Physics at Court
Galileo’s New
Sciences
Galilean relic in Florence
Institute and Museum of the History of Science
Galileo as “mathematician &
philosopher”

The chief works
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Operations of the Geometrical & Military Compass, 1606
Starry Messenger, 1610
Dialogue on the World Systems, 1632
Two New Sciences, 1638
New persona as natural philosopher
Saint
 Martyr
 Entrepreneur

– Founding member of Academy of the Lynxes

Publicist, polemicist and courtier
– Earliest use of vernacular in European science
Task of lecture
Galileo as a public Copernican
 Galileo’s kinematics of motion

 Early
challenges to Aristotle
 The law of free fall
 Circular inertia
 Projectile motion

Another conservative revolutionary?
Delayed responses to
Copernicus’s heliocentrism

Wittenberg Intepretation of De rev
Osiander preface
 Computational tool, not cosmology
 Only 10 authors discussed heliocentrism by 1600,
only 2 converts (Mästlin and Kepler)
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De rev on Catholic Index in 1616
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Must correct (not ban) the book
Galileo as closet Copernican, 1595
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Double motion of earth causes tides by sloshing
the oceans; high tides when rotations in “same”
direction, low tides when rotations in “opposite”
directions
Galileo as public Copernican
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Invention of the telescope, 1608
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Patent request by Dutch spectacle-maker, Lipperhey
Galileo’s telescopic discoveries, 1609-10
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Earth-like moon
New stars not reported by ancients
Satellites of Juptier (“Medicean stars”)
Phases of Venus
Ignored physics problems of heliocentrism
– What moves the planets?
– Why do bodies on earth fall “down” and not toward center
of cosmos?
Galileo’s
telescope
Institute and Museum of the
History of Science, Florence
Ghirlandaio, St. Jerome, fresco in
Church of Ognissanti, Florence, 1480
Contra Aristotle on motion
(kinematics)

Galileo’s early anti-Aristotelianism
– Empirical experimentation, not just logic
– “The language of nature is mathematics”
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Law of pendulum--Pisa cathedral
– Period independent of amplitude, weight
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Falling bodies--Pisa tower
– Time of fall independent of weight
– But if Aristotle is wrong, what is the
correct law of falling bodies?
Galileo’s law of free fall

Medieval definitions (from “latitude of
forms”)
V = ΔD/Δt (“change in distance/change in time”)
 a = ΔV/Δt = (Vf - Vi)/Δt
 If Vi = 0, then a = Vf/t, or Vf = at


Galileo’s “thought experiments”
Uniform motion: D = VT
 Uniformly nonuniform motion
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D = (1/2)Vft [Merton College Rule!] = (1/2)at2
Galileo’s inclined plane experiments
Is free fall a uniform acceleration?
 Two set-ups (keep time or distance intervals fixed)
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Galileo’s lab report (a C-?)
Manuscript
T2 T
D
1
4
9
16
25
36
49
64
Ms. Gal. 72, f. 107v, from
http://galileo.imss.firenze.it/ms72/INDEX.HTM
[33T2]
1
33
33
2 130 132
3 298 297
4 526 528
5 824 825
6 1192 1188
7 1620 1617
8 2104 2112
Measured D is proportional to T2!
Galileo’s law of “inertia”

Another thought experiment
– Motion accelerates down inclined plane
– Motion decelerates up inclined plane
– Motion unchanged on horizontal plane

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BUT “horizontal” means circular at earth’s surface
Thus, Galilean “inertia” is circular
– Aristotle’s circles remain
– Galileo also rejected Kepler’s ellipses
Projectile motion (impetus +
Aristotle)
Projectile motion (Galileo)
Separate into horizontal (constant v)
(accelerated) and vertical components
 Example of horizontal projectile

Cannon
Dh
Dv
 Dh
= VT
 Dv = 1/2at2
Cannonball
Galileo’s contributions

Kinematics rather than dynamics
Quantitative description of terrestrial motion
 Forces (Aristotle’s “causes”) are never discussed
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Combined thought and actual experiments
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Used latter to confirm former, unlike Aristotle
Another cautious revolutionary?
Preserves Aristotelian circles
 Preserves Platonic belief in number as basis of
cosmos
 But provoked controversy with Church; not as
cautious as Copernicus
 Wrote in vernacular; physics for court, not just
university audiences
