When Galileo died, his remains were awarded a great tomb most of them

1
They should have paid more attention to what was
in my head, and what they saw with their own
eyes
Apparently they thought that he must have been
pointing the right direction, because they kept
his middle finger, which can still be seen in a
museum.
When Galileo died, his remains were awarded a
great tomb - most of them!
Hey guys. Maybe we ought to rethink this
In 1992, 359 years later, Pope Paul II
acknowledged the church's error
2
Lets look a little at Galileos mechanics. This
was the other great achievement of Galileo.
Were going to do this with demonstrations.
And we will mention his two books 1) The System
of the World in Four Dialogues This is a
comparison of the Ptolemian and the Copernican
systems. 2) Dialogues on Two New Sciences
Who is this guy Simplicio anyway?
3
1) Pendulum Experiments 2) Inclined Plane
Experiments 3) Projectile motion (parabolic
path)
Siphon Water Clock
Galileo used simple ways of measuring time water
clocks.
Named clepsydras ("water thief by the Greeks,
who began using them about 325 B.C., these were
stone vessels with sloping sides that allowed
water to drip at a nearly constant rate from a
small hole near the bottom. Other clepsydras were
cylindrical or bowl-shaped containers designed to
slowly fill with water coming in at a constant
rate. Markings on the inside surfaces measured
the passage of "hours" as the water level reached
them.
Persistence of Memory by Salvador Dali
4
Keeping time was important, and water clocks were
used before the pendulum clocks
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I did!
Who discovered the pendulum clock?
In 1656, Christiaan Huygens, a Dutch scientist,
made the first pendulum clock, regulated by a
mechanism with a "natural" period of oscillation.
Although Galileo Galilei, sometimes credited with
inventing the pendulum, studied its motion as
early as 1582, Galileo's design for a clock was
not built before his death. Huygens' pendulum
clock had an error of less than 1 minute a day,
the first time such accuracy had been achieved.
His later refinements reduced his clock's errors
to less than 10 seconds a day.
6
Actually I thought of it already
This is a copy of the original diagram made by
Vincenzo Viviani and Galileo's son, Vincenzo. It
is mounted in an oval frame whose feet and frieze
are gilded. It embodies the idea described by
Galileo in a letter written to the Dutch scholar
Lorenzo Realio in June 1637. Galileo explained to
Realio the method he had in mind to determine
longitude at sea and on land by observing the
periods of the satellites of Jupiter. This
operation required a precise measurement of time
and Galileo mentioned that he had invented a
clock that was so precise that it could determine
very small intervals of time anywhere, without
any error whatsoever and in any season of the
year. The accuracy of this clock depended on the
isochronism of the oscillations of pendulums of
equal length which Galileo had demonstrated in
his research in the field of mechanics. The
discovery of this mechanism and the role played
by Vincenzo Galilei is described in a lengthy
account by Viviani in his Racconto Istorico of
the life of Galileo. In 1658 Christiaan Huygens
claimed that he had discovered how to apply the
pendulum to timing devices but his claim was
hotly contested by Viviani.
7
This is the chair from which Galileo gave his
lectures
Lectures are not what they used to be
Script where Galileo talked about the satellites
of Jupiter
8
Read about it here
http//es.rice.edu/ES/humsoc/Galileo/ Student_Work
/Trial96/index.html
The earth does move!
I think we will stick to other things
Woops!
Retraction!
http//www.its.caltech.edu/newman/sci-cp/sci-9211
.html
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Galileo and Viviani
Nineteenth century. Tito Lessi.
This painting depicts the aged Galileo with
Vincenzo Viviani, his last disciple. In 1639,
when he was seventeen years old, Viviani went to
stay with Galileo whom he worked with until the
death of the great scientist in 1642.
Monument at Galileos Tomb
The remains of Galileo were moved to this spot on
12 March 1737, the date on which the index finger
of his right hand was removed.
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grave where Galileo is buried in Santa Croce
Church in Florence, Italy
Will of Vincenzo Viviani
Several years ago the Testator ordered that a
marble statue be made of the face and bust of
that incomparable philosopher, geometer and
astronomer, Galileo Galilei, the Noble
Florentine. He intended to place it in the Church
of Santa Croce in this City, and to bury under
the bust the bones of his venerated Master that
are now in the Novitiate of the Conventual Friars
of the Church of Santa Croce. He also wished that
a suitable epitaph in marble be placed to record
the admirable discoveries that Galileo made in
the heavens and on earth. If during his life the
Testator was unable to fulfil this intention,
which was motivated by a feeling of gratitude
towards so great a Master, he asks that his wish
be fulfilled after his death at the order and
expense of his executors. He asks that his own
body be placed in the Church of Santa Croce under
the statue of the great Galileo, next to or under
his bones after they have been transported to
that place. If Galileo's bones are not yet in the
Church, the Testator asks that his own body be
placed close to that of Galileo. The Testator
requests that what he has stipulated be fulfilled
according to the plan of Giovanni Battista
Foggini, the celebrated Florentine sculptor and
dear friend of the Testator.
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Interesting facts about a pendulum swing
L
L
A
a
Does the frequency of the oscillation depend on
the amplitude of the swing? This was what Galileo
noticed about the swinging of the chandelier.
12
L
L
A
A
Does the frequency of the oscillation depend on
the size (mass) of the pendulum. Remember Galileo
did not really know, or understand the
ramifications about the mass.
13
Wee gonna have ta wait for this one!
L
L
h
?
A/2
If an object (acting as a thin post) is inserted
into the way of the string of the pendulum, how
high does the ball rise? What does this mean?
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Does it depend on the shape of the object?
Galileos inclined plane
v
s
time
time
These are the curves we want to investigate.
15
s
No friction
h
Does this make a difference if it does not roll?
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Projectile motion (parabolic path)
Start give an initial x velocity no
initial y velocity
MEASURE! QUANTIFY!

