ASTA01 at UTSC - Lecture 8

1. ASTA01 at UTSC - Lecture 8 Chapter 3The Origin of Modern Astronomy: • -Ancient astronomy • The Copernican revolution • De Brahe and Kepler • Galileo • Newton • Later developments

2. NicolausCopernicus (1473-1543) • MikołajKopernik (latin: Nicolaus Copernicus) was born in Toruń, Poland. • Studied at University of Cracow, Poland • Then at Univ. of Bolgna and Padua in Italy • Became church official: canon • Organized defense of city Frombork in Warmia province from the Teutonic Knights 2008 forensic reconstr. – grave found in 2005, DNA-id’d

3. NicolausCopernicus (1473-1543) • Diplomat (signed peace treaty) • Physician (advising dukes) • Economist (financial reform) • Classical scholar and translator • Jurist • Quadrilingual polyglot • Astronomer • Mathematician

4. Nicolaus Copernicus • At the time of his birth, and throughout his life, astronomy was based on Ptolemy’s (~150 CE) model of Aristotle’s universe. • In spite of many revisions, the Ptolemaic model was still a poor predictor of planet positions. • However, due to Aristotle’s authority, it was the officially accepted model.

5. Nicolaus Copernicus Moreover, in Aristotle’s philosophy, the most perfect region was in the heavens and the most imperfect region was at Earth’s centre, the classical geocentric universe model. So, it matched the commonly held Christian view of the geometry of heaven and hell. Anyone who criticized Aristotle’s model was risking a serious charge of heresy – with a possible death penalty. And that just 200 years after accepting Aristotle’s unique-Earth view was strictly forbidden by the same Church!

6. Copernicus’s Model Copernicus was associated with the Roman Catholic Church throughout his life. As a result of this connection to the Church and his fear of persecution** ridicule, he hesitated to publish his revolutionary ideas that challenged the Ptolemaic model and the geometry of heaven and hell. ** - the crossed over text is in the textbook but is misleading or incorrect

7. Copernicus’s Model What were these revolutionary ideas? Copernicus believed that the Sun and not Earth was the centre of the universe and that Earth rotated on its axis and revolved around the Sun.

8. Copernicus’s Model Copernicus apparently began doubting Ptolemy’s geocentric model during his college days. A heliocentric universe model had been discussed occasionally before Copernicus’s time. (for instance, by Ἀρίσταρχος, Aristarkhos of Samos , 310 BC – ca. 230 BC) Copernicus, however, was the first person to produce a detailed model with substantial justifying arguments.

9. Copernicus’s Model Sometime before 1514, Copernicus wrote a short pamphlet summarizing his model and distributed it in handwritten form to friends, while he worked on his major book. "Commentariolus" ("Little Commentary"), a forty-page manuscript

10. De Revolutionibus Copernicus’s book De RevolutionibusOrbiumCoelestium (On the Revolutions of Celestial Spheres) was essentially finished by about 1532. In 1533, Johann Albrecht Widmannstetter (secretary of the Pope) delivered a series of lectures in Rome outlining Copernicus' theory.

11. De Revolutionibus However, Copernicus hesitated to publish – even though other scientists, and even church officials including Pope Clement VII, concerned about reform of the calendar, knew about his work, sought his advice, and encouraged the publication. In 1542, he finally sent the manuscript off to be printed. Copernicus died in 1543 before the printing was finished, but saw the first prints on his death-bed.

12. De Revolutionibus The most important idea in the book was placing the Sun at the centre of the universe. That single innovation had an impressive consequence. The retrograde motion of the planets was immediately explained in a straightforward way without the epicycles that Ptolemy used.

13. De Revolutionibus In the Copernican model, Earth moves faster along its orbit than the planets that lie farther from the Sun. Consequently, it periodically overtakes and passes these planets.

14. De Revolutionibus Imagine that you are a runner on a track moving along an inside lane. Runners well ahead of you appear to be moving forward relative to background scenery. As you overtake and pass slower runners in outside lanes, they fall behind – seeming to move backward for a few moments relative to the scenery.

15. De Revolutionibus • The same thing happensas Earth passes a planetsuch as Mars. • Although Mars moves steadily along its orbit, as seen from Earth, it seems to slow to a stop and move westward (retrograde) relative to the background stars as Earth passes it.

16. De Revolutionibus • As the planets’ orbits donot lie in precisely thesame plane, a planetdoes not resume its eastward motion in precisely the same path it followed earlier. • Instead, it describes a loop with a shape depending on the angle between the two orbital planes.

17. De Revolutionibus • Copernicus’s model was simple and straightforward compared with the multiple off-centre circles of the Ptolemaic model.

