As we have mentioned, and will find throughout this class, revolutions in scientific thought have built upon what came before. Our modern view of the sun-centered ("heliocentric") solar system, or a more appropriately, the fact the universe does not revolve around the Earth, came to the fore in the sixteenth century. As we will show, however, this model was not new, it had been proposed by earlier philosophers. But we are getting ahead of ourselves, let us start back near the "beginning".

Back some 20,000 years or so, humans were not arranged in complex societies. They basically were "hunter-gatherers". A nomadic lifestyle. We do not know much about their belief systems because they left few traces of their existence, as they rarely stayed in one place long enough to leave a significant record of their presence (though they did leave some traces, such as the cave paintings at Lascaux, dating from 17,000 years ago). Some term them "intelligent animals". For reasons that are not yet completely clear, some 15,000 years ago, agriculture appeared on the scene. Various types of animals were domesticated, and humans began to purposely grow food, instead of merely "collecting" it.

Before the development of agriculture, the universe was surely quite mysterious, filled with all sorts of supernatural events. But these patterns were not easily recognized because you needed to keep moving to find food: There was not much time for reflection. It seems obvious, however, that these early peoples would be aware of some celestial motions: the rising and setting of the sun, the changing phases of the moon, and the yearly seasonal cycle. Probably it was the latter that most effected their lifestyle, as various types of game would migrate with the seasons, and of course, various types of plants fruit at different times throughout the year. One can surmise that this would certainly lead to some sort of life-pattern, belief system, or even a religion.

With the rise of agriculture, and we include ranching and fishing in this term, food was not so hard to come by. With experience, you could grow sufficient quantities of grain to get you through the winter. Or you could dry fish and other meats, or use your live animals for food during the winter. Some years you might end up with more of a particular type of food than you needed to survive the winter---you could trade this with a neighbor to get some different type of food. Thus, people were now able to stay in one place, and now could pay more attention to natural cycles. This was especially important for agriculture--you had to know when to plant your seeds, or when to move your sheep to better grazing lands.

This development of agriculture leads to the origin of astronomy. For example, you would quickly notice harbingers of the coming spring by watching the motion of the Sun and stars. Fisherman would notice how the movements of the moon would effect the tides. With sufficient observation you would notice that there was a predictable pattern: a certain number of days would have to elapse between when the sun would again rise at a particular spot on your horizon. You would develop a system that would allow you to predict when it was time to plant your grain. You would devise a calendar. The beginning of each new cycle may have been cause for a celebration---the first "New Year's" celebrations.

Of course, it became quite clear that just because it was officially spring, it did not mean it was warm enough to plant your grain. The weather was only partially tied to the motion of the sun in the sky--some years were good, some years were bad. A bad year might lead you to suspect that you had done something to upset nature, you may have angered the Sun for example. It is not too hard to envision the early rise of religion to attempt to understand these events, and with that, various ceremonies designed to placate these celestial beings. With these developments, we get a new type of profession: the priest. A person who's sole job it was to understand and read the signs of nature, and of course, to keep track of time so that all of the necessary ceremonies occurred on schedule to keep the gods happy. Of course, it was also the priest's job to suggest remedies when things went unexpectantly wrong.

With the rise of priests came more careful observation of natural cycles. The earliest records of "calendars" appear to be various alignments of stones, and of pre-historic buildings. Most of these are of the "horizon-intercept" kind, they were aligned with where the sun (or moon) rose (or set) along the local horizon. One example you are almost certainly familiar with is  Stonehenge.  Activity at the site of  Stonehenge appears to date back to 7,000 BC, but the construction of the main parts of the monument appear to have begun around 3,000 BC. The various structures we see today at Stonehenge appear to be carefully aligned with the horizon locations ("azimuths") of the risings and settings of the sun and moon at various extremes in their motion (furthest south, furthest north, etc.). During this time, similar structures were being constructed elsewhere in the world, in both the Middle East (Babylon and Egypt), and in the far east (India and China). Later, such structures arose with the Mayan culture in the Americas (reaching their peak circa 200 AD, though archeological evidence suggests their culture began about 1500 years before it reached its peak).

The first actual "calendars", as we would recognize them, appeared on the scene about 5,000 years ago (here is an excellent site on ancient calendars). The Chinese calendar appears to have begun in 2637 BC (go here  for more on Chinese calendars), while the Egyptian calendar (from which our modern calendar arose) appears to date from 4236 BC! These calendars even had systems to even account for the fact that the year is not exactly 365 days long (why we have "leap" years).

As observations become more careful and accurate, cycles were noticed, as well as other phenomena: the discovery of the planets, and their motions. The appearance of comets, and "new stars" were noted. Of course, to keep track of all of this, writing had to be developed, as well as mathematics! With these developments, ancient cultures were able to predict astronomical motions and events well into the future---the most extreme case probably occurred in Mayan culture, with some events recurring on cycles that had periods of 3 million years!

Thus, its pretty clear that the origin of science can be traced back to the rise of agriculture.

As exquisite as these developments appear to be, however, they were not much more than record keeping. The heavens displayed all kinds of cycles, but what were the origins for these cycles? These motions were attributed to supernatural influences, and thus were not believed to be understandable by humans. Thus, it was not really science as we have defined it. It was the philosophy of the Milesians, discussed in the last class, that marks the start of science as we know it.

