. But Mercury is so close to the sun that it is difficult to observe, leaving Mars as the ideal planet for checking a mathematical theory, which is why Kepler was so enthusiastic about being able to analyze its orbit.
Early in the autumn of 1601 Tycho brought Kepler to the imperial court and introduced him to the emperor Rudolph II. Tycho then proposed to the emperor that he and Kepler compile a new set of astronomical tables. With the emperor's permission, this would be named the Rudolfine Tables, and since it was to be based on Tycho's observations it would be more accurate than any done in the past. The emperor graciously consented and agreed to pay Kepler's salary in this endeavor.
Soon afterward Tycho fell ill, and after suffering in agony for eleven days, on 24 October 1601, he died. On his deathbed he made Kepler promise that the Rudolfine Tables would be completed, and he expressed his hopes that it would be based on the Tychonic planetary model. As Kepler later wrote of Tycho's final conversation with him: “Although he knew I was of the Copernican persuasion, he asked me to present all my demonstrations in conformity with his hypothesis.”
Two days after Tycho's death Emperor Rudolph appointed Kepler as court mathematician and head of the observatory in Prague. Kepler thereupon resumed his work on Mars, now with unrestricted access to all of Tycho's data. At first he tried the traditional Ptolemaic methods—epicycle, eccentric, and equant—but no matter how he varied the parameters the calculated positions of the planet disagreed with Tycho's observations by up to 8 minutes of arc. His faith in the accuracy of Tycho's data led him to conclude that the Ptolemaic theory of epicycles, which had been used by Copernicus, would have to be replaced by a completely new theory, as he wrote: “Divine Providence granted us such a diligent observer in Tycho Brahe, that his observations convicted this Ptolemaic calculation of an error of eight minutes; it is only right that we should accept God's gift with a grateful mind…. Because those eight minutes could not be ignored, they alone have led to a total reformation of astronomy.”
After eight years of intense effort, Kepler was finally led to what are now known as his first two laws of planetary motion. The first law is that the planets travel in elliptical orbits, with the sun at one of the two focal points of the ellipse. The second law states that a radius vector drawn from the sun to a planet sweeps out equal areas in equal times, so that when the planet is close to the sun it moves rapidly and when far away it goes slowly. These two laws, which appeared in Kepler's Astronomia Nova (The New Astronomy), published in 1609, became the basis for his subsequent work on the Rudolfine Tables
Kepler's first two laws of planetary motion eliminated the need for the epicycles, eccentrics, and equants that had been used by astronomers from Ptolemy to Copernicus. The passing of this ancient cosmological doctrine was noted by Milton in Book VIII ofParadise Lost, where he describes the debate between the two world systems, Ptolemaic and Copernican.
Hereafter, when they come to model Heaven,
And calculate the stars; how they will wield
The mighty frame; how build, unbuild, contrive
To save appearances; how gird the sphere
With centric and eccentric scribbled o'er,
Cycle and epicycle, orb in orb.
Kepler wrote two other works on his researches before the publication of his Astronomia Nova The first was the Appendix to Witelo, published in 1604, which dealt with optical phenomena in astronomy, particularly parallax and refraction, as well as the annual variation in the size of the sun. The second book was occasioned by another new star, which appeared in October 1604 in the vicinity of Jupiter, Saturn, and Mars. Kepler published an eight-page tract on the new star in 1606 entitled De Stella Nova, with a subtitle describing it as “a book full of astronomical, physical, metaphysical, meteorological, astrological discussions, glorious and unusual.” At the end of the tract Kepler speculated on the astrological significance of the new star, saying that it might be a portent of the conversion of the American Indians, the downfall of Islam, or even the second coming of Christ.
Kepler's first two laws of planetary motion. First law: the planets move in elliptical paths, with the sun at one of the two focal points of the ellipse. Second law: a radius vector drawn from the sun to a planet sweeps out equal areas in equal times.
Meanwhile, the whole science of astronomy had been profoundly changed by the invention of the telescope. Instruments called “perspective glasses” had been used in England before 1580 for viewing distant terrestrial objects, and both John Dee and Thomas Digges were known to be expert in their construction and use, though there is no evidence that they used them for astronomical observations. But their friend Thomas Harriot, the Wizard Earl, is known to have made astronomical observations in the winter of 1609-10 with a small “telescope,” which may have been a perspective glass.
