Kinematics - Galileo

Harry Varvoglis
University of Tübingen &
University of Thessaloniki

• Founder of modern Science
• The first of the six children of Vincenzo Galilei,
musician, and of Giulia Ammannati
• Born in Pisa
• At age 8 his family moved to Florence (80 km
away…)
• Galileo attended school in a monastery near
Florence and was thinking to follow an
ecclesiastical career, but...
2

• He entered the School of
Medicine of the University
of Pisa.
• But, finally, he got a Degree
in Mathematics.
• Salary of a professor: in
Medicine 2.000 scudi/year
(1 scudo ≈ € 200), in
Mathematics 80
scudi/year!
• In 1589 he was appointed
professor of Mathematics
in the University of Pisa.
• It is there that the
foundations of his later
scientific career were set. 3

• The oscillations of the
chandelier in the
Duomo (i.e. Cathedral)
of Pisa gave him the
idea that:
• The oscillations of a
pendulum (today we
know only those of
small amplitude) are
isochronous.
• Huygens, based on this
observation, built later
the first pendulum
clock. 4

• Professor of Mathematics in the University
of Padova, the second largest city in the
Republic of Venice.
• Construction of scientific instruments
(geometrical and military compass)
• Experiments with inclined planes
5

• Analog computer for
solving numerical and
geometrical problems
(e.g. square and cubic
roots!)
• Topographical works
• Note how he describes
himself: Nobile
Fiorentino, Lettore
delle Mathematiche
6

• Contrary to the
tradition, Galileo never
performed the
experiment of letting
several bodies of
different weight to fall
from the top of the
inclined Pisa Tower.
• Instead, he performed
experiments with
inclined planes, where
measuring time
intervals is easier.
• He says that he
measured time
intervals by counting
his heartbeat, but more
probably he did it by
singing, as he had
learned from his 7
father!

From Deutsches Museum
8

• The distances
covered are
proportional to
the squares of
the
corresponding
time intervals,
From Deutsches Museum
S = ½at 2
• The inclination
is small, in
order to make
the
measurement of
time easier.
9

• According to the
Aristotelian theory (top)
heavier bodies fall faster
(Fig. 1).
• But this leads to a
contradiction (we said
that already!): If we tie a
heavy and a light body,
the two will fall faster
(Fig. 2) or slower (Fig. 3)
than the heavier?
• Galileo solved the
problem, by showing
experimentally that all
bodies fall with the same
acceleration (bottom).
10

(From Galileo’s
notes)
11

• Geometrical methods for solving problems of
Calculus:
S = vt, S = ½γt 2 as the area of orthogonal triangles
• Books: Mechanics (1600), Discourses and
Mathematical Demonstrations Relating to Two New
Sciences (1638)
• Co-ordinate systems (perfected little later by
Descartes)
• Galilean transformations (we will come back to that)
x' = x – v 0 t, v' = v – v 0
12

• Galileo presented his
first telescope to the
Dogue of Venice on
August 25, 1609.
• He published his
theory of making
telescopes in his book
Sidereus Nuncius
(Starry Messenger),
which appeared in
1610.
14

• The first page of the
book, which was
published by a printing
house in Venice.
• Note, a change in how
he refers to himself:
Patritio Florentino,
Patavini (Paduan)
Gymnasii Publico
Mathematico.
15

• Mountains and craters
on the surface of the
Moon imply that it is a
heavenly body like
Earth, and not a
“perfect sphere”, as
believed by
Aristotelian
philosophers.
16

• Observations indicated,
beyond any doubt, that
Venus is revolving around
the Sun (left: Ptolemy’s
theory of epicycles, right:
Copernicus’ heliocentric
theory).
• Heracleides from Pontos
(from Black Sea, 380-310
BC) had suggested the
“intermediate” idea that
Mercury and Venus are
revolving around the Sun,
but the rest of the planets
(Sun included) are
revolving around the
Earth.
17

The struckout text,
appearing in the
manuscript
of the book
De Revolutionibus,
was not included
in the printed version.
18

• Galileo’s manuscript
(top) and pages from
Sidereus Nuncius
(bottom).
• The systematical
recording of Galileo’s
observations shows
that the “starlets” are,
in reality, satellites of
Jupiter.
• Therefore Jupiter is a
miniature of our Solar
System. 19

