Seeing+Stars+-+From+Copernicus+to+Galileo+(Shixuan's+Group)

=toc= =Introduction= By early sixteenth century, the old Roman calendar was significantly out of alignment with the movement of the heavenly bodies. Major saints’ days, Easter and other holy days were more than a week off where they should have been according to the stars. Catholic authorities spent nearly a century trying to correct the fundamental problem by summoning mathematicians and astronomers from all over Europe to try and solve this.
 * (done by Cara, Kai Wei, Shi Xuan, Nicole, Yiming)**

Conventionally, Nature is thought to be God’s responsibility and it is not in human nature to interfere with it; hence in the fifteenth and sixteenth centuries, people just believe in a geocentric system—the Aristotelian system. But with the advent of more precise measurements and scientific instruments, people began to think otherwise, resulting in the dawn of a new astrological age with numerous significant breakthroughs in theories and knowledge of the universe.

=Timeline of Key Events=
 * ~ Year (approximate) ||~ Key Event ||
 * = 19 Feb 1473 || Nicolaus Copernicus is born in Toruń, Poland ||
 * = 1506 - 1530 || Copernicus completes the manuscript of his famous book //On the Revolutions of the Heavenly Spheres// which advocates a heliocentric model of the universe and promotes many new theories ||
 * = 24 May 1543 || Copernicus publishes //On the Revolutions of the Heavenly Spheres// on his deathbed ||
 * = 14 Dec 1546 || Tycho Brahe is born in //Knudstrup borg//, Denmark ||
 * = 15 Feb 1564 || Galileo Galilei is born in Pisa, Italy ||
 * = 27 Dec 1571 || Johannes Kepler is born in Stuttgart, Germany ||
 * = 11 Nov 1572 || Tycho Brahe witnesses a supernova in the sky above the constellation Cassiopeia, though he does not realise it ||
 * = 1573 || Tycho Brahe writes //De nova stella// (The New Star), discussing his findings ||
 * = 1577 || Brahe sees a long-tailed comet and observes its path for 2 months. Measuring the parallax of the comets aids the discovery that planets orbit around the sun ||
 * = 1596 || Kepler writes the book //Mystery of the Cosmos// ||
 * = 24 Oct 1601 || Brahe dies in Prague, after contracting a bladder ailment ||
 * = 1609 || Kepler publishes //Astronomia nova// (The New Astronomy) in 5 parts, in which he conjectures that the orbit of planets is elliptical, not spherical. //Astronomia nova// also contains his laws of planetary motion ||
 * = 1609 || Galileo turns a telescope with a magnification of x9 to the skies ||
 * = 1610 || Galileo publishes his book //Sidereus Nuncius// (The Starry Messenger) ||
 * = 1612 || Galielo publishes a //Discourse on Floating Bodies// ||
 * = 1613 || Galileo writes //Letters on the Sunspots//, suggesting that the Sun and heavens are corruptible ||
 * = 1617 || Kepler publishes the first volume of //Epitome of Copernician Astronomy// ||
 * = 1619 || Kepler writes //The Harmonies of the World//, which discusses harmony and congruence in geometrical forms and physical phenomena. It also relates his discovery of the third law of planetary motion ||
 * = 1620 || Kepler publishes the second volume of //Epitome of Copernician Astronomy// ||
 * = 1621 || Kepler publishes the third volume of //Epitome of Copernician Astronomy// ||
 * = 1623 || Galileo publishes //The Assayer//, which deals with comets and argues that they are sublunary (belonging to this world, not a better, more spiritual one). In this book he makes some of his most famous methodological pronouncements, including the claim that Nature is written in the language of mathematics ||
 * = 15 Nov 1630 || Kepler dies in Regensburg, Germany ||
 * = 1632 || Galileo writes //Dialogo dei due massimi sistemi del mondo// (Discourse Concerning the Two Chief World Systems), in which 2 characters debate the positions of the sun and the Earth ||
 * = 1638 || Galileo writes //Discourses and Mathematical Demonstrations Relating to Two New Sciences// ||
 * = 8 Jan 1642 || Galileo dies, after spending his last year under house arrest. ||

=Write-ups of People Involved=

Nicolaus Copernicus
Born on 19th February 1473, Nicolaus Copernicus was the youngest of four children of Nicolaus Copernicus, Sr., a well-to-do merchant who had moved to Torun from Kracow, and Barbara Watzenrode, the daughter of a leading merchant family in Torun. They lived in a big house on St. Anne’s Street until an outbreak of the plague killed his father when he was 10. The children's maternal uncle, Lucas Watzenrode, (1447-1512), then took them under his protection and facilitated his nephew's advancement in the church, directing his education. Watzenrode became the Bishop of Warmia in 1489, and sent Copernicus to the University of Krakow (now the Jageillonian University). The University of Krakow was one of Europe’s best, known for its religious and political tolerance as well as its professors of mathematics and astronomy. Watzenrode also provided Coperniucs a position as a canon at Frombork Cathedral which helped pay for his studies.

