3.+Seeing+Stars,+From+Copernicus+to+Galileo

Xiaohan, Koshae, Clara, Hsin Pei


 * PART A: Timeline of Key Events **
 * Timeline of key events in astronomy from the time of Copernicus to Galileo**


 * 1462** -- The Epitome of Ptolemy's Almagest written by Georg Peurbach and Johannes Regiomontanus is published. This move symbolized a shift from reverence for Ptolemy and antiquity to respect coupled with confident innovation.
 * 1472** -- Georg Peurbach's New Theory of the Planets (1454) sought to reconcile geometric descriptive models for predicting planetary motions by employing homocentric (nested concentric) celestial spheres.
 * 1514** -- The initial appearance of the heliocentric theory of Nicholas Copernicus is associated with the private circulation of a manuscript known as the Commentariolus which was published many years later.
 * 1540** -- Georg Joachim Rheticus (1514-1574), a friend of Copernicus and the presumed author, provides an account of the heliocentric hypothesis in his Narratio prima (First Account).
 * 1543** -- Copernicus' De revolutionibus orbium coelestium was published; in it contained his explanations of the heliocentric theory. Symbolically, this work launched the 'Scientific Revolution'.
 * 1551** -- Deriving his results from Copernicus' data and planetary models, the Erasmus Reinhold publishes the Prutenic Tables, which replaced the outdated Alphonsine Tables.
 * 1572** -- Tycho Brahe discovers a supernova in constellation of Cassiopeia and published De nova stella in 1573. The significance of the new star was that it was clearly located beyond the sphere of the Moon, undermining the Aristotle’s belief that the heavens were immutable.
 * 1588** – Tycho Brahe’s geo-heliocentric model of Tycho Brahe was published despite controversy. Here Brahe argued for a model whereby the planets are imagined to revolve around the Sun while, in turn, the Sun revolved around the fixed, central earth.
 * 1596** -- Johannes Kepler's Cosmographic Mystery is published. Here, he presented a Copernican worldview dedicated to drawing together mathematical astronomy, physics, and a quasi-Pythogorean religious perspective in hope of a new astronomy.
 * 1607** -- Galileo Galilei demonstrates that a projectile follows a parabolic path.
 * 1608** -- The telescope is invented in the Netherlands; it employs a convex objective lens and a concave eyepiece.
 * 1609** -- Galileo Galilei constructs his first telescope and turns it toward the heavens.
 * 1609** -- Johannes Kepler's Astronomia nova is published. In it, he concluded that Mars moves non-uniformly in an elliptical path and proposes a quasi-magnetic power from the sun as partial explanation for the planetary motions.
 * 1610** -- Galileo observes phases of Venus and found that Venus shows all the phases from new to full. This observation was incompatible with the Ptolemaic model of the solar system.
 * 1610** – Galileo’s Sidereal Messenger was published. It contained his telescopic findings. Here, Galileo argues that there are innumerable stars invisible to the naked eye, mountains on the Moon and four satellites around Jupiter.
 * 1614** -- In mathematics, John Napier in his Mirifici logarithmorum canonis descripto establishes rules for logarithms and supplies useful tables.
 * 1616** -- Galileo is warned by the Inquisition not to hold or defend the heliocentric theory asserted in Copernicus' On the Revolutions.**1619** -- Johannes Kepler's Harmonice mundi is published. In it, he presents his third law of planetary motion.
 * 1623** -- Galileo publishes The Assayer. Here, he argues against Aristotle and the other ancient anstrologers in favor of mathematical and experimental methods, moving deftly across many topics, from statics and dynamics to his theory of matter.
 * 1627** -- Johannes Kepler's Rudolphine Tables is published.
 * 1632** -- In one of the major publications of the century, Galileo's Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican argues for a Copernican system; Galileo uses every tactic available to him, drawing on his telescopic findings, his new view of motion, and not a little rhetorical skill.
 * 1633** -- Galileo is called before the Inquisition in Rome for heresy due to his supporting and teaching of the Copernicanism hypothesis. After so, Galileo was placed under house arrest for the remainder of his life.


