Galileo as “mathematician &philosopher” The chief works
– 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 AristotleThe law of free fallCircular inertiaProjectile motion
Another conservative revolutionary?
Delayed responses toCopernicus’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) De rev on Catholic Index in 1616
Must correct (not ban) the book Galileo as closet Copernican, 1595
Double motion of earth causes tides by sloshingthe oceans; high tides when rotations in “same”direction, low tides when rotations in “opposite”directions
Galileo as public Copernican Invention of the telescope, 1608
Patent request by Dutch spectacle-maker, Lipperhey Galileo’s telescopic discoveries, 1609-10
– 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’stelescope
Ghirlandaio, St. Jerome, fresco inChurch of Ognissanti, Florence, 1480
Institute and Museum of theHistory of Science, Florence
Contra Aristotle on motion(kinematics)
Galileo’s early anti-Aristotelianism– Empirical experimentation, not just logic– “The language of nature is mathematics”
Law of pendulum--Pisa cathedral– Period independent of amplitude, weight
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
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)
Galileo’s lab report (a C-?)
Ms. Gal. 72, f. 107v, fromhttp://galileo.imss.firenze.it/ms72/INDEX.HTM
T2 T D [33T2]
1 1 33 334 2 130 1329 3 298 29716 4 526 52825 5 824 82536 6 1192 118849 7 1620 161764 8 2104 2112
Manuscript
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
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 (Galileo) Separate into horizontal (constant v)
(accelerated) and vertical components Example of horizontal projectile
Dh = VTDv = 1/2at2
Dv
Dh
Cannonball
Cannon
Galileo’s contributions Kinematics rather than dynamics
Quantitative description of terrestrial motion Forces (Aristotle’s “causes”) are never discussed
Combined thought and actual experiments 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