Plato

1. Plato Believed that certainty and truth were to be found in mathematical reasoning. Taught that the world was a cosmos, or systematic entity whose parts worked in orderly ways. Challenged astronomers to prove that the Sun, moon and planets moved around the Earth in uniform circles.

3. Earthly realm Composed of 4 elements earth, water, air, and fire. Each element had a natural home. Elements were defined in terms of wet or dry, cold or hot. Earth is corrupt and changing

4. Heavenly realm Made of ether, an unchangeable substance. Heavenly bodies were contained in spherical shells that fit around each other. Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, stars. Order was not included until Ptolemy. Problems: Planets went backwards, sped up and slowed down, and changed brightness.

5. Aristarchus of Somos After calculating the relative distances and sizes of the Sun, Moon, and Earth, proposed that if the Sun is so much bigger, it should be at the center of the solar system, and the Earth rotates once a day. Aristotle�s influence was too strong.

6. Hipparchus 2nd century BC Combined Babylonian records to create geometric model of motion of the Sun around an eccentric circle with Earth near the center. Discovered precession of the equinoxes (due to the precession of the axis).

8. Ptolemy- 2nd century AD We know little about his life, probably lived in Alexandria. Wrote Magale syntaxis, which means mathematical complication. Called �The greatest� or al-majistic by Islamic astronomers. It is called The Almagest today.

9. Ptolemy/Hipparchus Debate Used eccentric circle proposed by Hipparchus, which explains the varying speeds of orbiting objects. While Hipparchus is cited in The Almagest, some claim that he copied the star chart, systematically compensating for precession without giving enough credit.

10. Equant Point A point, opposite Earth from the center of the deferent circle. The speed of the planet varies so that it would look like it traveled at a constant speed if viewed from the equant point. The idea that planets moved with varying speeds was philosophically divisive, as it violated the rule that the heavens moved with uniform motion.

11. Epicycles In order to describe the varying speeds and brightness of planets, as well as retrograde motion, epicycles were used. Ptolemy borrowed this idea from Appolonius and other Greek astronomers.

12. Ptolemaic System Did not even try to pull them altogether into one system in the Almagest, except to mention the order of the planets. Almagest�s influence lasted 13 centuries, and was adopted by the Roman Catholic church.

13. Islamic Astronomy Baghdad was founded in 762 AD by Muhammad�s followers. They became interested in Greek works, purchased them, and translated them into Arabic in what is called the �House of Wisdom.�

14. Islamic Astronomy Based on three religious ideas. Religious calendar was lunar. Daily prayer at the same 5 times each day. Direction of prayer and orientation of mosques must be towards Mecca.

15. Islamic Observatories As Arab astronomy flourished, a number of large observatories were built. Most famous was built by Ulugh Beg, a governor in Samarkand. Greatest accomplishment was a book filled with immense tables of stars. Interest in astronomy led al-Tusi to change Ptolemy�s model to include dual epicycles, removing the equant.

16. Nicolaus Copernicus Born of wealthy, Catholic parents in Poland. Studied Latin, math, and astronomy at University of Krakow in 1491 where he learned about Aristotle, Aristarchus and Ptolemy�s ideas. Went to Univ. of Bologna to get a degree in church law. Got a position as a canon at a cathedral and he got paid and had few duties. Eventually asked if he could leave to go to Italy again to finish his studies in canon law, medicine, and astronomy.

17. Copernican Solar System �At the middle of all things lies the sun. As the location of this luminary in the cosmos, that most beautiful temple, would there be any other place or any better place than the centre, from which it can light up everything at the same time? Hence the sun is not inappropriately called by some the lamp of the universe, by others its mind, and by others its ruler.�

18. De revolutionibus orbium coelestium Explained why Venus and Mercury would always be near the sun, and untangled them from the Earth so that they had their own true period of orbit around the sun. Also explained why the distance from the Earth�s sun was such an integral part of observations of other planets. Allowed the order of the planets to be explained more clearly. Explained retrograde motion of planets Mentioned Aristarchus in the first draft, but crossed it out.

