Before we discuss Galileo, we should mention Giordano Bruno (1548-1600). He was an ordained priest, and was a well-known theologian, astronomer and philosopher.

Before we discuss Galileo, we should mention Giordano Bruno (1548-1600). He was an ordained priest, and was a well-known theologian, astronomer and philosopher.- He wrote a lot about the Copernican system- He thought the universe is infinite (one of the first to say this).- He thought the planets are like the earth so that people must populate them. He believed

these “people” had similar histories as “earth people”.- He believed the sun is a minor star. He believed that other planetary systems exist.

Therefore, we are not a unique creation of God, and our religious practices are not unique.

- He openly criticized Aristotle’s physics.- He said the bible should not be the basis of astronomy, but only used for moral teachings.- Rejected the Protestant principle of salvation by faith alone.

All this got him into trouble. He had no proof for his ideas, and was not what we would consider a modern scientist, but obviously he had a great imagination. In 1593 he was arrested by the Roman Inquisition, and tried for seven years. He refused to change his mind, and was burned alive at the stake in 1600. Dangerous times.

His writings would influence the entire future of scientific thought, including Galileo, but Galileo was not sympathetic to Bruno in their writings.

What did he do?

Galileo Galilei

We have all heard of him.

What was his imaginative background?

Tycho Brahe, 1546-1601Sir Isaac Newton, 1643-1727

Nicolaus Copernicus, 1473-1543

Claudius Ptolemy, 85-165Johannes Kepler, 1571-1630

Galileo Galilei, 1564-1642

Newton said he stood on the shoulders of these giants; the

last one is Galileo.

Egypt

Galileo Galilei 1581 Constancy of period of pendulum1589 Showed that objects fall at the same rate independent of mass1592 Suggests that physical laws of the heavens are the same as

those on Earth1592 Primitive thermometer 1600 Study of sound and vibrating strings1604 distance for falling object increases as square of time1609 builds a telescope1610 Observes the phases of Venus1610 Observes moons of Jupiter1610 Observes craters on the moon1610 Observes stars in the Milky Way1610 Observes structures around Saturn1612 Hydrostatics1613 Principle of inertia1624 Theory of tides1632 Galilean relativity1632 Support for Copernicus' heliocentric theory1638 Motion and friction

Vincenzo Galilei was born in Florence. He made his living as a lutenist, composer, theorist, singer, and teacher. He published a number of books of musical scores for the lute and several books on musical theory. What is important about V. Galilei for our purposes is that he combined the practice and theory of music. Since antiquity, the theory of music had consisted of a mathematical discussion of harmony, in other words what are the mathematical ratios of the lengths of strings producing consonances, and how does one divide the octave? It had always been thought that not only was the ratio of lengths of two strings sounding an octave 2:1, but that so also was the ratio of the tensions of strings of equal lengths tuned an octave apart. Galilei showed that this is not the case: the ratio of tensions is 4:1. He found that ratio by hanging weights from strings. Here was an experiment that produced numbers and bore directly on the age-old theoretical discussions. Galileo probably helped with these experiments.

Galileo’s father:

Florence was the city of such writers as Dante, Petrarch, and Macchiavelli, and artists and engineers such as Boticelli, Brunelleschi (who built the magnificent dome on the church of St. Mary of the Flowers), Alberti, Leonardo Da Vinci, and Michelangelo.

But Galileo was born. near Pisa

Galileo Galilei was born near Pisa in February 15, 1564 -- the same year in which Shakespeare was born and the year in which Michelangelo and Calvin died.After studying at the University of Pisa (he enrolled as a medical student), Galileo was appointed to the chair of mathematics (at 25).. Actually he never finished his degree, but he was recognized as being extremely talented in mathematics.At 28 years old he moved to Padua (150,000 people), in the Venetian Republic (until he was 46). This was an extremely active and exciting city, and he was one of the main participants in this intellectual and social activity. A good friend of his in Padua was Sagredo, a Venetian wealthy nobleman, who appears later in his famous book “Dialogue Concerning the “Two World Systems” and “The Two Sciences”.With his mistress, Marina [Gamba] of Venice, who he met in Padua, he had two daughters and a son. There is a recent book with the letters and history of one of his daughters, Maria Celeste, who became a nun in a convent. He was very attached to her, and they had a very close correspondence. See Galileo’s Daughter, by Dava Sobel. Very interesting material can be found in these letters, and book.