As true science arrived on the scene, it was probably a natural development that the Earth was considered the center of the universe--it was all they knew about. The Sun, the Moon, the planets and the stars all seemed to move in a more-or-less consistent fashion around the Earth. This lead to the Greek development of a geocentric view of the universe: humans were important, and where they lived had to be the center of everything. But the great change in the development of the Milesian's geocentric view of the universe was that in their prescription, the Sun, the Moon and such were physical objects that orbited about the Earth, and that their motions could be understood. This is a radical change, for they have now abandoned supernatural interpretations for these celestial objects! Thus, while it is easy to discard their theory with hindsight, it is important to note the great paradigm shift that is required to even arrive at this geocentric view of the universe.

As geometry and mathematics arose, the symmetry of circles, spheres, squares, cubes and triangles were prominent in Greek philosophy. The Moon and Sun appeared circular. Later the Moon and the Earth were considered to be spherical. It was the appeal of this symmetry that invoked the premise that all of the motions in the heavens obeyed this circular/spherical symmetry. Thus the Greeks knew that the Earth was spherical, as was the Moon. The Moon and Sun were physical objects that orbited around the Earth on circles (or attached to crystal spheres). With these findings, they could explain the eclipses of the Sun and the Moon. Note that they had discovered that the Moon shines by reflected sunlight. Thus, an elaborate geocentric model of the universe was crystallizing (pun intended) that culminates with Ptolemy (see below).

The first alternative to this model was provided by Herakleides (ca. 380 to ca. 310 BC) who developed a hybrid theory halfway between the geocentric and heliocentric systems, in which the planets Mercury and Venus were in orbit around the Sun, while the Sun itself and the planets Mars, Jupiter and Saturn were in orbit around the Earth.

The first recorded fully heliocentric view of the universe is due to  Aristarchus of Samos, (310 to 230 BC), the last of the Pythagorean astronomers. The record of Aristarchus' theory is attributed to a quote from Archimedes:

"You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. "

But Aristarchus' heliocentric theory did not gain acceptance by the Greeks. One of the problems that the other Greeks had with this theory was the lack of parallax exhibited by the stars. If the Earth orbits the sun, the stars should shift position because we are viewing them from different angles at different times of the year. To eliminate this effect, Aristarchus had to put the stars at an nearly infinite distance. This was something the other Greeks could not accept. But how right he was! We will encounter parallax a little bit later. Interestingly, Aristarchus goes on to attempt to measure the relative sizes and distances of the Sun and Moon. This is an important development, he is attempting to use mathematics to help prove a particular viewpoint. It does seem, however, that Aristarchus was not overly concerned with obtaining higher precision measurements (possible if attempted), which might have lead to further strengthening of his various ideas. 1700 years (!) would pass before the heliocentric theory would again be considered.

It is Ptolemy (ca. 100 AD) that is credited with creating a geocentric formulation of the universe that really withstood the tests of time. As mentioned in the last class, Ptolemy lived in Alexandria, Egypt at a time when Alexandria was the center of Greco-Roman learning. His full name is Claudius Ptolemy, suggesting he was a Roman citizen (the Claudius part) that had been born in Egypt (the Ptolemy part). Ptolemy apparently made astronomical observations from Alexandria during the period 127 to 141 AD. Ptolemy's most important work is the thirteen volume treatise Almagest. He prefaces this work with a statement of his goals:

"We shall try to note down everything which we think we have discovered up to the present time; we shall do this as concisely as possible and in a manner which can be followed by those who have already made some progress in the field. For the sake of completeness in our treatment we shall set out everything useful for the theory of the heavens in the proper order, but to avoid undue length we shall merely recount what has been adequately established by the ancients. However, those topics which have not been dealt with by our predecessors at all, or not as usefully as they might have been, will be discussed at length to the best of our ability. "

In Almagest, Ptolemy first outlines the Aristotelian view of the universe which

"...put forward his notion of an ordered universe or cosmos. It was governed by the concept of place, as opposed to space, and was divided into two distinct parts, the earthly or sublunary region, and the heavens. The former [earthly] was the abode of change and corruption, where things came into being, grew, matured, decayed, and died; the latter was the region of perfection, where there was no change. In the sublunary region, substances were made up of the four elements, earth, water, air, and fire. Earth was the heaviest, and its natural place was the center of the cosmos; for that reason the Earth was situated in the center of the cosmos. The natural places of water, air, and fire, were concentric spherical shells around the sphere of earth. Things were not arranged perfectly, and therefore areas of land protruded above the water. Objects sought the natural place of the element that predominated in them. Thus stones, in which earth predominated, move down to the center of the cosmos, and fire moves straight up. Natural motions were, then, radial, either down or up. The four elements differed from each other only in their qualities. Thus, earth was cold and dry while air was warm and moist. Changing one or both of its qualities, transmuted one element into another. Such transmutations were going on constantly, adding to the constant change in this sublunary region.