18. However, De Revolutionibus failed to disprove the geocentric model immediately for one critical reason. The Copernican model could not predict the positions of the planets any more accurately than the Ptolemaic model! In the first half a century after announcement of the heliocentric hypothesis, Copernicus’ main work kept being poorly known to most scientists and laymen. Maybe 20 of them professed to believe in the heliocentrism. De Revolutionibus

19. De Revolutionibus Although Copernicus proposed a revolutionary idea in making the solar system heliocentric, he was a classically trained astronomer with great respect for the old concept of uniform circular motion.

20. De Revolutionibus Copernicus objected to Ptolemy’s schemes for moving Earth slightly off-centre and varying the speeds of planet motions This seemed arbitrary and ugly to Copernicus

21. Why heliocentrism won with geocentrism • Motion of Mars (red) and Earth (blue) • 1. for an outside observer 2. relative to Earth, • or in the geocentric model • Which model is simpler?

22. Why heliocentrism won with geocentrism The ugly Ptolemaic, geocentric model for non-uniform motion of planets as observed in the sky: (i) ex-centric position of the Earth (blue) and (ii) the so-called equant point (black dot), around which the planet’s epicycle (litte circle) was supposed to move uniformly Geocentric model defeats it’s own goal of preserving uniform circular motion: Mars does not move uniformly on its big circle. Copernican explanation is simpler and thus more beautiful

23. De Revolutionibus Dislike toward the eccentric motion and the ugly equant made Copernicus return to a strong but incorrect belief in uniform circular motion. Therefore, even though his model put the Sun correctly at the centre of the solar system, it could not accurately predict the positions of the planets as seen from Earth. He had to reintroduce small epicycles to match minor variations in the motions of the Sun, Moon, and planets. Astronomers today recognize those variations as due to the planets’ real motions in elliptical orbits. That motion is slightly non-uniform and slightly non-circular

24. De Revolutionibus You should notice the difference between the Copernican model and the Copernican hypothesis. The Copernican model is inaccurate. It includes uniform circular motion and thus does not precisely describe the motions of the planets. However, the Copernican hypothesis that the solar system is heliocentric is correct. The planets circle the Sun, not Earth.

25. De Revolutionibus Why that hypothesis, very gradually,won acceptance is a question historians still debate. There are probably a number of reasons, including the revolutionary spirit of the times. The most important factor, though, may be the simplicity (beauty) of the idea. Also, through a dual motion of the Earth (spin+orbit, or rotation+revolution) many seemingly disconnected phenomena could be explained without resorting to separate explanations for each of them: rotation of the sky, loopy paths of the planets, phases of planets, … These are the hallmarks of a modern science, which started with De Revolutionibus.

26. De Revolutionibus - symmetry • For one thing, placing the Sun at the centre of the universe produced a symmetry among the motions of the planets that is elegant and pleasing to the eye and mind.

27. De Revolutionibus - symmetry In the Ptolemaic model, Mercury and Venus had to be treated differently from the rest of the planets. Their epicycles had to remain centred on the Earth-Sun line. In Copernicus’s model, all the planets were treated the same. They all followed orbits that circled the Sun at the centre.

28. De Revolutionibus Astronomers throughout Europe read and admired De Revolutionibus and found Copernicus’s astronomical observations and mathematics to have great intellectual and practical value. However, few (~15) believed, at first, that the Sun actually was the centre of the solar system and that Earth moved.

29. De Revolutionibus How the Copernican hypothesis was gradually recognized as correct has been called the Copernican Revolution. It was not just the adoption of a new idea but a total change in the way astronomers and the rest of humanity thought about the place of Earth.

30. De Revolutionibus The most important consequence of the Copernican hypothesis was not what it said about the Sun but what it said about Earth. By placing the Sun at the centre, Copernicus made Earth move along an orbit like any other planet!

31. De Revolutionibus By making Earth a planet, Copernicus revolutionized humanity’s view of its place in the universe. He also triggered a controversy that would eventually bring the astronomer Galileo Galilei before the Inquisition. This controversy over the nature of scientific and religious ideas continues even today. To those with good knowledge of science, science and religion are not necessarily in direct conflict, unless one holds too literal a view of religious texts.

32. Tycho Brahe, Johannes Kepler, and Planetary Motion As astronomers struggled to understand the place of Earth, they also faced the problem of planetary motion. How exactly do the planets move? Are they fixed to crystal spheres made of heavenly matter and propelled by angels?

33. Tycho Brahe, Johannes Kepler, and Planetary Motion • That problem was partially solved by two people: • A nobleman who built a fabulous observatory, and a poor commoner with a talent for mathematics.