Maria Celeste

Galileo was taught Aristotelian physics at the university of Pisa. But he quickly began questioning this approach. Aristotle had taken a qualitative and verbal approach. *Remember that Aristotelians maintained that that heavier bodies fell faster than lighter ones in the same medium, and therefore in the absence of the resisting force of a medium a body would travel infinitely fast and that a vacuum was therefore impossible.

Galileo eventually came to believe that in a vacuum all bodies would fall with the same speed, and that this speed was proportional to the time of fall.

Aristotlesaidbla-bla

time of fall

speed

Galileo developed a quantitative and mathematical approach. Actually he probably epitomizes best of all the early physical thinkers the modern scientific approach.

Galileo, early in his career, came to believe that the difference in speed depended on the densities of the bodies (he corrected this later, but it is somewhat correct when falling in a medium).

Oops!

Now I got it right!He did his works with motion first, but we will deal with them later.

Did Galileo ever perform his famous experiment on the leaning tower? Probably not; anyway a similar experiment-demonstration had already been published by Benedetti Giambattista in 1553, and the test had also been made and published by the Flemish engineer Simon Stevin in 1586.We will deal with this later.

Galileo said he first thought about falling objects during a hailstorm, when he noticed that both large and small hailstones hit the ground at the same time. If Aristotle were right, this could only happen if the larger stones dropped from a higher point in the clouds -- but at virtually the same time -- or that the lighter ones started falling earlier than the heavier ones -- neither of which seemed very probable to Galileo. Instead, the simplest explanation was simply that heavy or light, allhailstones fell simultaneously with the same speed. We will now go over his experiments and theories.

Galileo's made the discovery that the period of swing of a pendulum is independent of its amplitude.

Now this discovery had important implications for the measurement of time intervals. In 1602 he explained the isochronism of long pendulums in a letter to a friend, and a year later another friend, Santorio Santorio, a physician in Venice, began using a short pendulum, which he called "pulsilogium," to measure the pulse of his patients. The study of the pendulum, the first harmonic oscillator, date from this period.

1877 Eustachio Porcellotti, Florence

Pendulum Clock

The Pendulum

I, Galileo, got this idea by watching a chandelier swinging during a church service.

Measuring time accurately was very important for progress in physics! Many of Galileo’s experiments depended on knowing the time elapsed.

Clocks

“He took a small glass flask, about as large as a small hen's egg, with a neck about two spans long [perhaps16 inches] and as fine as a wheat straw, and warmed the flask well in his hands, then turned its mouth upside down into the a vessel placed underneath, in which there was a little water. When he took away the heat of his hands from the flask, the water at once began to rise in the neck, and mounted to more than a span above the level of the water in the vessel. The same Sig. Galileo had then made use of this effect in order to construct an instrument for examining the degrees of heat and cold.”

Measuring heat became a puzzle in the circle of practical and learned men in Venice to which Galileo belonged. The first solution was a thermoscope. Building on Pneumatics by Hero of Alexandria (1st century BCE), first published in the West in 1575, several authors had begun playing with the idea of the expansion of air as its heat increased, and vice versa. The first versions, usually called thermoscopes, were little more than toys. Benedetto Castelli wrote in 1638 about a device he had seen in Galileo's hands around 1603:

Hydrostatic Balance (an early device by Galileo)

Remember the "Eureka" story about Archimedes and the bath tub: He measured the amount of water displaced by the crown and by an equal weight of gold, and found that the crown displaced more water. Its specific gravity was thus less than that of gold, and therefore it had been adulterated with another metal.