The heavens, on the other hand, were made up of an entirely different substance, the ether or quintessence (fifth element), an immutable substance. Heavenly bodies were part of spherical shells of ether. These spherical shells fit tightly around each other, without any spaces between them, in the following order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed stars. Each spherical shell (hereafter, simply, sphere) had its particular rotation, that accounted for the motion of the heavenly body contained in it. Outside the sphere of the fixed stars, there was the prime mover (himself unmoved), who imparted motion from the outside inward. All motions in the cosmos came ultimately from this prime mover. The natural motions of heavenly bodies and their spheres was perfectly circular, that is, circular and neither speeding up nor slowing down."¹

But this Aristotelian geocentric view of the universe had problems. The most important was that the planets did appear to speed-up and to slow-down, sometimes they even moved backwards! The planets also varied in brightness, but this couldn't happen in this particular view of the universe, as their distance from the Earth never really changed. Ptolemy got around these problems with several inventions. The first is the "eccentric", basically offsetting the Earth from the exact center of the sphere²:

While this invention deviated from the perfectly concentric spheres of the Aristotelian view, it was not considered to be a gross violation of the principles.

The second invention of Ptolemy (though similar ideas existed before him) was the epicycle:

The planet moved on a little circle whose center moved along the larger circle. An epicycle allowed for the backward ("retrograde") motion of a planet to be explained. The last construction, the equant, proposed that the motion of the center of the epicycle is uniform around the equant point ("Q" in the diagram below):

In the final model for the motion of a planet all three can be invoked:

^{With these three constructions, Ptolemy could fully explain the motions of the planets to the accuracy to which they could be observed with the instruments of his time. While all three of these constructions violated the Aristotelian view, only the equant really bothered Ptolemy's contemporaries. In fact, Copernicus partly justifies his heliocentric model by ridding this "monstrous construction" from the theory for heavenly motions.}

With the fall of the Roman empire, it was left to the Arabs to keep the Ptolemaic view of the universe alive. In 622 AD, the Prophet Mohammed launched his holy war against the infidels. Within a century, the Islamic Empire extended eastwards across northern India to the borders of China, and westwards across Asia Minor, north Africa. With the Arabic conquest of Spain and Sicily, the empire made it into western Europe. Alexandria, the centre of classical learning, fell to the Arabs in 642. When the period of military expansion ended, Islamic scholars became enthusiastic students of classical philosophy. Many important manuscripts were translated from Greek into Arabic. In the world of medieval Islam, Aristotle and Ptolemy were the supreme authorities in matters of natural science and astronomy. They continued to make observations and to refine the data that went into the model, and streamlined/advanced some of the calculation techniques but they did not make any modifications. ⁵

"In 999 AD, Gerbert of Aurillac, the most accomplished mathematician, musician, astronomer and classical scholar in Europe, ascended to the papal throne as Sylvester II, known as 'the magician Pope' to his contemporaries. His papacy, at the symbolic date 1000 AD marks the turning point of the European 'dark ages'. Contact was established with Arabic centers of learning in Spain, where Muslim, Christian and Jewish scholars congregated. During the following centuries, Hebrew and Arabic versions of ancient Greek texts were translated into Latin and began to circulate in Europe. The works of Aristotle were translated from around 1200. The translation of Ptolemy's Almagest into Latin in 1175 re-vitalised European astronomy. King Alfonso X of Castile (1122-1184) commissioned new astronomical tables calculated according to Ptolemy's theory with Arabic mathematical refinements. Completed in 1252, the Alphonsine Tables remained the best astronomical tables available in Europe for the next three centuries. The complexities of the Ptolemaic system exasperated King Alfonso however. When the intricacies of epicycles, deferents and equants were explained to him Alfonso 'the Wise' is said to have remarked that if the Almighty had consulted him on the matter, he would have recommended something a little simpler... "5

Eventually, with the re-emergence of European learning in the 13th century,  the geocentric view of the universe be would adopted by the Catholic church. It is interesting that in the early European universities, Ptolemy's theory was relegated to the world of mathematics, calendars, and astrology. It was purely a mechanical model of the celestial motion, and not the "true" nature of the universe as described by Aristotle. The latter would be given a more revered place in higher learning, and especially in questions of philosophy and theology.

In the fifteenth century, a reform of European astronomy began. This was due to the fact that predictions made using the Ptolemaic system were less and less accurate. With the advent of ocean-going vessels, and the expansion of global trade and exploration, navigation using astronomical knowledge had become extremely important. Also, the calendar implemented in 44 BC by Julius Caesar was 10 days off, with the spring equinox now occurring on the 11th of March instead of the 21st (used to fix the date of Easter). Astronomical help was needed! Two astronomers, Peurbach and Regiomontanus (who set up the first European observatory at Nuremburg in 1474) took on the task of locating errors in the works of Ptolemy, as well as errors in published tables and in observations. They had refined some of astronomy, but they had not gotten rid of all of the mounting problems.

Copernicus (1473 to 1543) learned of the works of Peurbach and Regiomontanus while an undergraduate at the University of Cracow (Poland), then spent eight years studying in Italy (five years in Bologna studying liberal arts, and three years at the University of Ferrara where he got a degree in canon law) before returning to a position in the cathedral at Frombork, Poland. Here he spent the majority of his time as a physician, lawyer, and church administrator. In his spare time he dabbled in astronomy. Copernicus was very interested in the Pythagorean mathematics, for he also believed in a harmony of the cosmos. He was, however, not apparently very interested in making new astronomical observations.

