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The Newtonian Revolution
OutlineNew technology: TychoBrahe
Cosmology vs. computation
New technology: thetelescope
Galileo Galilei: physics
Newton
Descartes vs. Newton
LiteraturePannekoek
Koestler: The Sleepwalkers(esp. chapter on Kepler)
Westfal: Never at Rest(biography of Newton)
Dijksterhuis: Mechanizationof the World Picture (Dutch:Mechanisering van hetwereldbeeld)
lecture by Albert van Helden
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 1 / 27
Cosmology versus technical astronomy
Cosmologypart of natural philosophy
aim: describe causesbasis: physics ofAristoteles:
I mass strives towardcenter in sublunarworld
I circular motion insupra-lunar world
I practitioners:universities
Technical astronomypart of mathematics
aim: computation of planetposition
basis: methods outlined inCopernicus (before him:Ptolemaios)
whether constructions are realis not important (annotations inDe revolutionibus only intechnical sections!)
Brahe, Kepler: trained atuniversities, work mostly outsideuniversities
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 2 / 27
New technology: Tycho Brahe 1546 – 1601
General in Europeimproved techniques e.g.metal-working
book printing
Tycho Braheastronomical tables forplanets are wrong by asmuch as a month
problem for astrology. . .new, more accuratemeasurements
I special observatoryI instrument design
observatory and instrumentsdescribed in book!
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 3 / 27
New technology: Tycho Brahe
instrument design Improved accuracy
Nova Stella 1572
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 4 / 27
A new, very bright star: 1572
black βCep↔αCas; red ιCep↔δCas; blue βCas↔λUMa
ObservationsDigges (Cambridge)βCep↔αCas andιCep↔δCas
Mästlin (Tübingen)ιCep↔δCas andβCas↔λUMa
no parallax↔ at largerdistance than Moon
comets also abovemoon orbit
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 5 / 27
Improved accuracy
Ptolemaios Brahe
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 6 / 27
Improved accuracy
Ptolemaios
Brahe
Accuracy Star CataloguePtolemaios FWHM ∼ 40′
Brahe FWHM ∼ 5′
Brahe individualmeasurements: muralquadrant σ = 35′′
777 stars in first edition 1602
1004(−12 doubles) stars inedition by Kepler 1627
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 7 / 27
Identification of Catalogued Stars: results
Identifications1602 1627
secure 752 929sec. nn 9 14probable 4 18possible 7 17no ident. 5 14repeat 0 12all 777 1004
Kepler (from Linz) to Father GuldinYou ask me what I did with myselfduring the long siege. You ought to askwhat one could do in the midst of thesoldiery. . . The ears were constantlyassailed by te noise of the cannon, thenose by evil fumes, the eye by flames.All doors had to be kept open for thesoldiers who, by their comings andgoings, disturbed sleep at night, andwork during day time.cited in Koestler: The Sleepwalkers
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 8 / 27
Johannes Kepler 1571 – 1630
Scientific methodstruggles between medievaland modern outlook
‘medieval’: MysteriumCosmographicum: nestedregular polygons
‘modern’: law of areas fromdiminishing influence of Sunat larger distances
modern: details should alsobe in order
good mathematics
had very difficult life
Mysterium Cosmographicum
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 9 / 27
Kepler
Orbit of Marsuse observations from samepoint of Earth orbit
use constant increase ofangle from equant (orequivalent alternatives)
⇒ orbit of Mars
oval ‘flattened circle’
deviation: 8′
distance Sun from center:(‘eccentricity’) 0.0926
flattening: 0.00429
0.5 × 0.09262 = 0.00429
Ellips mathematics
b = a(1 − e2)1/2 ⇒a − b
a'
e2
2
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 10 / 27
Kepler
Laws of Kepler1 orbit planet is ellipse, Sun in
focal point2 radius sweeps equal areas in
equal time3 period P, semimajor axis a
are related viaP2 = constant a3; constantsame for all planets
Kepler computes horoscopes
book on Nova Stelladiscusses astrological effects
Horoscope Wallenstein
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 11 / 27
Galileo Galilei 1564 – 1642: the astronomer
Invention of telescopemade possible by improvedglass
first in NetherlandsGalilei made his own anddiscovered:
I new stars (what use?)I moons around Jupiter
(center of motion , Earth)I phases of VenusI sun spots (not perfect)I moon mountains (note:
Jan van Eyck 1430)
comets are atmosphericdisturbance
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 12 / 27
Galileo Galilei the physicist
Experimentsseparation horizontal-vertical
acceleration along inclinedplane
modern notation:
v = gt ; s =12
gt2
Huygens: concept ofmomentum:
circular orbit requires force:
v2
r
Christiaan Huygens 1629 –1695
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 13 / 27
Galileo Galilei the mathematician?
Philosophy is written in that great book which ever lies before oureyes – I mean the universe – but we cannot understand it if we donot first learn the language and grasp the symbols in which it iswritten. This book is written in the mathematical language, and thesymbols are triangle circles and other geometrical figures, withoutwhose help it is humanly impossible to comprehend a single word ofit, and without which one wanders in vain through a dark labyrinth.
but Galilei never understood Kepler’s work. . .