In 1496, he went to the Alps on foot to learn about medicine, church matters, philosophy and mathematics at universities in Bologna, Rome, Padua and Ferrara where he obtained a doctorate from the University of Ferrara in canon law. He studied ancient Greek and read Aristotle in his original language. When he returned to Poland, he was one of the most learned men of his day, during the Renaissance period. Copernicus was extremely interested in stargazing and studied the works of the experts on astronomy (Aristotle, Hipparchus and Ptolemy). He passed away on 24th May, 1543

Tycho Brahe
 Tycho Brahe was born on 14 December 1546 as Tyge Brahe in Skane, Denmark. He was raised by an uncle and an aunt and was sent at 12 to the university of Copenhagen. His uncle wanted him to enter political life as part of the privileged elite surrounding the king of Denmark, Frederick 2. During his first year in college, an eclipse was accurately predicted. Tycho was fascinated and bought a copy of Ptolemy’s Almagest.

He was then sent to the University of Leipzig to study law, accompanied by a companion to make sure he strictly studied law. However, he studied the stars at night when his companion slept. At 18, he built his own astronomical instruments and found that the existing star charts were wildly inaccurate and was convinced he could do better. His uncle refused but in 1565, his uncle died. Tycho was free to go to northern universities to look for experts to teach him. A chunk of his nose was sliced off during a duel. He became a canon in1567 at the Roskilde Cathedral which allowed him a steady income to support his experiments. Between 1571 and 1572, he fell in love and got married to Kirsten Jorgensdatter and had eight children together. In 1574, he was given funding and a small island, Hven, near Copenhagen by King Frederick to build his own observatory, called Uraniborg. He passed away on 24 October, 1601, in Prague.

Johannes Kepler
He was born on 27 December, 1571 in Germany to the daughter of an innkeeper and a mercenary solider. Kepler's early education was in a local school and then at a nearby seminary, from which, intending to be ordained, he went on to enrol at the University of Tübingen, then a bastion of Lutheran orthodoxy. At Tübingen, Kepler studied not only mathematics but also Greek and Hebrew, which were both necessary for reading the scriptures in their original languages. He studied under Michael Mästlin, a leading astronomer of the day who introduced him to the new concept of heliocentricism.

After graduation, he was offered a teaching position for mathematics and astronomy in a school in Ghaz, Austria. He spent 6 years there. In 1600, he became an assistant to Tycho Brahe. Tycho handed him his works before he died and he succeeded him as Imperial Mathematician to the Holy Roman Empire and took over Brahe’s work and data. Tycho passed away on 15 November, 1630, in Regensburg. His grave however, was destroyed less than two years later, due to the Thirty Years’ War.

Galileo Galilei
He was born on 15th February, 1564 in Pisa, Italy, the oldest child of Vincenzo Galilei, a famous musician and Guila Ammannati. Galileo and his family moved to Florence in 1572. He started to study for the priesthood, but left and enrolled for a medical degree at the University of Pisa. He never completed this degree, but instead studied mathematics notably with Ostilio Ricci, the mathematician of the Tuscan court. In 1589, with the help of Clavius and del Monte, he was appointed to the chair of mathematics in Pisa. In 1592 he was appointed, at a much higher salary, to the position of mathematician at the University of Padua.

While in Padua he met Marina Gamba, and in 1600 their daughter Virginia was born. In 1601 they had another daughter Livia, and in 1606 a son Vincenzo. However, Marina and he were not married and hence his children were considered illegitimate. In 1611 he became a member of what is perhaps the first scientific society, the Academia dei Lincei. In 1614, he was accused of heresy by the church for supporting the Copernican theory and in 1616 was forbidden to advocate or teach it. He was placed under permanent house arrest in 1634 for his book, //Dialogue Concerning the Two Chief World Systems// //. // He turned blind in 1638 before his death on 8th January, 1642.