• Galileo suggested the use of the position of
Jupiter’s satellites for the measurement of
“absolute” time and, therefore, for the calculation
of longitudes.
• The difficulty of observations from a ship made
this method not practical.
• The problem was solved after the invention of
marine chronometers by John Harrison (spring
balance & grasshopper escapement).
20

• Invitation by the Great Duke of Tuscan,
Cosimo II of Medici
• Big salary, freedom in residence and
teaching
• Return to his “fatherland”
• But return to the region of dominance of the
Pope.
21

• 1611: Galileo visits Rome.
• His work is recognized and he
becomes a member of the first
scientific society, Academia dei
Lincei.
• He organizes astronomical
observations with his telescope
for the Jesuit monks in Rome.
• Reaction: Why look through this
imperfect instrument, once we
know the truth from Aristotle
and the Bible? (Cesare
Cremonini, Paduan professor
Giulio Libri, Florentian
philosopher).
22

• God is perfect, and all of God’s creation is perfect.
Man is imperfect, and therefore his inventions are
imperfect. Why should we use an imperfect
invention, like Galileo’s telescope, to see God’s
perfect creation? Wouldn’t that corrupt God’s
creation?
• Where is the picture we see through the telescope?
In the real world or inside the telescope?
23

• The solar surface has
spots, which change
place as the Sun
rotates.
• Therefore, not only the
Sun is not “perfect”, as
declared by the
Aristotelian
philosophy, but it
rotates, as well, about
an axis.
24

• First warning, not to teach the heliocentric system.
• In order to “fight” Kepler’s book Astronomia Nova
and Galileo’s publications…
• The church adds the books by Copernicus, Kepler and
some of Galileo’s “letters” in the Index Librorum
Prohibitorum (1559-1948).
• They were withdrawn only in 1835!
25

• It started with Galileo disagreeing with the Jesuit monk
Orazzio Grassi, about the nature and the orbit of the comet
of 1619. Grassi insisted that the comet was closer than the
Moon (according to Aristotelian views), Galileo calculated
that it was further away.
• There was an “escalation” in exchanging arguments from
both sides (books and pamphlets published under a “nom
de plume” or written by “followers” of each side).
• The debate reached a climax with the publication of the
book Il Saggiatore (assayer=tester, a kind of stone used to
measure content in gold of an alloy ), written in Italian and
not in Latin, where Galileo brings forth all arguments for
the heliocentric theory and ridicules openly Grassi and his
other opponents.
26

Academico Lincei
Nobile Fiorentino
Filosofo e Matematico Primario
Del Serenissimo Gran Duca
di Toscana
27

• Discussion with Pope Urbanus VIII
(cardinal Maffeo Barberini , native of
Florence and Galileo’s friend).
• Papal “advice” to refer to the heliocentric
system only as a “mathematical hypothesis”.
• Within this framework, he gets the
“imprimatur” (=permit to publish) his next
book.
28

• Matematico Sopraordinario (Extraordinaire)
• dello Studio di Pisa
• e Filosofo e Matematico
• Del Serenissimo Gran Duca di Toscana
• (he was not any more “Academico Linceo…)
30

• Salviati (“heliocentric"), from the name of Filippo
Salviati, Galileo’s friend.
• Sagredo (“neutral"), from the name of
Giovanfransesco Sagredo, Galileo’s friend.
• Simplicio (“Aristotelian"), from the name of the
Greek Aristotelian philosopher of the 6 th century
AD Simplicius, but a play of words, as well
(=naïve).
31

• Inside cover of the first
edition of Dialogo
• Galileo had got the
imprimatur from the
Inquisition of Florence.
• But the Pope had a
different opinion…
32

• Galileo is charged by the
Jesuits for heretic
teaching.
• The permit of
publication of his book
is revoked.
• He is tried in 1633 by the
Inquisition and he is
shown the instruments
of torture.
• He is obligated to
renounce his ideas in a
monastery in Rome, in
June 22, 1633
• He was condemned to
home detention
(successively in Rome-
Sienna-Arcetri).
33

• Thermometer based on the
expansion of gases .
• Basic target: measurement of
the temperature of patients.
• Inaccurate, due to the
variability of the atmospheric
pressure.
• Torricelli, however, removed
completely the air and turned
it into the well known
barometer!
36

• Motion at constant
acceleration
• Galilean
transformations
• Independence of
motions
• Geometrical proofs
• Inertia principle (but
see reference to John
Philoponus in De motu
antiquitora, Pisa, ~1590)
37