 * PART B: Brief Biographies of the people involved and significance of their major discoveries **

The medieval world view -- the linchpin of the Christian matrix -- was fashioned from the ideas of four men. Two of them were from the ancient world -- Aristotle and Ptolemy. And the other two were of the medieval world -- St. Thomas Aquinas (c.1225-1274) and Dante Alighieri, (1265-1321).
 * Aristotle**

The general mindset that people held of the cosmos and the physics regarding them, from the time of Aristotle to Dante, was that all phenomena were composed of four fundamental elements – air, fire, earth and water. These elements were believed to follow their ‘ideal’ nature; for example, since water and earth are burdensome and rough, they move downwards. Similarly, since they are weightless and buoyant, air and fire move upward. Each of the four elements is constantly striving to reach its natural center, and this is what keeps the cosmos in constant movement. Another of Aristotle’s belief is that the elements of air and fire dominate the world and compounded together to create a fifth element, more pure than the rest, which the ancients called "the aether." And since the heavenly bodies are "up there," they must be composed of "the aether." Using this foundation of elemental physics, Aristotle then built his theory of the cosmos. In Aristotle’s view (and in the view that was held by the Church in many centuries to come), the Earth was the core of the universe and the centre of all natural motions. Furthermore, he believed that all motion on Earth were linear and finite, while the heavenly bodies executed motion in epicycles forever, moving on invisible concentric orbits. Also, a body's motion was a consequence of its composition (e.g. the amount of air, fire, earth, water or aether it contained).

Claudies Ptolemy (c.90-c.168) was an Egyptian geographer and astronomer who conceptualized much of the medieval world view of the universe. The system that he theorized – the Potlemaic System – was very similar to Aristotle’s, adopting its geocentricism. The Ptolemaic System fixed stars on a concentric sphere around the earth, and around the earth were nine other exactly spherical objects (the nine planets) set in their places. Beyond the earth, in their respective fixed positions, were the moon and the sun. Planets were attached, not to the concentric spheres themselves, but to circles attached to the concentric spheres. These circles were called "Epicycles", and the concentric spheres to which they were attached were termed the "Deferents". Then, the centers of the epicycles executed uniform circular motion as they went around the deferent at uniform angular velocity, and at the same time the epicyles (to which the planets were attached) executed their own uniform circular motion. As the center of the epicycle moves around the deferent at constant angular velocity, the planet moves around the epicycle, also at constant angular velocity. With the Ptolemaic model, one can see that the distance of the planet from the Earth also varies with time, which leads to variations in brightness. Thus, the idea of uniform circular motion is saved (at least in some sense) by this scheme, and it allows a description of retrograde motion and varying planetary brightness.
 * Ptolemy**

Nicolaus Copernicus was born on 19 February 1473. He was a Polish mathematician and astronomer and was the first to propose a comprehensive theory of the sun in the centre of the universe with the earth revolving around it, otherwise known as a heliocentric or “sun-centred” model of the universe. Though his ideas had some flaws and were initially controversial as they directly contradicted the Catholic Church’s geocentric or “earth-centred” model by Ptolemy, it nevertheless was a start of a change from the medieval worldview and would inspire many others, thus initiating the Scientific Revolution.
 * Nicholaus Copernicus**

Before Copernicus formulated his heliocentric model, astronomy in Europe had largely come to a standstill. The Ptolemaic theory of the sky as a crystal sphere with spherical heavenly bodies moving in circular orbits around the fixed earth was accepted as the standard model of the universe since the 2nd century. Despite the fact that certain astronomical observations did not always correspond to the system, European astronomers made no attempt to formulate new theories but instead tried to improve upon the Ptolemaic model. For example, when they observed that at certain times Mars would appear to stop, move backward, then forward again (known as a “retrograde” motion) instead of moving forward all the time like it should according to the system, they accounted for it through “epicycles” and “deferents”. This caused the Ptolemaic system to become cumbersome and cluttered. Nevertheless, it was accepted as it fitted in with Christian concept of the purposefulness of God’s universe with humans on earth in the centre. Though it is commonly believed that Copernicus was the first to propose a heliocentric model of the universe, this is not true as there have been similar theories by numerous other astronomers, including Aristarchus of the 3rd century B.C. and by Nicholas de Cusa in 1440. What sets Copernicus apart from them is that in his heliocentric theory, he combined physics and mathematics to work out his theory in full mathematical detail.

Despite this, Copernicus’ model of the universe was far from perfect, mainly because he was too conservative a thinker. He retained many aspects of the Ptolemaic system, including heavenly spheres moving in circular orbits and epicycles and basically swapped the positions of the sun and earth. Thus, Copernicus’ system, far from presenting a more mathematically simple and elegant approach to the world system, ended up almost as messy as Ptolemy’s. Furthermore, he had no new evidence and observations to back up his claims, thus his theory turned out no more accurate than the existing one. It was also met with complications, such as those related to gravity (for example, how objects on earth fell to the ground when the earth itself was flying around the sun at a tremendous speed), which Copernicus himself was unable to answer.

