Islamic Innovatorsand Copernicus

Problems with Ptolemy Equant violates Plato’s rule (uniform,

circular motion) No absolute distances, i.e., not a

physical picture of the cosmos Predicted change in lunar apparent

size not observed (if mechanisms are“real”)

Ad hoc links of all models to Sun

Task of lecture Arabic and Latin medieval critiques of

Ptolemaic astronomyGeocentrism vs heliocentrism not a simple

choice from observationsDoes physics rule astronomy?

How radical or novel was Copernicus? Problems with the Copernican

heliocentric cosmos

Moving Earth stellar parallax?

Earth

Sun

GeocentricHeliocentric

Earth

Sun

Expect no parallaxExpect parallax, notobserved until 1837

Moving Earth Venus parallax?

Earth VenusParallax angle

GeocentricPar (Ven) > Par (Sun)

S

VE

HeliocentricPar (Ven) > or < Par (Sun)Not observed until 1930s

S

VE

Moving Earth birds left behind?

re = 6400 km

Equator

Vequat = 1700 km/hr

Arabic astronomy, 850 - 1300 Islam and the need for astronomy

Prayer TimesDirection of MeccaQibbla for mosquesTypical astrological/medical concerns

Court translations of Ptolemy, Aristotle“Filosofa” (“foreign” philosophy)

Large observatories and “professionals”

Arabic critiques of Ptolemy Improve predictive accuracy

– Correct Ptolemaic parameters with obs.– Add “trepidation” to Ptolemy’s precession– Produce new tables to find positions (zijs)

Fix the physics (hay’a=real, physicalcosmology in Platonic-Aristotelian tradition)

– Ibn al-Haytham (d. 1040) defines hay’a as a problem tobe solved

– al-Bitruji (1200) replaces epicycles & equants withhomocentric spheres (model does not work)

– al-Tusi (1250): replace equant with Tusi-Couple– al-Shatir (1350): replace equant with double epicycles

Tusi Couple

a

2a

Uniform circular motion makes linear harmonic motion!

Medieval Latin astronomy Scholastics synthesize Aristotle and Christian

theology (Thomas Aquinas) Angels move celestial spheres Astrology accepted for everything but human will

Medieval universities Trivium (grammar, logic, rhetoric) Quadrivium (astronomy, music, geometry,

arithmetic) Attempted reforms in Latin West (Arabic

influence)? Peurbach/Angelus & Tusi (1460)? Regiomontanus & homocentrism (1460)

Copernicus, the isolated canon Born in Torin, merchant’s son Studied law, medicine in Cracow and Italy,

acquired best Latin astronomy books in print Time of printing, Columbus, fall of Constaninople

To Poland as Fromberg canon in 1503 The closet astronomer

Observations begin 1503 Commentariolus, manuscript written ca. 1508 De revolutionibus orbium coelestium [On the

revolutions of the heavenly spheres], 1543(Copernicus’s only published book)

A “Copernican Revolution”? The traditional view

– Moving earth from Greeks (Philolaos, Heraclides)– Explained solar links, retrograde motion “naturally”– Osiander’s “instrumentalist” preface– Better predictive accuracy than Ptolemy

New view: A “conservative revolutionary”– Employed Tusi’s mathematics to eliminate equant– Sought hay’a goal of restoring Plato’s uniform, circular

motion– Predicted Ptolemy’s positions, not improved accuracy– But did add novel aesthetic considerations (‘common

measure’)– Created problems for Aristotelian physics?– Refuted by lack of observed stellar parallax?

Coeprnican advantages

>>Explains retrograde asEarth “passing” outerplanet

>>Explains links of innerplanets to Sun as theirorbits around Sun

Steps to heliocentrism: 1

Ptolemaic SuperiorPlanet

r = epicycle radiusR = deferent radius

Mars

Earth

Sunr

R

Steps to heliocentrism: 2Mars

Earth

Sun

Complete theparallelogram

Steps to heliocentrism: 3

Add circle aroundEarth, circle aroundSun = “Tycho’smodel” for SuperiorPlanet

Mars

Earth

Sun

Steps to heliocentrism: 4

Let Earth orbit Sunrather than Sun orbitEarth, i.e., shift from“Tychonic” toCopernican model

Sun

Mars

Earth

Steps to heliocentrism: 5

Sun

Mars

Earth

Copernican

r = Earth’s distance =AU = “commonmeasure” of solarsystemR = Mars’ distance

From Ptolemy, R=60,r=39.5, thus R/r=1.52or Mars is 1.52 AUfrom Sun!

r

R

Aesthetics of new cosmology “… in this arrangement we discover a marvelous

commensurability [common measure] and an establishedharmonious linkage between the motion of the spheres and theirsizes, such as can be found in no other way.” De revolutionibus,Book 1

AU is “common measure” of planetarydistances from Sun

Planetary periods proportional to theirdistances from Sun

Mer .24 yrs, Ven .62, Ear 1, Mars 1.9, Jup 11.9, Sat 29.4

Heliostatic not heliocentric!Earth

Center of Earth’sOrbit

Sun •Sun fixed•Center of Earth’sorbit moves•Requires 3 circles

Copernican cosmology Eliminates equant with Tusi Couples (Arabic

influence) Provides “common measure” for distances and

“harmonious linkage” of period-distance– Aesthetic contribution

Heliostatic rather than heliocentric Retains small epicycles for each planet (not for

retrograde motion) Same number of circles as Ptolemy Same format as Almagest “Saves” Ptolemy’s predictions, not the heavens Creates crisis for Aristotle’s physics

– What is the status of Copernican model (physical realityor astronomical hypothesis)?