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Natural Science - Year I

Unit 29: Galileo and Mechanics

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History Weblecture for Unit 29

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History Lecture for Unit 29: Galileo's Mechanics

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Lecture:

Mechanics in the Seventeenth Century

The Scientific Revolution was marked in its beginning by the new observation techniques and precision drawing of Leonardo da Vinci and Andreas Vesalius, and by a radical application of mathematics to physical entities. We have seen how the new ways of looking at nature and portraying observations accurately with the tools of perspective and the microscope led to advances in anatomy and physiology. We've also looked at the revolution in astronomy, where the new methods of accurate observation with the telescope and the expectation that mathematical calculations should accurately reflect a physical model were in many ways more radical than the change from an earth-centered to a sun-centered universe.

By the beginning of the seventeenth century, this trend led to the use of mathematics to analyze data derived from close observation and measurements of simple phenomena, such as the motion of bodies. These explanations of motions divided analysis into kinematics, the study of movement and energy, and dynamics, the study of forces. Together, kinematics and dynamics combined to form a powerful new method of looking at the world: mechanics, in which nature was viewed less like a body and more like a precision machine, one whose every movement could be understood through observation, measurement and experimentation, and whose future state could be accurately predicted.

During the seventeenth century, this vision of a mechanical universe became the dominant theory which has controlled development of physical science from Galileo's day into the twentieth century.

Time line

I don't expect you to memorize all the dates below! Look through the time line and notice what social and political events occur as the publications of new theories in physics and astronomy appear. None of the scientific developments we discuss in this course happened in a vacuum—they grew out of and were influenced by many things.

1504 Copernicus publishes his "little commentary", proposing changes needed to the Ptolemaic system
1517 Martin Luther publishes a list of what he perceives as abuses by the institutional Roman Catholic Church
1543 Copernicus published his major work on the Revolutions of the Heavenly Bodies
1545-1563 The bishops of the Catholic Church meet at Trent to address issues raised by the Protestant Reformation
1564 Galileo, Shakespeare born; Michelangelo dies.
1572 - 1577 1572 (nova) 1577 (comet) Tycho Brahe observes a new star and motions in a comet which disprove the solid-sphere model of the solar system and challenge Aristotle's position that the stars never change
1590 Galileo publishes his studies on falling bodies, claiming that gravitational acceleration is constant
1599 Johannes Kepler begins working on Tycho Brahe's observations of Mars
1609 Kepler publishes his New Astronomy, claiming that planets move in ellipses [The Virginia Company establishes a colony at Jamestown, VA]
1610 Galileo publishes the Starry Messenger, which contains his telescopic observations of the phases of Venus, the moon's cratered surface, sunspots, and the moons of Jupiter.
1616 The Catholic Church condemns the heliocentric theory of Copernicus as contrary to the teachings of the Church and forbids Galileo to teach it.
1619 Kepler publishes the Harmony of the World, which contains his third law relating the period of the planets to their average distance from the sun
1620 Francis Bacon publishes the Novum Organum, outlining a new approach to nature involving close observation and experimentation where possible
1632 Galileo publishes A discourse on the Two Chief World Systems
1637 Rene Descartes publishes his Discourse on method which explains how to use deductive reasoning, along with his new analytic geometry.
1642 Galileo dies in Italy; Isaac Newton is born in England.
1661 Exiled by the plague to his farm, Newton begins his studies of gravity, motion, and optics.
1669 Newton returns to Cambridge to hold the chair in mathematics (currently held by Stephen Hawking).
1672 Newton sends papers to the Royal Society, expanding on some ideas previously published by Robert Hooke (of microscopes and cork cells fame), and offending Hooke in the process.
1687 Newton publishes his Mathematical Principles of Natural Philosophy in Latin
1704 Newton publishes the Optics in English

Galileo the Physicist

We've already looked at Galileo's contributions to observation astronomy, but his contributions to the study of motion are equally important.

Galileo was born in Florence in 1564 and studied medicine, like so many of his contemporaries who contributed to the sciences—but at Pisa, not Padua. He was apparently not a very congenial student and highly critical of his teachers, alienating enough of them that he failed to get a scholarship to continue his studies and had to return home in 1586 without a degree. He had been studying different problems in what we now call mechanics, and he used his free time to write and publish a small work on hydrostatics (how liquids which exert pressure on their containers). This work so impressed the Marquis Guidoboldo del Monte that the Marquis became his patron, using his own influence to first secure Galileo a teaching position at Pisa, then in 1592, the chair in mathematics at Padua. [A "chair" at a university is an endowed teaching position with a guaranteed salary; once a professor is given a "chair" he usually keeps it until he retires.] Galileo appears to have been a good teacher, and like Vesalius, preferred giving many classroom demonstrations to simply commenting on established texts.

Pendulum

According to his own works, Galileo's interests in mechanics began when he noticed a lantern swinging from the ceiling during a church service. He made several pendula and experimented with them, changing the length of the pendulum, the weight at the bottom, and the size of the starting arc. The best clock he had to time the length of a swing from one side to the other was his own pulse. He kept meticulous records of his experiments, and ultimately concluded that the period of the pendulum (one swing back and forth) did not depend on the weight at the bottom of the pendulum, or the size of the arc (for relatively small arcs, less than 15 degrees), but only on the length of the pendulum.

A pendulum swings because gravity causes the weight to fall, but the fall is restricted by the string attached to the weight, so the weight moves in an arc. Galileo expanded his research to the general problem of how bodies fall. There is a story that he dropped cannonballs of different weights from the top of the leaning tower of Pisa to disprove Aristotle's claims that the heavier an object is, the faster it falls, but the story is probably untrue. Galileo's recorded experiments involved rolling balls of different weights down long wooden tracks which he inclined at different angles. By measuring the length of time for a ball to roll down the slope and noting how far it had "fallen down", Galileo was able to show that the weight of the ball did not affect the final speed of the ball. Gravitational acceleration was always constant.

Inclined Plane with Rolling Body

In 1590, Galileo published his results in a book De motu gravium (on the motion of heavy bodies). It contained a formula for the motion of a falling body:

the distance a body falls is 1/2 times the acceleration due to gravity multiplied by the square of the time it has fallen:

s   =   ½ a t 2

His final conclusion is an early statement of the concept of inertia, the principle that bodies will tend to remain in motion, continuing with the same speed and direction, if no force acts to slow them down. This is the opposite of Aristotle's theory of antiperistasis, where bodies stay in motion only if a force continuously acts to keep them moving.

Galileo's book is important not only because he showed that Aristotle was wrong about how bodies fall, but because it also contains a good demonstration of what we now call the experimental method.

  1. Galileo made a hypothesis, or prediction, about how the rolling balls would behave.
  2. He then devised an experiment to test whether his prediction or description of the phenomenon was valid.
  3. He took measurements of things he could observe—the length of the track, its slope, the weight of the balls, their diameters, and the length of time it took the ball to roll down the track.
  4. He then made calculations to get values for quantities like velocity and acceleration that he could not measure directly. In making his calculations, he used rigorous mathematical methods similar to those of the Greek philosopher Archimedes, who (you'll recall) was responsible for early calculations of the value of pi.
  5. Based on these calculations and the pattern of his observations, he revised his hypothesis to make it more general.

Although Galileo wasn't the first to use mathematical calculations and experimentation, his published writings were clever and understandable, and since he popularized this "scientific method" with its dependence on mathematics and experimentation, it has since been credited to him.

Study/Discussion Questions:

Further Study/On Your Own

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