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.
Galileo Galilei
We have all
heard of him.
What was his
imaginative background?
What did he do?
Newton said he stood on the
shoulders of these giants; the
last one is Galileo.
Tycho Brahe, 1546-1601
Sir Isaac Newton, 1643-1727
Nicolaus Copernicus, 1473-1543
Johannes Kepler, 1571-1630
Galileo Galilei, 1564-1642
Claudius Ptolemy, 85-165
Egypt
Galileo Galilei
1581
1589
1592
1592
1600
1604
1609
1610
1610
1610
1610
1610
1612
1613
1624
1632
1632
1638
Constancy of period of pendulum
Showed that objects fall at the same rate independent of mass
Suggests that physical laws of the heavens are the same as
those on Earth
Primitive thermometer
Study of sound and vibrating strings
distance for falling object increases as square of time
builds a telescope
Observes the phases of Venus
Observes moons of Jupiter
Observes craters on the moon
Observes stars in the Milky Way
Observes structures around Saturn
Hydrostatics
Principle of inertia
Theory of tides
Galilean relativity
Support for Copernicus' heliocentric theory
Motion and friction
Galileo’s father:
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.
But
Galileo
was born.
near Pisa
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.
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.
Aristotle
said
bla-bla
Oops!
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).
Galileo developed a quantitative and mathematical approach. Actually he probably
epitomizes best of all the early physical thinkers the modern scientific approach.
speed
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.
He did his
works with
Now I got it right!
motion first,
but we will
deal with
them later.
time of fall
Did Galileo ever perform his famous experiment on the
leaning tower? Probably not; anyway a similar experimentdemonstration 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, all
hailstones fell simultaneously with the same speed. We will
now go over his experiments and theories.
The Pendulum
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.
Clocks
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.
1877 Eustachio Porcellotti,
Florence
Pendulum Clock
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:
“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.”
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.
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!
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!
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 farsightedness
Concave lenses for nearsightedness
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 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.
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).
Sketch of Giovanni
Battista della Porta’s
telescope (sketch
made in 1609)
But Galileo made the telescope
famous
Picture from Introducing Newton, William Rankin, Totem Books
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.
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.
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.
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.
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.
He continued to improve upon his telescope and began to aim
it at the heavens. What he found astounded even Galileo.
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 by
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.
Moon drawing by Leonardo da Vinci
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.
For two years Galileo was
the only one with a
telescope powerful
enough to see the moons
of Jupiter.
The Jupiter moon Io;
modern view
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
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.
Sunspots are dark
areas of irregular
shape on the
surface of the Sun.
Their short-term
and long-term
cyclical nature has
Sunspot plate from Scheiner's Tres
Sunspot drawings from Scheiner's Rosa Ursina.
Epistolae. He thought the spots were
been established in
revolving bodies (1611)). Wanted to
the past century.
preserve the perfection of the sun.
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?
The changing appearance of Saturn created a major problem to
explain for the astronomers. All this was created by the availability of
the telescope.
The composite figure from
Huygens's Systema
Saturnium (1650s).
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.
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.
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.
I, of course, never saw
such beautiful images.
But what I did see
and interpret, got me into
a lot of trouble
Image of the spiral galaxy NGC 4414
There was a liberal atmosphere in Rome; Galileo even had up to 6 audiences with the pope.
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 money
from his science.
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.
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!
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.