Galileo Galilei

Early Years Born 15 Feb in Pisa Born 15 Feb in Pisa Educated in Camaldolese Monastery Educated in Camaldolese Monastery Father wanted him to be a medical doctor Father wanted him to be a medical doctor Interested in mathematics Interested in mathematics

 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 Found that projectiles follow a parabolic path

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 Accurately measured the period for four of Jupiter’s moons Accurately measured the period for four of Jupiter’s moons Saw that Venus showed phases like the moon did and must therefore orbit the Sun rather than the Earth Saw that Venus showed phases like the moon did and must therefore orbit the Sun rather than the Earth

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.PtolemyAristotle In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican.,

Catholic Church Galileo found guilty of breaching the Inquisition of 1616 and sentenced to lifelong imprisonment Galileo found guilty of breaching the Inquisition of 1616 and sentenced to lifelong imprisonment Allowed house arrest rather than imprisonment Allowed house arrest rather than imprisonment On 31 October 1992 Pope John Paul II spoke on behalf of the Catholic Church admitting the theological advisors had made errors, but did not admit that the Church was wrong to convict Galileo on a charge of heresy because they were acting according to the best of their knowledge On 31 October 1992 Pope John Paul II spoke on behalf of the Catholic Church admitting the theological advisors had made errors, but did not admit that the Church was wrong to convict Galileo on a charge of heresy because they were acting according to the best of their knowledge

GALILEO AND SCIENTIFIC METHOD 1602-Pendulum experiments Inclined plane experiments of natural acceleration Systematic manipulation of shapes and weights of wax balls to study flotation. Investigation of projectile motion. Discovery of parabolic character of projectile motion Observations of Jupiter Moons

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.

 "...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

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

Total distance traveled is proportional to the square of time.

3. Projectile Motion

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

Vertical motion can be separated from the horizontal motion