Islamic Innovators
and 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 astronomy
 Geocentrism
vs heliocentrism not a simple
choice from observations
 Does physics rule astronomy?
How radical or novel was Copernicus?
 Problems with the Copernican
heliocentric cosmos

Moving Earth
stellar parallax?
Earth
Earth
Sun
Sun
Geocentric
Expect no parallax
Heliocentric
Expect parallax, not
observed until 1837
Moving Earth
Venus parallax?
Parallax angle
Earth
Venus
S
E
S
V
E
Geocentric
Par (Ven) > Par (Sun)
V
Heliocentric
Par (Ven) > or < Par (Sun)
Not observed until 1930s
Moving Earth
birds left behind?
re = 6400 km
Equator
Vequat = 1700 km/hr
Arabic astronomy, 850 - 1300

Islam and the need for astronomy
 Prayer
Times
 Direction of Mecca
 Qibbla for mosques
 Typical 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, physical
cosmology in Platonic-Aristotelian tradition)
– Ibn al-Haytham (d. 1040) defines hay’a as a problem to
be solved
– al-Bitruji (1200) replaces epicycles & equants with
homocentric spheres (model does not work)
– al-Tusi (1250): replace equant with Tusi-Couple
– al-Shatir (1350): replace equant with double epicycles
Tusi Couple
2a
a
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 as
Earth “passing” outer
planet
>>Explains links of inner
planets to Sun as their
orbits around Sun
Steps to heliocentrism: 1
Sun
Mars
r
R
Earth
Ptolemaic Superior
Planet
r = epicycle radius
R = deferent radius
Steps to heliocentrism: 2
Sun
Mars
Earth
Complete the
parallelogram
Steps to heliocentrism: 3
Sun
Mars
Earth
Add circle around
Earth, circle around
Sun = “Tycho’s
model” for Superior
Planet
Steps to heliocentrism: 4
Mars
Sun
Earth
Let Earth orbit Sun
rather than Sun orbit
Earth, i.e., shift from
“Tychonic” to
Copernican model
Steps to heliocentrism: 5
Copernican
Mars
Sun
R
r
Earth
r = Earth’s distance =
AU = “common
measure” of solar
system
R = Mars’ distance
From Ptolemy, R=60,
r=39.5, thus R/r=1.52
or Mars is 1.52 AU
from Sun!
Aesthetics of new cosmology

“… in this arrangement we discover a marvelous
commensurability [common measure] and an established
harmonious linkage between the motion of the spheres and their
sizes, such as can be found in no other way.” De revolutionibus,
Book 1
 AU
is “common measure” of planetary
distances from Sun
 Planetary periods proportional to their
distances 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’s
Orbit
Sun
•Sun fixed
•Center of Earth’s
orbit 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 reality
or astronomical hypothesis)?