Nevertheless, Copernicus’ model of the universe though not perfect, was a great shift from ancient views allowed others to think in new directions. It also questioned the very basis of Aristotlelian and Ptolemiac science and created uncertainty about humans’ role in the universe. (Fortunately though, he did not have to face denunciation from the Catholic Church because his publisher added an introduction declaring that Copernicus’ system was merely a device to simplify calculations, thus keeping his ideas politically harmless. He was however condemned by others.) It also provided the basis on which other astronomers who would who were also discontented with the Ptolemaic model could build their work on. Therefore, we should regard Copernicus’ work as not a revolution in itself, but as a preliminary though important step towards the scientific revolution.

Tycho Brahe was born on 14 December 1546 in Skane (then in Denmark but now in Sweden) to Otto Brahe and Beatte Bille whose families were in the high ranks of nobility in Denmark. Brahe attended the universities of Copenhagen and Leipzig and then traveled through the German region, furthering his studies there too. During this period, his interest in alchemy and astronomy was stirred up, and he bought several astronomical instruments. While studying at the university of Wittenberg, Brahe lost part of his nose in a duel with another student. For the rest of his life, he wore a metal insert over the missing part of his nose.
 * Tycho Brahe**

Brahe left Denmark in 1599, and after several years of travelling, he settled in Prague in 1599 as the Imperial Mathematician at the court of Emperor Rudolph II. He died there in 1601.

Tycho Brahe’s contributions to astronomy were enormous. He not only designed and built instruments, but also calibrated and checked their accuracy periodically. In this light, he revolutionized astronomical instrumentation. Brahe also brought to the table a new way of observational practice. Previous astronomers had only observed the positions of planets and the Moon at certain important points of their orbits like opposition and quadrature, but Tycho and his cast of assistants had observed these bodies throughout their orbits. Thus, orbital anomalies never before noticed were discovered by Tycho.

Also, Tycho was the first astronomer to make corrections for atmospheric refraction (defined as the displacement in apparent direction of a celestial object caused by the refraction of its light in passing through the Earth's atmosphere). This helped Tycho make more accurate observations. This can be inferred from how previous astronomers made observations accurate to about 15 arc minutes, while those of Tycho were accurate to about 2 arc minutes, and at his best, at about half an arc minute.

During his lifetime, Tycho produced many works, including De Nova et Nullius Aevi Memoria Prius Sextant Visa Stella (“On the New and Never Previously Seen Star” in 1573), De Mundi Aetherei Recentioribus Phaenomenis (“Concerning the New Phenomena in the Ethereal World” in 1588), Astronomiae Instauratae Mechanica (“Instruments for the Restored Astronomy” in 1598”) and Astronomiae Instauratae Progymnasmata (“Introductory Exercises Toward a Restored Astronomy” in 1602). Though his works were never published while he was alive, Johannes Kepler, one of his assistants, used Tycho’s work in his own studies. Kepler’s close analysis of Brahe’s work helped him offer the first credible physical explanation of a moving earth and the astronomy behind it.

Tycho’s observations of the new star of 1572 and comet of 1577 and his publications on these phenomena were instrumental in establishing the fact that these bodies were above the Moon, and therefore, contrary to what Aristotle had argued and philosophers still believed, the heavens were not unchanging.

Johannes Kepler was born on December 27 1571. He was a German mathematician, astronomer and astrologer. Known as the founder of ‘celestial mechanics’, he was the first to correctly explain the planetary motion.
 * Johannes Kepler **

Born to protestant parents, Kepler was profoundly religious, finding ways to credit God for each and every discovery he made. In fact, much of Kepler’s enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual. He was introduced to astronomy at an early age, observing both the Great Comet of 1577 a lunar eclipse in 1580 at a tender age. At the Protestant university of Tübingen, Kepler studied theology. Here, Kepler got acquainted with both the Ptolemaic and Copernican systems and became an avid Copernican.

In 1594, Kepler became a professor of mathematics at the Protestant seminary in Graz. He was also appointed district mathematician and calendar maker. While teaching, he pursued his private studies in astronomy and astrology in his spare time.

However, in 1600, during the Counter Reformation, Kepler was forced to leave Graz due to his Protestant status. In the same year, Kepler was invited by Tycho Brahe, the court astronomer to Emperor Rudolf II, to Prague to become his assistant and calculate new orbits for the planets from Brahe’s observations. It was during this period of time in Prague that Kepler published some of his greatest works.