By 1514 Copernicus had laid out his heliocentric view of the universe in a manuscript entitled Commentariolus. This short work would put forward most of the elements of the heliocentric system some 39 years before his major manuscript on the theory, De revolutionibus orbium coelestium ("On the Revolutions of the Heavenly Spheres"), was published.  While many of the ideas Copernicus was proposing were radical, he still adhered to the Aristotelian view that everything moved in perfect circles, on solid celestial spheres, and moved via the physics espoused by Aristotle. Indeed, he even kept Ptolemy's epicycles in modified form in his new model. But Copernicus knew that his new theory would upset the Church, and he kept it relatively quiet. By moving the Sun to the center of the universe, man was no longer so important, and this could not stand in the view of the Church.

In the intervening years, Copernicus worked very hard at fully developing his view, and this included a number of mathematical devices that greatly advanced the art of calculation. In fact, De revolutionibus closely resembled Almagest in its structure and content. Copernicus feared the repercussions of his work, and was extremely reluctant to publish it. Only after the publication of a summary of Copernicus' system by an enthusiastic supporter named Rheticus in 1540, called Narratio prima, did the aging Copernicus agree to publish his theory. The story goes that Copernicus received a printed copy of his De revolutionibus on his deathbed in 1543.

A diagram from De revolutionibus orbium lays out his system:

^{Note that this system proposed a radical new idea: the Earth spun on its axis once per day! His theory also gave a simple explanation for the retrograde motions of the planets: the Earth catches up and passes them once each year. He also argued that his system was more elegant than the traditional geocentric system. However, the predictive power of his model was not substantially better than its competition. Besides removing humanity from the central place in God's creation, there were some obvious "problems" with this theory:}

1) If the Earth is spinning so fast, how do we remain attached to it--how do birds find their way home again with all of this spinning?

2) Why do the stars not show a parallax? They have to be at immense distances to show no parallax, and thus there is this great empty space in between the last sphere (Saturn) and that containing the stars.

All in all, the Copernican heliocentric model of the universe was very slow to gain acceptance.  In fact, during his lifetime and after his death, Copernicus was often the subject of ridicule. But he was never formally charged with any heresies, as the heliocentric model would not really make it on the "radar screen" of the church for  another 50 or 60 years (note also that De revolutionibus orbium was dedicated to Pope Paul III!). While the model may not have been accepted, much of the new tabular material and calculation methods were adopted by geocentrically-oriented astronomers for their own calculations on planetary motion.

The next player in the Copernican revolution was Tycho Brahe (1546 to 1601). Tycho was from a privileged background of Danish aristocracy, and thus had a good education and the resources necessary to engage in a variety of pursuits:

"He was brought up by his paternal uncle Jörgen Brahe and became his heir. He attended the universities of Copenhagen and Leipzig, and then traveled through the German region, studying further at the universities of Wittenberg, Rostock, and Basel. During this period his interest in alchemy and astronomy was aroused, and he bought several astronomical instruments. In a duel with another student, in Wittenberg in 1566, Tycho lost part of his nose. For the rest of his life he wore a metal insert over the missing part.

He returned to Denmark in 1570. In 1572 Tycho observed the new star in Cassiopeia and published a brief tract about it the following year. In 1574 he gave a course of lectures on astronomy at the University of Copenhagen. He was now  convinced that the improvement of astronomy hinged on accurate observations. After another tour of Germany, where he visited astronomers, Tycho accepted an offer from the King Frederick II to fund an observatory. He was given the little island of Hven in the Sont near Copenhagen, and there he built his observatory, Uraniburg, which became the finest observatory in Europe. "³

Tycho went about building the finest astronomical instruments that he could, he ran his own printing press, and he began to train astronomers from all over Europe. He was an excellent observer, and the quality of his observations were higher than any that came before him, and were much better than his contemporaries. Two of his most important observations were of the "new star" of 1572 (now known to be a supernova), and of the comet of 1577. In Aristotle's view, no new stars could occur, the heavens were immutable! He showed that the comet of 1577 had to be further away than the Moon, and that comets were not an atmospheric phenomena as previously believed. These two observations meant that Aristotle's view of the universe was incorrect, the heavenly realm could change. But Tycho could not accept the heliocentric view either, preferring the Aristotelian physics, and the view that man was important and at the center of the universe.

What Tycho did to resolve this was a peculiar halfway step that was a hybrid of the old geocentric view, and Copernicus' new heliocentric view: the "Tychonic" model. In this model, he placed the Earth at the center, and the Moon and the Sun orbited about it. But the other planets all orbited around the Sun!

After a falling-out with the King, Tycho left Denmark and moved to Prague in 1597. There he hired Johannes Kepler (1571-1630) to help him in reducing the data he had collected at Uraniburg. This extensive data base would not get published for many years after Tycho's death in 1601. Kepler was born in Weil der Stadt in Swabia, in southwest Germany.