y
h
floor
0
1
2
3
x
What is the path of the red balls ?
How long does it take the different balls to drop
to the floor?
We will do the shoot the monkey experiment.
Here is a page from one of Galileo's manuscripts
in which he writes down the figures he obtained
in performing this experiment himself.
17
This illustration reflects the general opinion
before Galileo which followed largely
Aristotelian lines but incorporating as well a
later theory of "impetus" -- which maintained
that an object shot from a cannon, for example,
followed a straight line until it "lost its
impetus," at which point it fell abruptly to the
ground.
Later, simply by more careful observation, as
this illustration from a work by Niccolo
Tartaglia clearly shows, it was realized that
projectiles actually follow some sort of a curved
path
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Galileo got his ideas by making
experiments independent coordinates
Number, Weight and Measure
It was another essential insight that led
Galileo, finally, to his most remarkable
conclusion about projectile motion. First of all,
he reasoned that a projectile shot from a cannon
is not influenced by only one motion, but by two
-- the motion that acts vertically is the force
of gravity, and this pulls the projectile down by
the times-squared law. But while gravity is
pulling the object down, the projectile is also
moving forward, horizontally at the same time.
And this horizontal motion is uniform and
constant according to his principle of inertia.
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Riccioli's dramatic depiction of the hand of
God, creating the world according to mathematical
principles.
Where are the limits of man's possible
exploration?
Frontispiece to Francis Bacon's great work, the
Instauratio Magna, 1620 sailing through the
Pillars of Hercules "True Direction Concerning
the Interpretation of Nature."
Close relation between the Renaissance artists
and the new discoveries that science
exploration of the world depends upon observation
using scientific instruments -- as well as
mathematics iconography of an atlas by Marco
Coronelli
"Many will pass through and knowledge will be
increased."
20
See text 4-3
Shooting the Monkey(tranquilizer gun)

• Where does the zookeeper aim if he wants to hit
  the monkey?
• ( He knows the monkey willlet go as soon as he
  shoots ! )

The next slides are taken from Physics 111
lecture notes
See examples 4-3 and 4-6
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See text 4-3
Shooting the Monkey...

r r0

• If there were no gravity, simply aim

at the monkey
r v0t
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See text 4-3
Shooting the Monkey...
r r0 - 1/2 g t2

• With gravity, still aim at the monkey!

r v0 t - 1/2 g t2
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See text 4-3
RecapShooting the monkey...
x v0 t y -1/2 g t2

• This may be easier to think about ,
• Its exactly the same idea!!

x x0 y -1/2 g t2
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Yeah! - ???
Was he talkin about?
NOW - were ready for Newton!
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Remember to hand in the problem set 2 on Monday
(February 12) Remember to hand in the problem set
3 on Monday (February 19) There is the first
hour exam on February 19, during the class time.
Bring your class notes - it is an open notes
exam. The topics covered up to today will be on
the exam.
Remember to be thinking about your semester
report. It is only due at the end of the
semester, but you will probably want to be
working on it earlier
Next time we start with Newton. This will not be
on the exam.