In Prague, he published the Astronomia pars Optica (1604) in which he gave the modern explanation of its workings. Also, he published De Stella Nova (1606) on the new star that had appeared in 1604.

In 1612, he moved to Linz to be a district mathematician. In Linz, Kepler published several works such as the Harmonice Mundi (1619) and the Epitome Astronomiae Copernicanae (1617-1621), which became the most influential introduction to heliocentric astronomy. Kepler’s Three Laws of Planetary Movements that he published in his books were one of the greatest and most influential work in the field on Astrology during the Scientific Revolution. The significance of Kepler setting forth the first astronomical model that actually portrayed planetary motion, showed that scientists of this age had now destroyed the foundations of medieval logic, but instead had a new way of understand nature.

In 1627, Kepler published the Rudolphine Tables, another of his significant acheivements. However, just before the publication of the Rudolphine Tables, Kepler left Linz. This was due to the Counter Reformation measures, which pressurised Protestants in the region. Though he was exempted from a decree that banished all Protestants from the province as he was a court official, he nevertheless suffered persecution. However, he was forced to leave when a peasant rebellion broke out in Linz. He died in Regensburg in 1630.

Kepler’s laws of planetary motion were his greatest contribution to science. These laws had an enormous impact on scientific thinking, and provided the groundwork for other scientists. However, Kepler also made many other achievements in the fields of mathematics and optics. He founded modern optics by postulating the ray theory of light to explain vision and made improvements to the telescope. In the field of Mathematics, Kepler gave the first proof of how logarithms worked, provided faster methods of calculation and investigated the volume of many solid bodies.

Galileo Galilei was born on 15 February 1654. He was an Italian physicist, mathematician, astronomer, inventor and philosopher and is widely known as the father of modern astronomy and science. He was also a faithful Roman Catholic. His many notable achievements and contributions to the Scientific Revolution include significant improvements to the existing telescope and consequent astronomical observations, and also a concrete case for Copernicanism, backed up with solid evidence that the earth actually moved.
 * Galileo Galilei **

Galileo’s father, Vincenzo Galilei, was a financially troubled musician who was of noble birth. His nobility saved Galileo, and his siblings from extreme poverty. However, as Vincenzo wanted his son to have a better life, Galileo was sent to a monastery at a tender age to be tutored by a Jesuit priest. Under the tutelage of the priest, Galileo wanted to become a priest at first. However, Vincenzo was against this decision, resulting in Galileo enrolling into the University of Pisa in 1581 to study Medicine. He did not complete this degree, but instead he went on to study Mathematics there and was appointed to the chair of mathematics in 1589. It was back at Pisa that the intellectual life of Galileo began to take off. In 1581, Galileo invented the pendulum clock through experimentation as he found out that the duration of swing was only dependent on the string's length.

In 1592, he moved to the University of Padua to teach geometry, mechanics, and astronomy. He stayed there till 1610. There, Galileo made significant discoveries in various fields, notably the invention of a geometric and military compass. This compass could be used to solve practical mathematical problems. However, this was not all that he accomplished while he was at Padua. In 1609, just a year after the telescope was invented by Hans Lippershey, Galileo improved it and built a telescope of his own. This telescope was with about 3x magnification. The telescopes he made later on had up to about 30x magnifications too. However, with this new device, Galileo could now use it to observe the sky. Thus, in 1610, another year later, Galileo published Sidereus Nuncius (The Starry Messenger). From there, Galileo began to pursue his work on the Copernican heliocentric model in astronomy.

Unfortunately, his work questioning the old Ptolemaic model of the universe as well as Aristotelian physics had offended the Catholic Church, who championed the latter. It also believed that Galileo had challenged the teachings of the Bible and its many passages that referred to “a fixed earth and moving heavens” by claiming that the sun and not the earth was in the centre of the universe. This led to the famous debate between Galileo and his important critic, Cardinal Robert Bellamine, where the former argued that though religion and science should remain in harmony, each had a different role and the Church therefore should not interfere and dictate how people should think in the aspect of science. Despite impressing and winning the sympathy of many including Cardinal Maffeo Barberini who was also Galileo’s close friend, Galileo was warned by the church not to teach heliocentrism as a fact, but only as a theory.