"Kepler's teacher in the mathematical subjects was Michael Maestlin (1580-1635). Maestlin was one of the earliest astronomers to subscribe to Copernicus's heliocentric theory, although in his university lectures he taught only the Ptolemaic system. Only in what we might call graduate seminars did he acquaint his students, among whom was Kepler, with the technical details of the Copernican system. Kepler stated later that at this time he became a Copernican for "physical or, if you prefer, metaphysical reasons".

In 1594 Kepler accepted an appointment as professor of mathematics at the Protestant seminary in Graz (in the Austrian province of Styria). He was also appointed district mathematician and calendar maker. Kepler remained in Graz until 1600, when all Protestants were forced to convert to Catholicism or leave the province, as part of Counter Reformation measures. For six years, Kepler taught arithmetic, geometry (when there were interested students), Virgil, and rhetoric. In his spare time he pursued his private studies in astronomy and astrology. In 1597 Kepler married Barbara Müller. In that same year he published his first important work, The  Cosmographic Mystery, in which he argued that the distances of the planets from the Sun in the Copernican system were determined by the five regular solids, if one supposed that a planet's orbit was circumscribed about one solid and inscribed in another."⁴

^{Kepler's peculiar construction actually produced very good results when predicting the positions of the planets (except for Mercury). Tycho was impressed with Kepler's mathematical skills, and invited him to Prague to be his assistant. When Tycho died, Kepler assumed the position of Imperial Mathematician. With Tycho's excellent data base, Kepler had all the data he needed to launch a new heliocentric view of the universe. In 1609 he published Astronomia Nova ("New Astronomy") which contained his first two laws of planetary motion:}

1. Planets move in elliptical orbits with the sun as one of the foci:

2) A planet sweeps out equal areas in equal times:

It was not until 1618 that Kepler came up with his final law (published in 1619 in Third Law in Harmonices Mundi):

3. The square of the planet's orbital period is proportional to the cube of the orbital size (semi-major axes).  In equation form, P² = K a³, where P is the period, a is the semi-major axis, and K is a constant. In a log-log plot, this relationship looks like this:

The time taken to complete one orbit grows more than in direct proportion to orbital size. The orbital period is the circumference of th orbit divided by the planet's mean velocity. Since the circumference of an orbit increases in direct proportion to its semi-major axis, the Third Law implies that the velocities of planets in larger orbits are slower than for planets nearer the Sun. A planet with an orbital diameter 5 times the Earth's will require 11 Earth years to complete an orbit.

The timing of the publication (in 1609) of Kepler's original two laws could not have been better, for in 1610, Galileo, under the pseudonym of the "Sidereal Messenger" published his discovery of the four main moons of Jupiter (which we call the Galilean satellites after their discoverer). This discovery showed for the first time that not all celestial objects orbit around the Earth (more on this later!). Kepler quickly published a letter supporting the author and the discovery of these moons. He obtained a telescope that year, and begun his own observations of these moons leading to a write-up describing his observations entitled Narratio de Observatis Quatuor Jovis Satellitibus ("Narration about Four Satellites of Jupiter observed"). These two manuscripts were published in Galileo's home city of Florence, and were a great relief to that beleaguered scientist. By 1611 Kepler had published a preliminary description of how a telescope works in Dioptrice.

Kepler's crowning achievements were his publications entitled Epitome Astronomiae
Copernicanae ("Epitome of Copernican Astronomy") in 1621, and his Tabulae Rudolphinae ("Rudolphine Tables" ) in 1627. In Epitome Astronomiae Copernicanae Kepler fully laid out a new heliocentric model for the universe with the planets on elliptical orbits. This was the first accurate description of how the planets moved. Unfortunately, during the period of 1615-16 there was a witch hunt in Kepler's home country, and his mother was accused of being a witch. Kepler spent several years defending her in court, finally winning her freedom in 1620. On top of this, in 1618 the "Thirty Years War"  broke out. Most of Germany and Austria were affected. Kepler suffered some persecution during these years due to the fact that he was a protestant, and during this time there was a Catholic counter-reformation movement that was attempting to keep people from leaving the church (as well as attempting to quash the Protestant movement). During these years he was attempting to have his new tables on the motions of the planets, the Tabulae Rudolphinae, published in Linz, but a peasant revolt broke out, and the printer's shop where the manuscript was being printed was burned. He left Linz, and finally had the Tabulae Rudolphinae published in Ulm in 1627. The Tabulae Rudolphinae were the most accurate predictions for the motions of the planets that had ever been published, and Kepler had laid the theoretical foundation for the acceptance of the heliocentric theory. This does not mean, however, that Kepler's new theory was quickly adopted as the correct view of the universe--it was not!