19. Influence of Copernicus� work Osiander wrote an introduction saying the the book was not intended as truth. It was this that allowed the book to be read and not immediately put on the list of banned books. It was not widely publicized as it was highly mathematical, and written in Latin. He also died during the year of its publication. Most were unconvinced. Also, he still had to include epicycles to account for observational data (because his orbits were circular)

20. Tycho Brahe

21. Tycho�s Solar System Brahe was convinced that Copernicus was wrong. Developed his own version of world system in which the Sun and Moon revolve around the Earth, but other planets revolved around sun.

22. Tycho�s accomplishments and influences Tycho discovered innovations in instrumentation including the famous quadrant, practiced un-paralleled observational practice, saw a new star and a comet that helped to establish the idea of the �changeability of heavens.� Hired Kepler as an assistant. After he died, Kepler was appointed to his position, and used his data

23. Johannes Kepler (1571-1630) Born in Germany to a family whose fortune was failing. Had enough money to study theology at the University of Tubingen. Learned about Copernican theory. Was going to enter Lutheran ministry, but appointed to a teaching position and taught math and astronomy.

24. Cosmographic Mystery Originally believed that the orbits of the planets could be represented as spheres, with the separation defined by the regular solids (tetrahedron, cube, etc). Sent a copy to Tycho Brahe.

25. Kepler as Imperial Mathematician Moved to Prague to assist Tycho Brahe, who died nearly a year later. He engaged in a �war with Mars� with three main tools. Copernicus� Sun-centered system Brahe�s incredibly accurate data Idea that the Sun exerted some sort of force on the planets. Realized that Mars� orbit wasn�t circular. Didn�t like the idea of an ellipse because what would be at the other focus?

26. Kepler�s New Astronomy First Law: Planetary orbits are ellipses with the Sun at one focus. Second Law: The line from the Sun to the planet traces out equal areas in equal times. Third law: P2 (Earth years) = a3 (in astronomical units) ANIMATION Used these laws to produce Rudolphine Tables, which predicted Mercury crossing the face of the Sun, validating their accuracy.

27. Galileo Galilei (1564-1642) Went to school in Florence and studied medicine at University of Pisa. Taught math at University of Pisa and Padua. Gave up teaching after inventions earned him a post as mathematician to the Duke of Tuscany.

28. Galileo�s Discoveries Was in contact with Kepler, but was not totally convinced of his own �Copernicism� until� Built a telescope. Saw the craters on the moon and reported it in Starry Messenger. Kepler wrote an enthusiastic response. Also saw Jupiter�s moons, Venus� phases, rings around Saturn, sunspots.

29. Dialogue on the Great World Systems A woman of nobility didn�t understand how that could be true, according to the Bible. Galileo offered his own interpretation in Letter to the Grand Duchess Christina. Was brought to the inquisition, and was found innocent and not allowed to teach Copernican theory. Wrote Dialogue on the [Two] Great World Systems

30. Sources http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Copernicus.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahe.html http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Kepler.html Hoskin, Michael, ed. The Cambridge Illustrated History of Astronomy. Cambridge University Press. Cambridge, UK. 1997 Chaisson, E; McMillan, S. Astronomy Today. Prentice Hall, Inc. Upper Saddle River, New Jersey. Third Edition. 1999

31. Post-presentation Activity Using the cardboard, thumbtacks, string, and pencil, draw 2 elliptical orbits, one with a small eccentricity (where the foci are close together), and one with greater eccentricity. Textbook pg. 38. Label the following Perihelion, aphelion, major axis, semi-major axis (a), sun, empty focus. Calculate the eccentricity, given that Distance from perihelion to the sun equals a(1-e) Distance from aphelion to the sun equals a(1+e) Explain what all the points on the ellipse have in common. Hint: The distance from �