Chapter 2: Galileo and Terrestrial Mechanics
Chronology of Galileo’s Life (important dates)
1564 – Birth of Galileo Galilei in Pisa on February 15, the son of a cloth merchant and musician, Vincenzio Galilei.
1597 – In a letter to Kepler, Galileo states that he had accepted Copernicanism a few years earlier.
1609 – Galileo makes his own telescope and begins using it for astronomical observation.
1632 – Publishes his Dialogo (Dialogue concerning the Two Chief World Systems –Ptolemaic and Copernican), vigorously advocating the Copernican system.
1633 – Trial of Galileo in which his Dialogue is banned; Galileo abjures Copernican system.
1638 – Publishes Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Discourses and Demonstrations Concerning Two New Sciences), which is the beginning of modern mechanics.
1642 – Galileo dies on January 8.
Introduction
Galileo Galilei (1564 – 1642): two great works, Dialogue Concerning the Two Chief World Systems – Ptolemaic and Copernican (1632), and Discourses and Demonstrations Concerning Two New Sciences (1638).
Important questions to take into account (scientific)
- How do bodies move on the Earth? Galileo’s primary concern was with bodies in free fall, but he also investigated pendula, balls rolling down inclines planes, and projectile motion.
- Did Galileo have a notion of inertia and did he discover the law of inertia?
- What was the relation between Galileo’s mechanics and the Copernican system?
Other questions (historical and philosophical)
- What role did experiment play in Galileo’s methodology?
- To what extent was Galileo’s thought indebted to the ideas of his predecessors?
- What overall philosophical position did he espouse?
- In general, how significant was his contribution to mechanics?
Does a Falling Body’s Weight Influence Its Rate of Fall?
In his Dialogue, Galileo employs a dialogue form with three speakers: Simplicio (defends Aristotelianism), Salviati (presents Galileo’s ideas), and Sagredo (neutral intermediary although he always agrees with Salviati).
In the part where they talk about the rate of fall of bodies with different weight, Galileo challenges Aristotle’s doctrine on the basis of an experiment (thought experiment). His point is that a claim that entails mutually contradictory conclusions must itself be erroneous. Galileo is not making a physical experiment.
An important thing to observe in Galileo’s claim is that it goes far beyond what it would have been possible for him to observe.
In general, one sees that it was very easy to exaggerate the role of observation and experiment in the early history of mechanics.
15/05/13
Galileo on the Motion of Pendula
Sagredo: “…the innate condition of men is to look askance on others working in their field whose studies reveal truth or falsity which they themselves fail to perceive.”
Isochronism of the pendulum
- The time of swing of any pendulum is the same, no matter what the weight or material of the pendulum bob may be and no matter what the size of the arc through which it swings.
- The length of the cord does make a difference.
Relationship between the length and time
- Pendulum bobs of identical materials but different sizes gradually move through different arc, although retaining the same period.
- “Irregularities” or roughness per unit of surface area of the spheres (these cause the object to swing through shorter arcs, the smaller body suffers more retardation).
- The length that the strings have to one another the (inverse) ratio of the squares of the number of vibrations made in a given time.
- (T1/T2) = (√L1 / √L2)