While Kepler had escaped much of the wrath of the Church, his contemporary, and probably the staunchest supporter of his work, Galileo, would not. Galileo was born in Pisa in 1564, twenty one years after the publication of Copernicus' De revolutionibus orbium, and seven years before Kepler's birth. Galileo's early years would show the personality that would come back to haunt him later in life:

"Galileo received an excellent education at a monastery near Florence, and in 1581, aged 17, showed enough talent for his father to send him to the University of Pisa to study medicine. Though born into the ranks of lower nobility, the Galilei family struggled to make ends meet and were unable to afford the university fees. It was hoped that Galileo would secure one of 40 scholarships available. [he did]

 In the second year he showed enough promise to discover that a pendulum of any given length swings at a constant frequency, which led to the invention of the 'pulsilogium', a medical device used for timing the pulse of patients. However, Galileo was already attracting animosity by his reluctance to accept the common philosophy and the scholarship was refused, forcing him to leave the university without attaining his degree. Naturally, biographers have looked upon this as an early resistance to his liberal ideas, though Arthur Koestler in his book, The Sleepwalkers, writes: "It is more likely that the refusal of the scholarship was not due to the unpopularity of Galileo's views, but of his person - that cold, sarcastic presumption, by which he managed to spoil his case throughout his life".

Excluded from university life, Galileo tutored privately and managed to maintain his studies. He developed his interest in mechanics, writing treatises on his inventions which he circulated in manuscript. Another early invention was a hydrostatic balance which attracted the attention of a number of scholars, one of whom, Marchese Guidobaldo del Monte, befriended Galileo and began a chain of recommendations that brought him to the attention of Ferdinand de Medici, the Duke of Tuscany. In a rather ironic twist of fate the Duke was so impressed with Galileo that he appointed him as a lecturer at the university which four years earlier had refused his scholarship. Just three years on, aged 28, he rose to the position of Chair of Mathematics at the esteemed University of Padua, where he remained until 1610.

In 1597, Galileo was to receive his first contact from Johannes Kepler, then aged 26 and employed as Professor of Mathematics at Grantz in Austria. Kepler had completed The Cosmic Mystery, a treatise which expressed arguments in favor of Copernicus' Sun-centered universe. He sent a copy as a gift to the Chair of Mathematics at Padua, anxious for academic feedback. Galileo replied immediately, and wrote in cordial terms:

                 "I indeed congratulate myself on having an associate in the study of Truth who
                 is a friend of Truth. For it is a misery that so few exist who pursue the Truth
                 and do not pervert philosophical reason.... I adopted the teachings of
                 Copernicus many years ago, and his point of view enables me to explain many
                 phenomena of nature which certainly remain inexplicable according to the
                 more current hypotheses. I have written many arguments in support of him and
                 in refutation of the opposite view - which, however, so far I have not dared to
                 bring into the public light, frightened by the fate of Copernicus himself, our
                 teacher who, though he acquired immortal fame with some, is yet to remain to
                 an infinite number of others (for such is the number of fools) an object of
                 ridicule and derision. I would certainly dare to publish my reflections at once if
                 more people like you existed; as they don't. I shall refrain from doing so."

Although Kepler replied, imploring him to take a different stance and air his views, Galileo ignored his letter and ended the correspondence. It was 16 years before he would produce the first public indication of his beliefs; throughout the interim he continued to teach, and appeared to endorse the traditional Aristotelian arguments that the Earth did not move."⁶

The letter to Kepler provides us with excellent insight into the political realities of life in the late 16th century--you had to be careful what you said in a public forum, for you could face serious penalties for going against Church doctrine. But Galileo would not remain quiet for too much longer, for he was a brilliant experimentalist, and as his fame and reputation grew, so did his confidence that he could challenge the status quo. The problem was that while the Copernicun system might explain the details of the motions of the planets better than the Ptolemaic system, these were mere details, and were not sufficient reason to overthrow the established system--what was needed was observations that could not be explained by a geocentric view.

We have already noted the two discoveries by Tycho (the supernova and comet) that showed the "superlunary" world was not immutable, contrary to the view of Aristotle. But again, this did not violate the geocentric model for the motions of the planets. Other evidence was needed. This evidence required a new instrument, the telescope.

The invention of the telescope has been credited to Hans Lippershey, a Dutch spectacle maker. But this may or may not be correct  (go for  here  a list of possible suspects). The story goes that in July of 1609 Galileo had heard that a Dutchman had devised an instrument composed of two lenses that made objects appear closer. Not wanting to be scooped, Galileo quickly came up with his own version and:

"In August 1609 he invited the Venetian senate to inspect his own 'spy-glass' which, through a combination of a convex and concave lens, was able to magnify objects nine times greater than normal vision. The senate was greatly impressed, particularly by his suggestion that in matters of defense it would enable them to see the sails of ships two hours before they could be seen by the naked eye. When he presented his spy glass to them as a present they expressed their appreciation by doubling his salary to a thousand scudi a year and guaranteeing his position at Padua for the rest of his life. No doubt he felt some embarrassment when local spectacle makers were soon able to replicate his instruments for just a few scudi, but he committed himself to improving the power of his instruments and began to turn his attention to the heavens.

In March of the following year, 1610, he published Sidereus Nuncius, the 'Messenger of the Stars', which revealed the fruits of his observations. The tract was kept deliberately short in order to make it widely accessible and the style of language was uniquely devoid of philosophy. Combined with explosive contents, it made a remarkable impact worldwide. He wrote about the surface of the Moon, dismissing the common view that it was perfectly smooth, and  describing it as full of lofty mountains and deep hollows. He wrote about the fixed stars, and told how he had witnessed "other stars, in myriads, which have never been seen before, and which surpass the old, previously known stars in number more than ten times". Most importantly, he wrote of his discovery of  four new planets, the Moons of Jupiter which had never been imagined before.

