Physics at CourtGalileo’s New

Sciences

Galilean relic in Florence

Institute and Museum of the History of Science

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 (impetus +Aristotle)

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