Weighing precious metals in air and then in water was presumably a practice that was common among jewelers in Europe. Galileo had some ideas for refining the practice and, at the age of 22, he wrote a little tract about it, which he entitled La Bilancetta, or "The Little Balance." What Galileo described was an accurate balance for weighing things in air and water, in which the part of the arm on which the counter weight was hung was wrapped with metal wire. The amount by which the counterweight had to be moved when weighing in water could then be determined very accurately by counting the number of turns of the wire, and the proportion of, say, gold to silver in the object could be read off directly. Remember what we did in class!

Hey Galileo, this could be worth a lot of money!

Hallo! - I thought of that! It is below my dignity to make a practical instrument out of it, or make money!

Galileo made many instruments from 1597 onwards, and earned much money for them. This instrument is his "proportional compass” (Galleria degli Uffizi, Archivio degli Uffizi, Florence). This could be the instrument that Galileo gave to Cosimo II along with the treatise on the manner in which to use the compass that he dedicated to the Grand Duke, and that he published in Padua in 1606. This instrument is a sophisticated and versatile calculating device. It renders possible several geometrical and arithmetical operations by comparing the sides of similar triangles. The invention of this instrument by Galileo was questioned by the Milanese Baldassare Capra in a book which he published in Padua in 1606. Galileo denounced Capra, and obtained full legal redress from the impostor against whom he wrote an elegant Difesa

Galileo's compass is made up of four parts: the two arms, with several scales inscribed on the front and back, hinged to a round disc called the nocella; the quadrant, graduated with different scales, which is fixed into the holes through the arms of the compass by means of screws known as galletti (literally "cockrels") the leg, a sliding-rule screwed into one of the arms of the compass which allows the instrument to be held in a vertical position and also permits the arm in which it is screwed to be lengthened.

On the quadrant of the compass the following can be seen: a division into twelve points which functions as a bomber's sight. The use of the bomber's sight, according to Galileo, "...is that one of its sides is placed in the hole in the piece [of artillery], having first suspended the thread along the perpendicular from the center of the instrument. This thread shows us the elevation of the piece"; the lines for the astronomical quadrant, which are used to calculate the height of a star above the horizon, with the aid of a plumb-line; the scale used to measure the inclination of the slopes of the wall; the scale used to measure heights, distances and depths by sight. By looking through this and comparing similar triangles, measurements can be made.

Galileo developed (actually improved upon) the telescope.

In the 1200s Bacon introduced the reading glasses. This spread rapidly, mainly because many of the older intellectuals could not work after their eyesight diminished.

One could get reading glasses from “spectacle makers” on the market place. The word “lens” means “lentil” in Italian (the lenses had the shape of the beans)Convex lenses for farsightednessConcave lenses for nearsightedness

The simple spy glass gives you a non-inverted image. It was common in Galileo’s time, but because the concave lenses were fragile, the maximum magnification was x3. This type of telescope is also known as a Galilean telescope, because it was first built by Galileo and used by him when he discovered the moons of Jupiter.

Galileo could not buy the right lenses to make a more powerful telescope (the lensmakers were not so good) so he learned how to grind lenses, and made his own (all in a few months). Galileo’s telescope had a magnification of x9.

The problem with the first telescopes was they had only weak concave lenses (fragile)

So,

These spy glasses had been first made in 1589 by Giovanni Battista della Porta (Italy), and in 1600 by Johannes Lippershev (Holland).

Galileo did not invent the telescope, but he improved (1609) it in a short time - 5 months - (first to a magnification of x8 , then x20), and this let him make important astronomical discoveries. He was not particularly finicky about giving others credit for their discoveries. He also made a lot of money by informing politicians of the military importance of his telescope (observe and identify ships at a distance)- and as a result was granted tenure with a lifelong income. Smart fellow who could look after himself.

Picture from Introducing Newton, William Rankin, Totem Books

Sketch of Giovanni Battista della Porta’s telescope (sketch made in 1609)

But Galileo made the telescope famous

Aside

One of the first applications of more powerful telescopes was by insurance companies. They would be stationed on the coast waiting to see the ships coming. With the powerful telescopes they could determine which ships they were and whether they were in good shape. Then they would run back to the company with this information, and the company would adjust the insurance rates, using this information. In this way they could undercut their competitors, who needed to charge higher rates without this information. So, even then, such information and policies were important for insurance companies. Just like today.