With this, he justified his first ever 'outing' of his heliocentric beliefs, writing:

                 "Moreover, we have an excellent and exceedingly clear argument to put at rest
                 the scruples of those who can tolerate the revolution of the planets about the
                 Sun in the Copernican system, but are so disturbed by the revolution of the
                 single moon around the earth while both of them describe an annual orbit
                 around the Sun, that they consider this theory to be impossible."⁶

Galileo was assembling the ammunition to mount the final assault on the geocentric model. That objects could orbit Jupiter instead of the Earth, showed that the Earth could in no way be considered the sole center of the universe. A page from Galileo's journal showing some observations of the movements of the moons of Jupiter:

But this, by itself, was not quite sufficient to de-throne the geocentric model, since Tycho had already proposed a hybrid model where Mercury, Venus, Mars, Jupiter and Saturn orbited the Sun, while the Moon and Sun orbited the Earth.

Galileo's observations continued to mount, and one of the most important came in late 1610 when he found that the planet Venus showed phases just like those of the Moon:

[The top part of this figure also shows Galileo's impression of (from left to right) Saturn, Jupiter and Mars.]

This observation finally ruled out the Ptolemaic system (but, unfortunately, not the Tychonic system!).

He also showed that neither the Sun nor the Moon were perfect, as envisioned in the Aristotelian view of the universe:

These dramatic discoveries were having their impact--as more observers obtained telescopes (including Jesuit astronomers), Galileo's observations were confirmed, and the Church was going to have to modify its view. But the Church did not yet believe that sufficient proof existed to rule out Tycho's model, and hence it was best to stick with tradition. Also, such discoveries were scientific in nature, and would not be sufficient to undermine the established philosophy unless they could be shown to be absolutely true. This is where Galileo's personality gets him in trouble:

"...Galileo became aware of an after-dinner discussion involving, amongst others, the Dowager Duchess Christina and a professor of Mathematics at Pisa, Father Castelli. The Dowager had questioned Castelli over the new discoveries taking place, and whether he believed them to be fact. The way that it was reported to Galileo was that Castelli had assured the Dowager of their truth, adding only that the motion of the Earth remained unbelievable "in particular because Holy Scripture was obviously contrary to this view".

Galileo's response to the report was a published Letter to Castelli which was expanded and published a year later as Letter to the Grand Duchess Christina. It was an opportunity for Galileo to argue that science need not be tied too rigidly by Holy Scripture. It also implied that the Copernican system should be taken as a fact unless anyone could prove it to be false:

                 "Hence in expounding the Bible, if one were always to confine oneself to the
                 unadorned grammatical meaning, one might fall into error. Not only
                 contradictions and propositions far from true might be made to appear in the
                 Bible, but even grave heresies and follies?. if truly demonstrated physical
                 conclusions need not be subordinated to biblical passages, but the latter must
                 rather be shown not to interfere with the former, then before a physical
                 proposition is condemned it must be shown to be not rigorously demonstrated -
                 and this is to be done not by those who hold the proposition to be true, but by
                 those who hold it to be false."

The unspoken implication is that the Copernican system is a 'truly demonstrated physical conclusion' which the Church should realize, or accept the responsibility for disproving. To some, in particular Galileo's opponents, this was seen as a dangerous challenge to the authority of the Church, whose attitude had been to accept and readjust theological teachings as and when scientific advances had disproved them beyond doubt.⁶

Galileo's confrontational personality is now going to get him in trouble. I think the quote by Galileo above is even more radical than the above author gives it credit for, in that it basically says that the words of the Bible are not to be read in a literal sense. The letters from Galileo caused quite a commotion, and the Church was forced to act. It reviewed his writings, concluded they were not particularly blasphemous, and warned him to confine his views to science, and not to meddle in scripture or Church philosophy.

Unfortunately for him, Galileo was unable to do so. He continued to pester the Church to officially investigate the heliocentric theory. After much lobbying, the Pope had the "Qualifiers of the Holy Office" to form an official opinion on the following two propositions:

1) The Sun is the centre of the world and wholly immovable of local motion.

2) The Earth is not the centre of the world, nor immovable, but moves as a whole, also with a diurnal motion.

Their decision was that the first proposition was: "foolish and absurd, philosophically and formally heretical inasmuch as it expressly contradicts the doctrine of Holy Scripture" and the second was held to "deserve the like censure in philosophy, and as regards theological truth, to be at least erroneous in faith".