Other than these perspective glasses, one of the earliest telescopes seems to have appeared in 1604, when a Dutch optician named Zacharias Janssen constructed one from a specimen belonging to an unknown Italian, after which he sold some of them at fairs in northern Europe. Hearing of the telescope, Galileo built one in his workshop in 1609 and then offered it to the Doge of Venice for use in war and navigation. After improving on his original design, he began using his telescope to observe the heavens, and in March 1610 he published his discoveries in a little book called Siderius Nuncius (The Starry Messenger).
The book begins with his observations of the moon, which he found to look very much like the earth, with mountains, valleys, and what he thought were seas. Seen in the telescope, the planets were pale illuminated disks, whereas the stars remained brilliant points of light. The Milky Way proved to consist of numerous stars, not a nebula reflecting the light of the sun, as some had thought, nor an atmospheric phenomenon, as Aristotle had concluded. He counted more than ninety stars in Orion's belt, where only nine are visible to the naked eye. He discovered four moons orbiting around Jupiter, a solar system in miniature, which he used as an additional argument in favor of the Copernican theory. He called the Jovian moons the “Medicean Stars” in honor of Cosimo de’ Medici, the Grand Duke of Tuscany. Cosimo responded by making Galileo his court philosopher and appointing him to the chair of mathematics at the University of Pisa. Galileo had no obligation to teach at the University of Pisa or even to reside in the city, and so after his appointment, in September 1610, he departed to take up residence in Florence.
Galileo sent a copy of the Siderius Nuncius to Kepler, who received it on 8 April 1610. During the next eleven days Kepler composed his response in a little work called Dissertatio cum Nuncio Sidereal (Answer to the Starry Messenger), in which he expressed his enthusiastic approval of Galileo's discoveries and reminded readers of his own work on optical astronomy, as well as speculating on the possibility of inhabitants on the moon and arguing against an infinite universe.
Kepler borrowed a telescope from the elector Ernest of Cologne at the end of August 1610, and for the next ten days he used it to observe the heavens, particularly Jupiter and its moons. His excitement over the possibilities of the new instrument was such that he spent the next two months making an exhaustive study of the passage of light through lenses, which he published later in 1610 under the title Dioptrice, which became one of the foundation stones of the new science of optics.
The death of Rudolph II in early 1612 forced Kepler to leave Prague and take up the post of district mathematician at Linz, where he remained for the next fourteen years. One of his official duties was a study of chronology, part of a program of calendar reform instituted by Archduke Ferdinand II, son of the late emperor Rudolph. As a result of his studies he established that Christ was born in what in the modern calendar would be 5 B.C.
During that period when Kepler lived in Linz he continued his calculations on the Rudolfine Tables and published two other major works, the first of which was the Harmonice Mundi (Harmony of the World), which appeared in 1619. The title of this work was inspired by a Greek manuscript of Ptolemy's treatise on musical theory, the Harmonica, which Kepler acquired in 1607 and used in his analysis of music, geometry, astronomy, and astrology. The most important part of the Harmonice Mundi is the relationship now known as Kepler's third law of planetary motion, which he discovered on 15 May 1618 and presented in Book V. The law states that for each of the planets the square of the period of its orbital motion is proportional to the cube of its distance from the sun (or, strictly speaking, the semimajor axis of its elliptical orbit).
There had been speculations about the relation between the periods of planetary orbits and their radii since the times of Pythagoras, Plato, and Aristotle, and Kepler was terribly excited that he had at last, following in the footsteps of Ptolemy, found the mathematical law “necessary for the contemplation of celestial harmonies.” He wrote of his pleasure, “That the same thought about the harmonic formulation had turned up in the minds of two men (though lying so far apart in time) who had devoted themselves entirely to contemplating nature… I feel carried away and possessed by an unutterable rapture over the divine spectacle of the heavenly harmony.”
Kepler dedicated the Harmonice to James I of England. The king responded by sending his ambassador Sir Henry Wooton with an invitation for Kepler to take up residence in England. But after considering the offer for a while Kepler eventually decided against it.