=Major Discoveries and Significance=

Discoveries and Achievements
Nicolaus Copernicus first proposed a heliocentric model of the universe in his attempt to achieve mathematical elegance to astronomy by making Ptolemaic geocentric model much less complicated and messy. He realized that if the position of the Sun and the Earth was switched, the mathematics of the universe and the orbits of the planets make much more sense and the calendar could hence be put right again. He was the first known person to have conceptualized the heliocentric system of the universe.

Copernicus also discovered that:

1) the earth completes one orbit of the Sun each year; 2) the universe is much larger than anyone has believed; 3) earth is a planet among others; 4) earth makes a full turn on its axis every day, causing night and day.

He was then able to figure out the order of the planets by tracking and timing their orbits: mercury, Venus, earth, mars Jupiter and Saturn and was the first to be able to sequence the ordering of the planets.

Between 1506 and 1530, he completed the manuscript of his famous book—On the Revolutions of the Heavenly Spheres (insert brief description) which advocated and justified a heliocentric universe, overthrowing the Aristotelian geocentric model. This provides an intellectual springboard for a complete criticism of the then dominant view of the position of the earth in the universe. It initiates and helps start an intellectual debate over this issue—gives more possibility.

Although his model was still greatly flawed as he was too conservative to reject Aristotle’s principle of the existence of heavenly spheres moving in circular orbits, the epicycles were still smaller than those in the Ptolemaic model. The retrograde motion of the planets was now explained as a result of an optical illusion that arose because people were observing the planets from earth, which was moving itself. He also argued that the farther planets were from the sun, the longer they took to revolve. The length of these individual revolutions made it easier to determine the order of the planets and how they ranked in terms of distance from the sun.

Significance
Copernicus’ theories rejected the traditional thought that earth is the centre of a created world which does not move and the planets that travel around Earth travel in perfect circular paths called orbits. Ancient views that contradicted the Ptolemaic, earth-centered conception of the universe resurfaced due to him. His ideas challenged the whole system of medieval thought that kept science and faith together. All in all, the shift from a geocentric to a heliocentric system raised serious questions about Aristotle’s astronomy and physics. It also created uncertainty about the human role in the universe as well as God’s location. An increasing number of astronomers were being attracted to Copernicus’ idea after a while.

Although his system was no more accurate than the rest and he had not used any new evidence, his work provided another way of confronting some of the difficulties inherent in Ptolemaic astronomy and the Copernican system allowed other people who were also discontented with the Ptolemaic view to think in new directions. Even though Copernicus had made no observations and stated no general laws and his theory was of a very ad hoc nature, Copernicus's achievements acted as a springboard; a preliminary step towards scientific revolution. His work (through questioning accepted scientific thought) stimulated further scientific investigations, becoming a landmark in the history of science that is often referred to as the Copernican Revolution

**Discoveries and Achievements**
Tycho Brahe managed to collect the finest set of astronomical data in Europe after spending over twenty years carefully mapping out the motion of each significant object in the night sky, accurate to within the tiniest fraction of a degree in his Uraniborg castle which he outfitted with a library, observatories and instruments he had designed for more precise astronomical observations. He also measured the relative distances between stars as they appear in our sky to plot star charts and with the use of equipment of his own design, his measurements are far more precise than others of his time which allowed him to reject the Aristotelian-Ptolemaic model of the universe.

He came up with the Tychonic model which believed that the moon and sun revolved around the Earth but the other planets revolve around the Sun. Tychonic system was an enormous success as it allowed accurate astronomical and astrological predictions to be made more easily than in the old Ptolemaic system and it avoided the upsetting theological implications of the Copernican system. In 1572, Brahe observed that a new star appeared in the constellation of Cassiopeia which was brighter than the other stars for two years. In 1600, another new star appeared (it was observed by Johannes Kepler). Although they did not know it, they had witnessed supernovas, the explosion of old stars. This was important because people used to believe that the universe is definite and unchanging but such occurrences challenged these medieval thoughts.

In November, 1577, he saw a long-tailed comet travelling through the skies. For two months, he observed it and plotted its course. As he was unable to detect any parallax, he knew that the comet is beyond the Moon and in the region of the supposed spheres which means that Aristotle’s crystal spheres do not exist. While looking for the comet’s parallax, he watched the comet move in front of the Sun, then get dimmer and seem to move away from Earth then appear back near the Sun again, this shows that the comet was orbiting the Sun. This helped him come to the conclusion that the planets orbit the Sun. and help other thinkers and philosophers accept the Copernican heliocentric system.

