Galileo: Early Years

1. Galileo: Early Years • Born 15 Feb. 1564 in Pisa • Educated in Camaldolese Monastery • Father wanted him to be a medical doctor • Interested in mathematics

2. Discoveries • Observed swinging lamps in Cathedral of Pisa and found period to be independent of the amplitude – idea for a pendulum clock • Used inclined planes to prove that bodies do not fall with velocities proportionate to their weight but proportionate to time. Found that projectiles follow a parabolic path

3. Galileo and the Telescope • Galileo is correctly credited with the first use of the telescope for viewing objects in the heavens, but letters between him and friends suggest that he first had other, more pragmatic applications for the telescope. He believed that he could make money selling his telescopes to wealthy Italian princes so that they could use them for military purposes

4. 1609 Letter: The power of my cannocchiale [telescope] to show distant objects as clearly as if they were near should give us an inestimable advantage in any military action on land or sea. At sea, we shall be able to spot their flags two hours before they can see us; and when we have established the number and type of the enemy craft, we shall be able to decide whether to pursue and engage him in battle, or take flight. Similarly, on land it should be possible from elevated positions to observe the enemy camps and their fortifications. 1610 Letter: "I have many and most admirable devices; but they could only be put to work by princes because it is they who are able to carry on wars, build and defend fortresses, and for their regal sport make most splendid expenditures."

5. Galileo’s Telescope • Improved Dutch spyglass to achieve 8-9X magnification • Observed mountains on the moon, the Milky Way composed of tiny stars, and sunspots Reconstruction of Galileo Telescope – about 1.5 inches in diameter, with very long focal length (meaning rather small field of view) You will behold through the looker a host of other stars, which escape the unassisted sight, so numerous as to be beyond belief. Stars of the seventh magnitude appear with the aid of the looker larger and brighter than stars of the second magnitude seen with the unassisted sight

6. Copernican Theory • I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy's and Aristotle's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it. • In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican . ,

7. Galileo Astronomy book • In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. • In 1633 he was suspected of heresy based on this book which was then placed on the Forbidden book list • It was removed from that list in 1835 (not that stellar parallax still had not been detected) • Note that his observations that confirmed the Copernican theory to him were made in 1610 • Note also, that Kepler's’ first and second law are published in 1609 – did Kepler and Galileo communicate?

8. 1638: Dialogues Concerning the Two New Sciences • Galileo's ideas about motion are presented in lively fashion as a dialogue involving three characters, Salviati, Sagredo and Simplicio. The official Church point of view, that is, Aristotelianism, is put forward by the character called Simplicio, and usually demolished by the others. Galileo's defense when accused of heresy in a similar book was that he was just setting out all points of view, but this is somewhat disingenuous---Simplicio is almost invariably portrayed as simpleminded. • the Salviati character remarks: I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of, say, 100 cubits, would so differ in speed that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.

9. Galileo and Scientific Method • 1602-Pendulum experiments. • 1604- Inclined plane experiments of natural acceleration. • 1607-Systematic manipulation of shapes and weights of wax balls to study flotation. • Investigation of projectile motion. Discovery of parabolic character of projectile motion. • 1609 Observations of Jupiter Moons

10. Three Experiments • 1. The Pendulum: Used to demonstrate the law of inertia and that heavy and light bodies fall at the same rate. Galileo also discovered the mathematical laws governing the length of the string, the period of the motion, and the amplitude of the swing. • 2. The Inclined Plane and the Rate of Acceleration: Galileo used the inclined plane to slow the motion of falling objects enough to accurately measure how their speed increased. • 3. Projectile Motion: Galileo also used the inclined plane to control the speeds and heights of projectiles in order to discover the mathematical properties of their paths.

11. Pendulum • "...repeat many times the fall through a small height in such away that I might accumulate all those intervals of time that elapse between the arrival of the heavy and light bodies respectively at their common terminus, so that this sum makes an interval of time which is not only observable, but easily observable."   • "...two balls, one of lead and one of cork, the former more than a hundred times heavier than the latter, and suspended them by means of two equal fine threads, each four or five cubits long. "This free vibration repeated a hundred times showed clearly that the heavy body maintained so nearly the period of the light body that neither in a hundred swings nor even in a thousand will the former anticipate the latter by as much as a single moment, so perfectly do they keep step."         Galileo  

12. Inclined Plane"...in such a plane, just as well as in a vertical plane, one may discover how bodies of different weight behave..."  Galileo

13. Inclined Plane Total distance traveled is proportional to the square of time.

14. Projectile Motion

15. Projectile Motion • The object goes into free fall as it exits the inclined plane

16. Vertical motion can be separated from the horizontal motion