1. Galileo Galilei (1564-1642) and his Theory of Motion Prof. Alexander Hahn

2. A New Opera “Galileo Galilei” by Philip Glass http://www.bam.org/asp/performance.asp? perfID=GalileoGalilei http://www.bam.org/asp/performance.asp? perfID=GalileoGalilei

3. New Scholarship Galileo in Context Edited by Jürgen Renn © 2002 Cambridge University press From the NY Times

4. A Wonderful Book Galileo’s Daughter Dava Sobel ©2000 Penguin

5. The Recent ND Conference Galileo and the Church www.nd.edu/~hps/galileo.html Combined with performances of Brecht's “Life of Galileo” www.nd.edu/~isla/ISLA/webpages/ thearts/FTT/calendar/galileo.htm www.nd.edu/~isla/ISLA/webpages/ thearts/FTT/calendar/galileo.htm

6. Galileo and his Time http://es.rice.edu/ES/humsoc/Galileo/

7. Galileo's Science The Basic Question: How do things move?

8. Basic Question #1 How do the planets move? Answers before Galileo Ptolemy (200 AD) Geocentric epicycles (example of epicycle Sun-Earth-Moon). Copernicus (1473-1543) Heliocentric circles and epicycles.

9. Galileo's Contributions What is actually happening? The telescope: Moon, Venus, Jupiter. Vocal supporter of Copernicus Dialogue Concerning the Two Chief World Systems, 1632. Problems with the Church

10. This Morning: Basic Question #2 How do thrown objects (projectiles) move? The balls that we observe every day in lots of different sports? Answers before Galileo Aristotle's Physics: Heavy objects fall more quickly. The notion of Impetus.

11. Galileo's Contributions What is actually happening? Breaking the mold. A new theory and an experiment. Discourse about Two New Sciences, 1638.

12. Galileo's Theory of Motion round bronze ball inclined plane table (about 30.5 inches high) floor

13. d is proportional to h shorthand: d  h Means: d’ h’ d h = d d’ h’ h The Meaning of Proportion

14. Start a ball from rest anywhere and let it roll Let h be the height at the start and let t be the time it takes to reach the bottom Let v be its velocity or speed at the bottom and let d be the distance that the ball has travelled

15. Then v  t and d  t 2. Therefore, d  v 2 But also, d  h. So h  v 2. Therefore, v 

16. Vertical Component: free fall from rest will take the same time t 0 to reach the ground no matter what v is Horizontal Component: continues with velocity v

17. R = v x t 0 and therefore, R  v Because v , we finally get R .

18. Galileo tests this Relationship with an Experiment A page of Galileo's Working Notes http://www.mpiwg-berlin.mpg.de/ Galileo Prototype/index.htm http://www.mpiwg-berlin.mpg.de/ Galileo Prototype/index.htm Confirmation by Experiment

19. Galileo Galilei (1564-1642) and his Theory of Motion Prof. Alexander Hahn