He not only designed and built instruments; he also calibrated them and checked their accuracy periodically. He thus revolutionized astronomical instrumentation. He also changed observational practice profoundly. Earlier astronomers had been content to observe the positions of planets and the Moon at certain important points of their orbits (e.g., opposition, quadrature, station), Tycho and his cast of assistants observed these bodies throughout their orbits. As a result, a number of orbital anomalies never before noticed were made explicit by Tycho. Without these complete series of observations of unprecedented accuracy, Kepler could not have discovered that planets move in elliptical orbits. Tycho was also the first astronomer to make corrections for atmospheric refraction. In general, whereas previous astronomers made observations accurate to perhaps 15 arc minutes, those of Tycho were accurate to perhaps 2 arc minutes, and it has been shown that his best observations were accurate to about half an arc minute.

Significance
Tycho was known for his accurate and comprehensive astronomical and planetary observations. Although Tycho's planetary model was soon discredited, his extensive astronomical observations were an essential contribution to the scientific revolution. His extremely detailed and precise naked-eye astronomical observations of the time allowed for future references and aided in the discovery of new and more accurate astrological and mathematical theories about the universe. His observations and data collected ended the doctrine of the presence of celestial spheres, hence smashing the conventional thought that fixed spheres existed in heavens. This marked a significant breakthrough in the history of astronomy.

The Tychonic model was also revolutionary in the sense that it played a major role in changing the mindsets of astronomers of that time by preventing theological disputes and implications that came along with Copernicus’ model and yet allowed much more accurate astronomical and astrological predictions to be made easily than the old Ptolemaic model. The huge success and general uniform acceptance of the Tychonic model made it possible for the new idea to sink in to the minds of the common-people and not just among the literates and elites, hence allowing for astronomers to think in new directions too.

**Discoveries and Achievements**
Johannes Kepler was determined to find in Brahe’s numbers mathematical harmonies that would support a heliocentric universe. His work offered the first credible physical explanation of a moving earth and the astronomy that went with it. He discovered that to keep the sun at the center of things, he must abandon the circular components of Copernicus’ model, particularly the epicycles. From the mathematical relationships that emerged from his consideration of Brahe’s observations, he derived that the motion of the planets was elliptical. He realized that the planets travel along paths that are slightly elliptical and the Sun is always located at one of the two foci of those ellipses. Hence, he was the first man to create an astronomical model that portrayed the motion of the planets and that the orbits were elliptical. He published his findings in his 1609 book (The New Astronomy) and hence solved the problem of planetary motion by using Copernicus’s heliocentric universe and Brahe’s empirical data.

He also came up with Kepler’s Laws of Planetary Motion to explain the relationship between planets in motion that are in orbit around one another. The first law stated that the orbits were not circular but elliptical with the sun at one focus of the ellipse rather than at the center. The second law stated that the speed of a planet is greater when it is closer to the sun and decreases as its distance from the sun increases. The third and final law established that the square of a planet’s period of revolution is proportional to the cube of its average distance from the sun. In other words, planets with larger orbits revolve at a slower average velocity than those with smaller orbits.

He wrote two books in 1819---The Harmonies of the World which discusses harmony and congruence in geometrical forms and physical phenomena as well as the Epitome of Copernican Astronomy.

Significance
Kepler was the first strong advocator of the heliocentric theory of Copernicus and his laws of planetary motion laid the groundwork for future scientific discoveries, such as providing one of the foundation for Newton's theory of universal gravitation. His three laws effectively eliminated the idea of uniform circular motion as well as the idea of crystalline spheres revolving in circular orbits. He disproved the basic structure of the traditional Ptolemaic system and people were now free to think in new ways of the actual paths of planets revolving around the sun in elliptical orbits.

Thanks to Kepler, the Ptolemaic system was rapidly losing grounds to new ideas. His laws also destroyed a fundamental Aristotelian tenet that Copernicus had shared—that the motion of the planets was steady and unchanging. His theory of the presence of magnetic attractions between the sun and the planets to keep the planets in orbital motion paved the way for the law of universal gravitation formatted by Isaac Newton at the end of the seventeenth century. Furthermore, Kepler introduced a new way of thinking to the world, hence revolutionizing the way men think. He was credited with causing the transformation from ancient to modern world views. Instead of formulating mathematics formulas that fit the boundaries and ideas of a theory, he chose to come up with a theory based on observations and mathematical and astronomical data.