The English poet John Donne was familiar with the work of Copernicus and Kepler, probably through Thomas Harriot. Donne had in 1611 said to the Copernicans that “those opinions of yours may very well be true… creeping into every man's mind.” That same year Donne lamented the passing of the old cosmology in “An Anatomy of the World”:
And new Philosophy cals all in doubt,
The Element of fire is quite put out;
The Sun is lost, and th'earth, and no man's wit
Can well direct him, where to look for it.
Kepler's second major work at Linz was his Epitome Astronomiae Coper-nicanae (Compendium of Copernican Astronomy), published in 1621. In the first three of the seven books of the Epitome Kepler refutes the traditional arguments against the motions of the earth, going much further than Copernicus and using principles that Galileo would later give in greater detail. His three laws of planetary motion are explained in great detail in Book IV, along with his lunar theory. The last three books treat practical problems involving his first two laws of planetary motion as well as his theories of lunar and solar motion and the precession of the equinoxes.
In 1626 Kepler was forced to leave Linz, which had undergone a two-month siege during a peasant uprising, and move to Ulm, where he published the Rudolfine Tables in September 1627, dedicating them to Archduke Ferdinand II. The new tables were far more accurate than any in the past, and they remained in use for more than a century. Kepler used his tables to predict that Mercury and Venus would make transits across the disk of the sun in 1631. The transit of Venus was not observed in Europe because it took place at night. The transit of Mercury was observed by Pierre Gassendi in Paris on 7 November 1631, representing a triumph for Kepler's astronomy, for his prediction was in error by only 10 minutes of arc as compared to 5 degrees for tables based on Ptolemy's model.
But Kepler did not live to see his theories vindicated, for he passed away on 15 November 1630. His tombstone, now lost, was engraved with an epitaph that he had written himself:
I used to measure the heavens,
Now I measure the shadow of the earth.
Although my soul was from heaven,
The shadow of my body lies here.
Meanwhile, Galileo had been active in advancing the cause of Coperni-canism against the accepted cosmology of Aristotle, which in its reinter-pretation by Saint Thomas Aquinas formed part of the philosophical basis for Roman Catholic theology. At the beginning of March 1616 the Holy Office of the Inquisition in Rome placed the works of Copernicus and all other writings that supported it, including those of Kepler, on the Index, the list of books that Catholics were forbidden to read. The decree held that believing the sun to be the immovable center of the world is “foolish and absurd, philosophically false and formally heretical.” Pope Paul V instructed Cardinal Bellarmine to censure Galileo, admonishing him not to hold or defend Copernican doctrines any longer. On March 3 Bellarmine reported that Galileo had acquiesced to the pope's warning, and that ended the matter for the time being.
After his censure Galileo returned to his villa at Arcetri, outside Florence, where for the next seven years he remained silent. But in 1623, after the death of Gregory XV, Galileo became hopeful when he learned that his friend Maffeo Cardinal Barbarini had succeeded as Pope Urban VIII. Heartened by his friend's election, Galileo immediately proceeded to publish a treatise entitled Il Saggiatore (The Assayer), which appeared later that year, dedicated to Urban VIII.
Il Saggiatore grew out of a dispute over the nature of comets between Galileo and Father Horatio Grassi, a Jesuit astronomer. This had been stimulated by the appearance in 1618 of a succession of three comets, the third and brightest of which remained visible until January 1619. Grassi, who supported the Tychonic model of planetary motion, took the Aristotelian view that the comets were atmospheric phenomena, while Galileo insisted that they were in the celestial region. Il Saggiatore was favorably received in the Vatican, and Galileo went to Rome in the spring of 1623 and had six audiences with the pope. Urban praised the book, but he refused to rescind the 1616 edict against the Copernican theory, though he said that if it had been up to him the ban would not have been imposed. Galileo did receive Urban's permission to discuss Copernicanism in a book, but only if the Aristotelian-Ptolemaic model was given equal and impartial attention.
Encouraged by his conversations with Urban, Galileo spent the next six years writing a book called the Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican, which was completed in 1630 and finally published in February 1632. The book is divided into four days of conversations among three friends: Salviati, a Copernican; Sagredo, an intelligent sceptic who had been converted to Copernicanism; and Simplicio, an Aristotelian.