It is not difficult to construct a simple refracting astronomical telescope. All that is required are two convex lenses (thicker in the middle) and an appropriate mounting. As a general rule, the objective lens should be large and fairly weak, and the eyepiece should be small and strong.

Two convex lenses will create an upside down image, which is exactly what the telescope described above does. An upside down image really doesn't matter so much when you are exploring the surface of the moon. But you can make more powerful telescopes this way.

Kepler, in 1611, was the first to show that such a telescope with two concave lenses could be used, but then the image is inverted. He also showed that a third lens could be added to right the image.

Galileo made many important astronomical discoveries using his telescopes. These discoveries were scientifically important, and had a tremendous impact on the general thinking of the time (church and scholars). He was very stubborn, and not interested in appeasing any scholastically conservative opinions.

The moon:He mapped out the surface of the moon, not smooth as previously thought, but covered with valleys and mountains. He is credited as the first to discuss “earthshine”, the illumination of the moon with reflected sunlight from the earth.

Moon drawing byGalileo Moon drawing by Leonardo da Vinci

He continued to improve upon his telescope and began to aim it at the heavens. What he found astounded even Galileo.

Galileo’s first major astronomical discovery was that the moon surface is mountainous (not a “crystalline perfection”, as Aristotle had said). He estimated the height of the mountains (up to four miles!) by sketching the shadows and lighting on the moon at different times of the month, and using trigonometry. He was not the first to say this, but he showed many prominent people, and they had to agree. Now Galileo started to doubt the official doctrine too.

Some interesting historical facts. Galileos telescope observations delivered the coup de grace to the perfections of the heavenly bodies. BUT:

1) The Greek writer Plutarch (46-120 AD) suggested that the moon had deep recesses where the sun could not reach, and that the spots were due to rivers or deep chasms.

2) The Greek satirist Lucian (120 - 180 AD) wrote of an imaginary trip to the moon, and the fact that the moon, the sun, and Venus were inhabited.

3) People were so convinced that the moon was a perfect sphere, that almost all the depictions of the moon showed a perfectly smooth surface, with no spots whatsoever (the story was that the sphere was perfect, but there were differences in the density that caused the spots. If you look at the moon, this is NOT the way it looks. You do not need a telescope to see this!

4) Thomas Harriot (1609) drew actually the first representations of the moon seen through a telescope.

5) Christoph Scheiner (1614) made extensive sketches of the moons surface.

By the 1630s it was pretty much accepted (by all astronomers) that the moon surface had mountains and valleys.

He discovered that Jupiter had four moons that orbited around it. All of this convinced Galileo that Copernicus, a Polish astronomer, had been right 70 years earlier in his theory that the Earth and all the planets orbited around the sun.

He published his results in his popular book, Siderius Nuncius (Starry Messenger) in 1610. Galileo dedicated The Starry Messenger to the Grand Duke Cosimo de' Medici. He also named the moons of Jupiter "the Medicean stars". This flattery gained him a secure position in Florence as Chief Mathematician and Philosopher to the Grand Duke of Tuscany, leaving him plenty of time for research

The Jupiter moon Io;modern view

For two years Galileo was the only one with a telescope powerful enough to see the moons of Jupiter.

Sunspots

Galileo discovered sunspots in 1610, looking through his telescope (started studying them in 1612). He saw that the Sun had dark patches on it. Actually eventually he went blind, maybe as a result of his observations of the sun through the telescope. He also observed that the sunspots moved (rotated) indicating that the Sun was rotating on an axis. Galileo maintained that these sunspots were on the surface of the sun, not some sort of planets. These ”imperfections" on the Sun were not in agreement with the doctrine of an unchanging perfect substance in the heavens; however, the rotation of the Sun made it easier to accept that the Earth might rotate on an axis too, as required in the Copernican model. These facts were unknown to Aristotle and Ptolemy. But we can see how the experimental facts (observations using technological instruments) were beginning to change the “imaginative background” of the people.