The Church had spoken, the geocentric universe was the official position. Fortunately for Galileo, the final, adopted statement did not include the word "heretical". But the Qualifiers suggested (in 1616) that:

"..."the Lord Cardinal Bellarmine to summon before him the said Galileo and admonish him to abandon the said opinion: and in case of his refusal to obey, that the Commissary is to enjoin on him, before a notary and witnesses, a command to abstain altogether from teaching or defending his opinion and doctrine and even from discussing it: and, if he do not acquiesce therein, that he is to be imprisoned"."⁶

Galileo acquiesced, and kept relatively quite for the next seven or eight years. When the conservative Pope Paul V died and was replaced by the more liberal Pope Barberini, Galileo decided to press the case again. Apparently, Galileo had a good relationship with Pope Barberini, and the Pope encouraged him to keep working. Galileo completed his treatise Two Chief World Systems in 1630. The book "...took the form of a dialogue between three characters: Salviati, a brilliant philosopher, who speaks for Galileo; Sacredo, who takes a neutral, questioning stance, and Simplicio a good natured simpleton who argues for Aristotle."⁶ His motives were all to clear. By 1632 copies of Two Chief World Systems were in circulation. The Pope and the rest of his minions were greatly offended, and Galileo was summoned to Rome to stand trial for heresy.

During the trial Galileo was convinced to plead guilty to obtain a more lenient sentence, and on June 22, 1632, he was sentenced to permanent house arrest, and all copies of Two Chief World Systems were to be burned. Galileo died in 1642. In 1979, Pope Pope John Paul II reopened  the case, and in October 1992 a papal commission acknowledged that Vatican records showed Galileo had not been restrained from teaching or discussing Copernicanism in 1616, as maintained at his trail, and they admitted the Vatican's error.

While the 17th century Church was sticking to a geocentric view, the heliocentric view was now the accepted theory for most scientists. Yet, there had not been absolute confirmation of the motion of the Earth around the Sun. It would take nearly a hundred more years before the absolute proof of the Earth's motion would be found (both parallax and the aberration of starlight, (to be discussed a bit later). In the meantime mathematics and physics had been evolving during the 17th century. Into the picture came Isaac Newton (1643 to 1727). Newton had begun work on his theories of mechanics and optics in 1665, but did not get around to publishing many of his discoveries until well after their publication by others. It was not until 1687 that Newton published Philosphiae Naturalis Principia Mathemtica ("Principia"). In it Newton put forward his three laws of motion:

I. Every body continues in a state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

II.  The change of motion is proportional to the force impressed; and is made in the direction of the straight line in which that force is impressed. (F=ma)

III. To every action there is an equal and opposite reaction: or, the mutual actions of two bodies upon each other are always equal, and act in opposite directions.

Newton quickly realized that if that Kepler's elliptical orbits were a consequence of an inverse square law in the force of gravitation attraction between two bodies. Newton went on to fully elaborate his new physics:

"The Principia is recognized as the greatest scientific book ever written. Newton analyzed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalized that all heavenly bodies mutually attract one another.

Further generalization led Newton to the law of universal gravitation:-

    ... all matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton explained a wide range of previously unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon as perturbed by the gravity of the Sun. This work made Newton an international leader in scientific research. The Continental scientists certainly did not accept the idea of action at a distance and continued to believe in Descartes' vortex theory where forces work through contact. However this did not stop the universal admiration for Newton's technical expertise."⁷

What Newton accomplished was to develop a model that could fully explain the motions of all of the celestial bodies, and in doing so developed the theoretical underpinnings for Kepler's laws, and thus showed why the heliocentric model was the correct one. Thus, few serious scientists still doubted the heliocentric model. But it was left until the 18th century to prove once and for all that the Earth orbited the sun by the measurement of "stellar aberration":

In order to keep a telescope pointed at starlight arriving perpendicular to the Earth's orbit, the telescope must be tipped in the direction of motion of the Earth in its orbit. The tilt angle is given in the box above, since the earth moves by the distance x during the time it takes light to travel down the telescope tube. [where v is the velocity of the earth in its orbit and c is the velocity of light]. The aberration of light was discovered in 1727 by the astronomer James  Bradley, based on an observed seasonal displacement in the apparent positions  of stars,  especially for stars in the direction perpendicular to the orbital plane of the Earth.

The final "proof" of the Earth's motion was due to Frederich Bessel (1784 to 1846). Bessel was given the unenviable task of putting together over 50,000 observations of the positions of stars to determine a fundamental coordinate system, and to measure the "proper motions" of these stars. Edmund Halley (of comet fame) had found in 1718 that several stars observed were a long way away (well 1/2 degree!) from where Hipparchus had plotted them-they must have moved in the intervening centuries. Thus he discovered that "fixed" stars moved! Anyway, Bessel was putting together his catalogue and amongst his many results were refinements in the Earth's motion, as well as in the quantification of stellar aberration. Bessel postulated that maybe the stars with the largest proper motions might also be the closest ones. So, he observed the star 61 Cygni, the star with the largest proper motion in his catalogue. In 1838 Bessel measured the parallax for 61 Cygni, and found the star was 10 light years from Earth (the modern value is 11.1 ly).

Case closed!
 
¹ From Ptolemaic System http://es.rice.edu/ES/humsoc/Galileo//Things/ptolemaic_system.html
²From Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution.
³  From http://es.rice.edu/ES/humsoc/Galileo//People/tycho_brahe.html
⁴  From http://es.rice.edu/ES/humsoc/Galileo//People/kepler.html
⁵ From http://www.skyscript.co.uk/copernicus.html
⁶ From http://www.skyscript.co.uk/galileo.html
⁷ From http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html