After a decade of complying to this, Galileo saw another chance to present his ideas about Copernicanism to the world when Bellamine died and Barberini became Pope Urban VIII. He drafted the manuscript for another book. This book was edited for content by the Catholic Church authorities and named A Dialogue Between the Two Great World Systems. Despite this, it caused an uproar as it not only promoted Copernicanism, but also insulted the church by portraying Barberini as the foolish character Simplicito, meaning “simple-minded one”. Thus Galileo was charged with defying the church and made to recant his belief in Copernicanism on threat of death and torture and placed under house arrest for the rest of his life.

Nevertheless, Galileo left a legacy of knowledge of not only in the field of astronomy and astrology, but also in the field of Physics and Mathematics. In Physics, he theorized that objects of different masses accelerated toward the ground at the same rate. This theory was derived through experimentation and provided evidence against Aristotle's ideas about objects falling under gravity. **Sources:** http://highered.mcgraw-hill.com/sites/dl/free/0072465700/78777/atm1s1_3.htm http:www.windows.ucar.edu/tour/link=/the_universe/uts/timeline.html&sw=f http:www-groups.dcs.st-and.ac.uk/~history/Biographies/Copernicus.html http:plato.stanford.edu/entries/copernicus/ http://scienceworld.wolfram.com/biography/Copernicus.html http:www.sjsu.edu/depts/Museum/galile.html http:galileo.rice.edu/chron/galileo.html http:www.biographyshelf.com/galileo_galilei_biography.html http:www.astronomy-for-kids-online.com/galileo-galilei-biography.html http:www.321books.co.uk/biography/galileo-galilei.htmhttp://cnx.org/content/m11933/latest///

**PART C: Major discoveries and achievements and PART D: Reasons why these major discoveries and / or achievements were significant**

Unlike all these other astronomers who corrected only minor errors of logic, Copernicus decided to do away with one fundamental Ptolemaic principle: that the earth was in the centre of the universe. This theory was proposed first in an early book, Commentariolus in 1512, then later and more significantly in his famous book, De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres), published just before his death in 1543.
 * Copernicus publishes his heliocentric model of the universe: **