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 14 / 27
Further development of telescopes
Johannes Wiesel (Augsburg)
Eustachio Divini (Rome)
Christiaan Huygens
Giuseppe Campani (Rome)
Further discoveries
HuygensI rings of SaturnI Titan
CassiniI division in ring of Saturn
RömerI velocity of light
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 15 / 27
Römer discovers velocity of light: 1676
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 16 / 27
Sphere of stars or infinite universe?
Thomas Digges 1546 – 1596 Huygens: life on planets?
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 17 / 27
Revival of atomism
Pierre Gassendi 1592 – 1655 Tenets of atomismLucretius De rerum natura
known throughout middleages
matter is made up ofindivisible particles a-tomos
natural processes must beexplained by size, shape,and motion of these particles
atoms move in vacuum
forces governing motion ofplanets are mysterious
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 18 / 27
Descartes 1596 – 1650 and vortices
stars are centers of vortices Mechanical philosophycausal explanations in termsof mechanical actionspushes or impact
no vacuum
find mathematicaldescriptions for phenomenaon earth and in sky
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 19 / 27
Synthesis: Isaac Newton 1643 – 1727
Portrait in 1689 Multi-faceted scientistmathematics: invents calculus(‘fluxions’); also Leibniz
theoretical physics: explains planetaryorbits
practical astronomy: builds besttelescope of his time: mirror telescope(with ball bearing)
chemistry: weighs ingredients inreactions (writings not published)
theology: Arian heretic (Christ as Sonof God is 3rd century invention) basedon detailed bible study
optics: white light consists of coloursFrank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 20 / 27
Synthesis: Isaac Newton 1643 – 1727
DefinitionsThe quantity of matter is themeasure of the same, arising fromits density and bulk conjointly
The quantity of motion is themeasure of the same, arising fromthe velocity and quantity of matterconjointly.
The vis insita, or innate force ofmatter is the power of resisting bywhich every body, as much as in itlies, continues in its present state,whether it be of rest or of movinguniformly forward in a right line.
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 21 / 27
Synthesis: Isaac Newton 1643 – 1727
Absolute TimeAbsolute, true, and mathematicaltime, of itself and from its ownnature, flows equably withoutrelation to anything external, andby another name is called‘duration’; relative, apparent, andcommon time is some sensibleand external (whether accurate orunequable) measure of durationby means of motion, which iscommonly used instead of truetime, such as an hour, a day, amonth, a year.
Absolute SpaceAbsolute space, in its own nature,without relation to anythingexternal, remains always similarand immovable. Relative space issome movable dimension ormeasure of the absolute spaces,which our senses determine by itsposition to bodies and which iscommonly taken for immovablespace.
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 22 / 27
Synthesis: Isaac Newton 1643 – 1727
Laws of motion1. Every body continues in itsstate of rest or of uniform motionin a right line unless it iscompelled to change that state byforces impressed on it.
2. The change of motion isproportional to the motive forceimpressed and is made in thedirection of the right line in whichthat force is impressed.
3. To every action there is alwaysopposed an equal reaction; or,the mutual actions of two bodiesupon each other are always equaland directed to contrary parts.
Law of gravity
F =GMm
r2
powerful mathematics! but whatis the physics? ‘actio in distans’
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 23 / 27
Synthesis: Isaac Newton 1643 – 1727
Second edition 1713But hitherto I have not been ableto discover the cause of thoseproperties of gravity fromphenomena, and I frame nohypotheses; for whatever is notdeduced from the phenomena isto be called a hypothesis, andhypotheses, whethermetaphysical or physical, whetherof occult qualities or mechanical,have no place in experimentalphilosophy
Laws of equal areas
no force: Bc=AB in equaltime interval
at B: force in direction S
Cc ‖ BS hence area BSC =area BSc =area ABC
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 24 / 27
Synthesis: Isaac Newton 1643 – 1727
The apple and the moon
gMoon
gearth=
(Ra
)2
Galilei:
gearth = 30 feet/s
Moon, with Huygens,
gmoon =v2
a=
(2πaP
)2 1a
a ' 60R ⇒ gmoon = 0.0073 feet/sDiscrepancy of ∼ one in eight dueto inaccurate Earth radius
Reactionvery impressive! Newtongreatest physicist
but. . . actio in distans difficultto accept
France: we stick toDescartes’ vortices
await the return of the comet!
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 25 / 27
Halley’s list of comets – 1705; next appearance 1758?
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 26 / 27
Exam questions
Three technologicaldevelopments were crucial tothe Copernican andNewtonian revolutions.Describe briefly for each ofthese why they were soimportant
Kepler, Huygens and Galileieach contributed importantknowledge about (celestial)mechanics that Newtonembedded in his theory ofgravity. Describe these threecontributions, and explainhow they are contained inNewton’s theory.
Frank Verbunt (Astronomical Institute Utrecht) The Newtonian Revolution July 15, 2011 27 / 27