Sunspot plate from Scheiner's Tres Epistolae. He thought the spots were revolving bodies (1611)). Wanted to preserve the perfection of the sun.

Sunspots are dark areas of irregular shape on the surface of the Sun. Their short-term and long-term cyclical nature has been established in the past century.

Sunspot drawings from Scheiner's Rosa Ursina.

Saturn was another object in the heavens for which the telescope presented all sorts of new data and created new problems and controversy. What was needed was a theory to explain the variable appearance of Saturn (see below).

Galileo’s drawings of Saturn

“I discovered another very strange wonder, which I should like to make known to their Highnesses . . . , keeping it secret, however, until the time when my work is published . . . . the star of Saturn is not a single star, but is a compsite of three, which almost touch each other, never change or move relative to each other, and are arranged in a row along the zodiac, the middle one being three times larger than the lateral ones, and they are situated in this form: oOo.”, Galileo in a letter to Medici (his patron), 1610.

In 1612, Galileo revealed another mystery about the planet: the lateral bodies had disappeared. Galileo confidently predicted that they would return, and they did. Sometimes Saturn was seen as oval (denied by Galileo), sometimes with two lateral bodies, and at other times round and solitary, how could one explain all these appearances? And the mystery grew deeper as time went on. In 1616 Galileo announced to his patrons that he had now observed Saturn in yet another shape. The shape changed - why?

Christiaan Huygens had discovered a satellite of Saturn, now named Titan. In 1656 he published this together with his own theory about Saturn's appearances. In 1659 he published this in a book entitled Systema Saturnium ("The Saturnian System"). Huygens's theory was that the planet was surrounded by a thin flat ring that nowhere touched it. Although Huygens did think that the ring had an appreciable thickness, this was basically the modern solution of the problem.

In 1658 Christopher Wren (remembered more for his later architecture) proposed a model in which a "corona" so thin it could be considered a mere surface was attached to the planet; the entire formation rotated or librated about its major axis.

The composite figure from Huygens's Systema Saturnium (1650s).

The changing appearance of Saturn created a major problem to explain for the astronomers. All this was created by the availability of the telescope.

Galileo discovered a number of other things, such as the phases of Venus, which were easily observable through his telescope, and even a spiral galaxy.

Image of the spiral galaxy NGC 4414.

This was the first time that so many observations had been reported in an organized way. Galileo was usually not the first to make many of these observations. But he compiled and emphasized them, and he presented them to many influential intellectuals (not just “scientists”). He had powerful and influential friends. Especially powerful in this respect were people such as Barberini, who became Pope Urban VII in 1623. This pope was a supporter of Galileo, and encouraged Galileo to write on these subjects provided that he confine himself to theory.This was not in Galileo’s taste! One realizes that Galileo was a real operator and knew how to get official attention, and even make moneyfrom his science.

There was a liberal atmosphere in Rome; Galileo even had up to 6 audiences with the pope.

I, of course, never saw such beautiful images.

But what I did see and interpret, got me into

a lot of trouble

In the beginning, Galileo could write and do what he wanted; even with the blessing of the pope. But in 1614, there was denouncements from priests that the Copernican theory, and Galileo’s reports of his observations were heresy. Galileo thought he could just show them the images through the telescope, and they would understand. He invited a group of Jesuit priests to look through his telescope. Only one would look through, and he said that the telescope altered reality.

So Galileo published the book “Dialogue on the Two Chief World Systems”; this is one of his most famous books, and was praised by scholars throughout Europe. But this book got him in real trouble.

Eventually in 1632, Galileo was arrested, and brought to trial by the Holy Office for defending the Copernican system. He had no defense attorney, and could not see the evidence or hear the charges against him. He did not want to end as Bruno, so he never taught the Copernican system again. But he could live in peace under house arrest until he died, January 9, 1642. This is very interesting, but not physics, so we will not cover the interesting happenings.

We would not think about looking through

such a thing.

Obviously this thing distorts my view. I know these things can’t be there. I think the lenses are dirty!