The first day is devoted to a refutation of the Aristotelian view of the universe. On the second day the objections against the earth's motions are refuted on physical grounds. Many of Galileo's arguments here, though persuasive, are based on his erroneous notion of the inertia of circular motion. The third day is concerned with arguments for and against Copernicanism. Here, in comparing the two world systems, Galileo is often unfair in his criticism and exaggerates his claims for the superiority of the heliocentric theory. The fourth day is devoted to Galileo's erroneous theory of tidal action, which he believed to be conclusive proof of the earth's rotation.
Despite these defects, the arguments for Copernicanism were very persuasive and poor Simplicio, the Aristotelian, is defeated at every turn. Simplicio's closing remark represents Galileo's attempt to reserve judgment in the debate; he says, “It would still be excessive boldness for anyone to limit and restrict the Divine power and wisdom to some particular fancy of his own.” This statement was apparently almost a direct quote of what Pope Urban had said to Galileo in 1623. When Urban read the Dialogue he remembered these words and was deeply offended, feeling that Galileo had made a fool of him and taken advantage of their friendship to violate the 1616 edict against teaching Copernicanism. The Florentine ambassador Francesco Niccolini reported that after he'd discussed the Dialogue with Urban, the pope broke out in great anger and fairly shouted, “Your Galileo has ventured to meddle with things that he ought not, and with the most grave and dangerous subjects that can be stirred up these days.”
Urban directed the Holy Office to consider the affair and summoned Galileo to Rome. Galileo arrived in Rome in February 1633, but his trial before the court of the Inquisition did not begin until April. There he was accused of having ignored the 1616 edict of the Holy Office not to teach Copernicanism. The court deliberated until June before giving its verdict, and in the interim Galileo was confined in the palace of the Florentine ambassador. He was then brought once again to the Holy Office, where he was persuaded to acknowledge that he had gone too far in his support of the Copernican “heresy,” which he now abjured. He was thereupon sentenced to indefinite imprisonment and his Dialogue placed on the Index. The sentence of imprisonment was immediately commuted to allow him to be confined in one of the Roman residences of the Medici family, after which he was moved to Siena and then, in April 1634, allowed to return to his villa at Arcetri.
Once Galileo returned home he took up again the researches he had abandoned a quarter of a century earlier, principally the study of motion. This gave rise to the last and greatest of his works, Discourses and Mechanical Demonstrations Concerning Two New Sciences, of Mechanics and of Motions, which he dictated to his disciple Vincenzo Viviani. The work was completed in 1636, when Galileo was seventy-two and suffering from failing eyesight. Since publication in Italy was out of the question because of the papal ban on Galileo's works, his manuscript was smuggled to Leyden, where the Discourses was published in 1638, by which time he was completely blind.
The Discourses is organized in the same manner as the Dialogue, divided into four days of discussions among three friends. The first day is devoted to subjects that Galileo had not resolved to his satisfaction, particularly his speculations on the atomic theory of matter. The second day was taken up with one of the two new sciences, now known in mechanical engineering studies as “strength of materials.” The third and fourth days were devoted to the second of the two new sciences, kinematics, the mathematical description of motion, including motion at constant velocity; uniformly accelerated motion, as in free fall; nonuni-formly accelerated motion, as in the oscillation of a pendulum; and two-dimensional motion, as in the parabolic path of a projectile.
Galileo died at Arcetri on 8 January 1642, thirty-eight days before what would have been his seventy-eighth birthday. The Grand Duke of Tuscany sought to erect a monument in his memory, but he was advised not to do so for fear of giving offense to the Holy Office, since the pope had said that Galileo “had altogether given rise to the greatest scandal throughout Christendom.”
After Galileo's death a note in his hand was found on the preliminary leaves of his own copy of the Dialogue He probably wrote it after the Holy Office imprisoned him for supporting the Copernican “heresy.”
Take note theologians, that in your desire to make matters of faith and of proposition relating to the fixity of sun and earth you may run the risk of eventually having to condemn as heretics those who would decide the earth to stand still and the sun to change position—eventually, I say—at such a time as it might be physically or logically proved that the earth moves and the sun stands still.