The Newtonian Revolution - Astrophysicsfverbunt/iac2011/newton.pdf · The Newtonian Revolution...

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


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!


New technology: Tycho Brahe

instrument design Improved accuracy

Nova Stella 1572


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


Improved accuracy

Ptolemaios Brahe


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


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


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


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


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


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


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


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. . .


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


Römer discovers velocity of light: 1676


Sphere of stars or infinite universe?

Thomas Digges 1546 – 1596 Huygens: life on planets?


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


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


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


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.



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.



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’



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



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!


Halley’s list of comets – 1705; next appearance 1758?


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.


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