Galileo Galilei (1564-1642) and his Theory of Motion

Prof. Alexander Hahn

A New Opera

“Galileo Galilei” by Philip Glass http://www.bam.org/asp/performance.asp?

perfID=GalileoGalilei

New Scholarship

Galileo in Context Edited by Jürgen Renn © 2002 Cambridge University press

From the NY Times

A Wonderful Book

Galileo’s Daughter Dava Sobel ©2000 Penguin

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

Galileo and his Time

http://es.rice.edu/ES/humsoc/Galileo/

Galileo's Science

The Basic Question:How do things move?

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.

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

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.

Galileo's Contributions

What is actually happening? Breaking the mold. A new theory and an experiment. Discourse about Two New Sciences,

1638.

Galileo's Theory of Motion

round bronze ball

inclined plane

table (about 30.5 inches high)

floor

d is proportional to h

shorthand: d h

Means:

d’ h’ d h

=

d

d’h’

h

The Meaning of Proportion

Start a ball from rest anywhere and let it roll

Let h be the height atthe start andlet t be the time it takesto reach the bottom

Let v be its velocity or speed at the bottom andlet d be the distance that the ball has travelled

Then v t and d t 2.

Therefore, d v

2

But also, d h. So h v 2.

Therefore, v

€

h

Vertical Component:free fall from restwill take the same time t0 to reach the groundno matter what v is

Horizontal Component:continues withvelocity v

R = v x t0 and therefore, R vBecause v , we finally get

R .

€

h

€

h

Galileo tests this Relationship with an Experiment

A page of Galileo's Working Notes http://www.mpiwg

-berlin.mpg.de/Galileo Prototype/index.htm

Confirmation by Experiment

Galileo Galilei (1564-1642) and his Theory of Motion

Prof. Alexander Hahn