**Discoveries and Achievements**
Galileo achieved an important breakthrough to a new cosmology by answering what were the planets made of and made important strides towards answering how one explains motion in the universe. By early 1600s, Galileo Galilei had begun work on the problem of motion, particularly the motion of objects on a moving earth. He found Aristotle’s explanation of motion inadequate. He then developed the first rough theory of inertia, suggesting that only a change in motion required a cause; otherwise, objects either stayed in motion or remained at rest. He also began work on theories about moving objects, using a combination of small, practical experiments and ideal cases drawn up with mathematics.

In 1609, he first turned a telescope on the heavens. He observed sun spots, which he sketched and documented as real irregularities on the surface of the sun. He also showed the craters of the moon to be features of its landscapes, not shadows. He also discovered evidence of orbiting moons around Jupiter, providing proof that the earth was not the only body with objects in orbit around it. He published his results in his book (The starry Messenger) in 1610.

Galileo also came up with a few laws.

1) The Law of Free Fall which defines that all objects (regardless of their mass) experience the same acceleration when in a state of free fall. He supposedly threw a cannonball and a musket ball from the Pisa’s Leaning Tower and found that the two balls hit the ground at the same time, hence starting his discovery of the law of free fall.

2) The principle of relativity, that all steady motion is relative and cannot be detected without reference to an outside point. His experiments with motion lead him to understand the flight of balls and bullets and other projectiles. That path of a moving object through space is called its trajectory.

3) The Law of inertia which defines that an object that is moving will continue moving at the same velocity forever; an object that is at rest will stay at rest if there is no net force acting on the object. He figures that all trajectories are combinations of steady horizontal motion with changing vertical speed and showed that the result is a parabola. Hence, the path through space of any thrown or fired object is always in the shape of a parabola. Trajectories in fact have two independent motions. One is horizontal and carries a constant velocity that is initiated by a propelling force. The other motion is vertical and changes according to Galileo’s formula of free fall.  4) The law of uniformly accelerated motion---the inclined plane experiment gives a measure of gravity which will help explain things about the way the universe works. He discovered that the balls do not roll the length of the board at a constant speed. In fact, their roll gets faster and faster but the acceleration is constant.

Significance
Galileo combined abstract mathematics and practical experiments to produce a new physics, one that explained how objects behaved “normally” on a moving earth. He popularized the Copernican system and also articulated the concept of a universe subject to mathematical laws. He argued that nature displayed mathematical regularity in its most minute details and believed that the universe was rational but not of scholastic logic but of mathematics. He changed the way the world views the things around them—all aspects of the world would increasingly be described in terms of mathematical relationships among quantities. Mathematical models would eventually be applied even to social relations. The new natural philosophy portrayed nature as cold, rational, mathematical, and mechanistic.

For many, the power of the mathematical arguments that appeared irrefutable proved more persuasive than the new information from physical observation that produced so much controversy. His laws of motion made it possible to figure out where a cannonball will fall when fired with a given velocity and a given angle of elevation which led to the science of ballistics and changed the design and placement of guns and cannons. Many welcomed this scientific breakthrough because of it military advantages. His revelations did more to make Europeans aware of the new picture of the Universe than the mathematical theories of Copernicus and Kepler did and made a case for a new relationship between religion and science, a proposal that challenged some of the most powerful churchmen of his day. Through his and Kepler’s discoveries, the idea of a heliocentric system garnered more support than ever and at the end of the 17 th century, it was generally accepted by astronomers, resulting to a major breakthrough in the Scientific Revolution.

=Acknowledgements= Books: 1) Joy Hakim, //The Story of Science: Newton at the Center, //Smithsonian Books 2005, Pg 44-80, 118-129 2) Clay Farris Naff, //<span style="font-family: Arial,Helvetica,sans-serif;">Exploring Science and Medical discoveries: Astronomy, //<span style="font-family: Arial,Helvetica,sans-serif;">Greenhaven press, 2006

Websites: 1) School of Mathematics and Statistics, University of St. Andrews, Scotland (November 2002), Nicolaus Copernicus, Retrieved February 7th, 2010 [] 2) Eric W. Weisstein (1996-2007), Copernicus, Nicolaus, Retrieved February 7th, 2010 [] 3) Peter Machamer (2009), Galileo Galilei, Retrieved February 7th, 2010 [] 4) D. Paar (March, 9th 1996), Johannes Kepler, Retrieved 9th February 2010 [] 5) University of Tennessee, Department of Physics and Astronomy, Retrieved February 9th, 2010 []