In De Revolutionibus, Copernicus proposed the idea that the sun was in the centre of the universe with the earth circling it as the third planet after Mercury and Venus. This made much more sense and simplified the mathematics involved, and the old Roman calendar, which was based on the Ptolemaic model of the universe and over the centuries had fallen significantly out of alignment with the actual positions of the heanenly bodies, could then be put right. Also, his theory could explain many natural phenomena, such as the retrograde motion of Mars, which is when the earth overtakes Mars on its orbit causing it to seem to move backwards (relative to the positions of the distant fixed stars) as well as the apparent movement of the sun from east to west, which is actually the earth’s rotation about its own axis. Tycho Brahe observes a new star: ** In 1572 back in Denmark, Tycho observed a completely new star in Cassiopeia and published a brief tract about it the next year. Soon after, Brahe became convinced that the improvement of astronomy was dependent on accurate observations. Once again, this was another blow at the foundation of Aristotle’s belief (who said that founding a new star was impossible) and only served to raise more questions and garner more supporters for the newly emerging theories. This was also the starting point where Tycho began correcting other flaws in ancient astronomy by observing the movement of the whole heavens, and not just basing conclusions on theoretical ideals. Tycho is granted possession of an island near Copenhagen by King Federick II, on which he built a castle outfitted with a library, observatories and instrument ****s: ** T his demonstrates the growing popularity of scientists and the various sciences such as astronomy amongst the aristocrats, and reflects how specialized equipment (e.g. the instruments he had designed and calibrated for more precise astronomical observations) and environments are starting to be employed by scientists who desired to seriously consider their subject and to ensure a certain degree of certainty in their findings. For over twenty years, Brahe instituted nightly observations, carefully and very accurately mapping out the motion of every significant object in the night sky. Apart from that, Tycho ran his own printing press, and also trained a generation of young astronomers there in the art of observing. This was a significant turning point as it showed that scientists were starting to refer to empirical data through precise instruments instead of simply observations made with their naked eye, and also evidence of how individuals like Tycho shared their work and experiences with the younger generation, thus influencing mindsets and initiating change. Tycho developed his own system of the star ****s: **This new system rejected the Aristotelian-Ptolemaic system but also avoided the upsetting theological implications of the Copernican system (i.e. the earth actually moved). He based this theory on his new collated evidence; while previous astronomers had only observed the positions of planets and the Moon at certain important points of their orbits like opposition and quadrature, Tycho and his cast of assistants had observed these bodies throughout their orbits. Furthermore, this changing way of thinking could have made it easier for future discoveries and contradicting astronomic theories (against Aristotle and Ptolemy) to be more easily accepted.  Using the precise data that Tycho had collected, Kepler published the first two laws of planetary motion, which was one of the most important works in his life. The first law was: the orbit of a planet about the Sun is an ellipse with the Sun's center of mass at one focus. The second law was: a line joining a planet and the Sun sweeps out equal areas in equal intervals of time. These laws were published in The New Astronomy. He then published Harmonice Mundi, where his third law can be found, which established that the square of a planet’s period of revolution is proportional to the cube of its average distance from the sun. Kepler’s Three Laws of Planetary Movements was one of the greatest and most influential work in the field on Astrology during the Scientific Revolution. The significance of Kepler setting forth the first astronomical model that actually portrayed planetary motion, showed that scientists of this age had now destroyed the foundations of medieval logic, but instead had a new way of understand nature. Also, Kepler’s publication of the Three Laws of Planetary Motion and have also showed that people now could combine the empirical with the theoretical. Additionally, the publication of the planetary movements were signs which showed that by now, the power of opposing forces, like the Church, was diminishing. This can be seen as Copernicus hesitated to publish his findings during the 15th Century.
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Galileo Galilei first turns his self-improved ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">telescope on the heave ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">ns: **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">This simple action caused Galileo to observe sunspots, craters of the moon, Jupiter’s moons and Saturn’s rings; he recorded and documented all his findings, only to publish them in a book titled The Starry Messenger<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">. It was the first scientific treatise to be published based on observations made through a telescope. In it, he reported discoveries of the 4 orbiting moons around Jupiter (the Galilean moons), craters on the Moon’s surface, which were once thought to be smooth, the existence of a huge number of stars which were invisible to the naked eye such as those in the Milky Way and he also reported discoveries made about the difference between the appearances of the planets and those of the fixed stars through the observation of Venus’ phases. He also sketched sunspots and documented them as real irregularities on the surface of the sun, thus disproving the medieval belief of heavenly bodies as perfect and flawless spheres. The publication of this book won him fame and admiration from his contemporaries as well as patronage from the powerful in Italy. From there, Galileo began to pursue his work on the Copernican heliocentric model in astronomy. The book made many Europeans more aware of the new picture of the Universe than the mathematical theories of Copernicus and Kepler did and reflected a growing interest by the general public in this area of study. The act of creating, improving and using a telescope – and then subsequently publishing the scientifically precise proofs he had gathered – showed a growing need for empirical data to prove or disprove theories. The publication of this book won him fame and admiration from his contemporaries as well as patronage from the powerful in Italy. Galileo writes a Letter to the Grand Duchess Christina di Medici: **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">In response to Cardinal Robert Bellarmine’s disapproval of Galileo’s theories (which were severely distanced from the Church’s ideals), Galileo launched his first and most famous reply to his critics, and his clearest defense of a Copernican science. This showed a growing antagonism towards the Church and also their diminishing authority as Galileo had the courage to send such a letter, demonstrating how the name of science was slowly overwhelming that of religion. Galileo’s argument impressed his Medici patrons and kept the sympathy of important figures in the church, particularly his close friend Cardinal Maffeo Barberini. However, he was still disallowed from discussing his Copernican theories afterwards. Galileo published ‘A Dialogue Between the Two Great World Systems’ **:// <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">The church having allowed its publication, Galileo published this book in which he presented a mock debate between supporters of the old and new world systems. Though the Ptolemaic system won in the end, Galileo’s real purpose – of presenting a thorough and well-supported case for Copernicanism – had been achieved. Galileo was put on trial: **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Charged with two dangerous attacks on the authority of the church, Galileo went to Rome by order of the Roman Church (one of his biggest mistakes yet) and was threatened with torture. Using forged accounts of Galileo’s previous charges, the Church backed its weak case against the philosopher with threats of death and excommunication. While these threats worked on the surface – Galileo publicly recanted his belief in Copernicus’ ideas – it also showed how weak the Chuch’s authority had become; they even had to refer to forged documents and empty threats to oppose the growing number of Copernican supporters.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Kepler published the Rudolphine Tables: **<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">These contained positions of stars with directions and tables for locating the planets of the solar system. It used Brahe's accurate observations together with a heliocentric model of the solar system and Kepler’s own discovery of the elliptical orbits of the planets. Compared to earlier tables, the Rudolphine Tables yielded significantly improved predictions of planetary positions. The accurate data on the positions of stars and planets were of immense value to navigators, and also placed more emphasis on the use of empirical data.
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