34. TychoBrahe (1546-1601) • The Danish nobleman Tycho Brahe was sort-of abducted by his uncle Joergen Brahe from the castle where his parents lived, at the age of 2. • Was wearing false noses to hide a duelling scar from his college days. The reason for the duel in 1566 was a disagreement over a mathematical formula with a fellow student. (please! use UTSC math help center in such cases)

35. Tycho Brahe In 1572, astronomers were startled to see a new star – now called Tycho’s supernova – appear in the constellation of Cassiopeia Aristotle had argued that the heavens were perfect, and therefore unchanging.Thus, astronomers concluded that the new star had to be nearer than the Moon. Tychomeasured the new star’s positions and showed it had to be far beyond the Moon. Something was changing in the supposedly unchanging starry sphere.

36. Tycho Brahe When Tycho wrote a book De Stella Nova about his discovery, the king of Denmark honoured him with a generous income and the gift of an island, Hven, with peasants and all. Tycho built a fabulous observatoryUraniborg on the island. It was like a graduate school with 100 research assistants

37. Uraniborg and Stjerneborg

38. Tychonian system of the world – geo-heliocentric

39. Tycho lived before the invention of the telescopes. So, his observatory was equipped with wonderful instruments for measuring the positions of the Sun, Moon, and planets using the naked eye and peep sights. Quadrant For 20 years, Tycho and his assistants measured the positions of the stars and planets with fantastic accuracy (for naked-eye observations, in any case) Tycho Brahe

40. Tycho Brahe After the death of the Danish king, Tycho fell out of favor with the new king Christian IV, and had to leave the country He moved to Prague, where he became the Imperial Mathematician to the Holy Roman Emperor Rudolph II. Tychohired a few assistants, including a German school teacher named Johannes Kepler.

41. Tycho Brahe After the death of the Danish king, Tycho moved to Prague, where he became the Imperial Mathematician to the Holy Roman Emperor Rudolph II. Tyco hired a few assistants, including a German school teacher named Johannes Kepler.

42. Tycho Brahe • Just before Tycho died in 1601, he asked Rudolph II to make Kepler the Imperial Mathematician (=Astrologer!)

43. Johannes Kepler • No one could have been more different from Tycho Brahe than Johannes Kepler.

44. Johannes Kepler He was born in 1571, the oldest of six children in a poor family living in southwest Germany. His father was employed as a mercenary soldier, fighting for whomever paid enough, and he eventually disappeared. Kepler’s mother was apparently an unpleasant woman. She was accused of witchcraft in her later years, and Kepler defended her (successfully) in a trial that dragged on for three years. During his last year of study, he accepted a high-school teaching job in the town of Graz, in Austria, which allowed him to continue his studies in mathematics and astronomy.

45. Johannes Kepler While still a university student in Tübingen, Germany, he had become a believer in the Copernican hypothesis. His eyesight was poor; he never attempted to be a leading observer. He wanted to be a theorist and to decipher God’s design for the world through the study of numerology, astrology, astronomy, physics and metaphysics, even the occult (magic)

46. Johannes Kepler Life was unsettled for Kepler in Graz because of the persecution of Protestants in that region. When Tycho Brahe invited him to Prague in 1600, Kepler went eagerly, ready to work with the famous astronomer.

47. Johannes Kepler – did he steal & murder?! Tycho’s sudden death in 1601 left Kepler in a position to use Tycho’s extensive records of observations to analyze the motions of the planets. Tycho several times declined Kepler’s request for a complete access to his data. After Tycho’s death, just days after attending an important dinner and falling ill, Kepler came into possession of data illegally (the rightful owners, family of Brahe, sued him & won) The fact that a recent exhumation showed a large amount of poison (mercury) in the hair of Tycho Brahe adds to the mistery of his death… some even suspect a foul play by Kepler. But mercury was a common alchemical element and Tycho, like most of his epoch (and later even Newton), was active in alchemy and astrology. So Kepler probably stole the data but did not kill Brahe.

48. Johannes Kepler and his overturning of ancient astronomy Kepler began by studying the motion of Mars – trying to deduce from the observations how the planet actually moved. In the course of his intense work, Kepler had to abandon everything he deeply believed in. According to Plato only the circle is a pure figure worthy of heavens. So initially he was calling the idea of elliptic orbits “a heap of horse dung” However, through his correct conviction that small (8’) deviations of theoretical predictions from Brahe’s precise observations of Mars are not to be dismissed, but are crucially important, he came to believe in elliptic orbits. Such orbits reproduced the observations.

49. Johannes Kepler By 1606, he had solved the mystery of Mars’ movement. In 1609 he published Astronomia Nova (The New Astronomy). The orbit of Mars is an ellipse – not a circle.

50. Johannes Kepler & the non-uniform motion However, the mystery was even more complex. The planets do not move at uniform speeds along their elliptical orbits. Kepler recognized that they move faster when close to the Sun and slower when farther away. The angle to the planet from the sun changes in a given time is inversely proportional to the current sun-planet distance. There was no such correlation with the distance to Earth Thus, Kepler understood that the body that governs the motion of planets is the Sun, not Earth. This was a proof that Copernicus was right!