THE COPERNICAN REVOLUTION
NOTE: This is an outline for a set of lectures on the
Copernican Revolution. It includes references to Ptolemaic astronomy, which was
the precursor of the Copernican system. These are all topics that are addressed
in class lectures.
Between 1500-1700 there was a vast change in viewpoint of educated public in
This is the scientific revolution. The first
step in it, at the beginning of this period is the Copernican Revolution.
NICHOLAS COPERNICUS (1473-1543)
Copernicus' life:
Born in 1473 of German parents in
Father died when Copernicus was 10.
Raised by uncle who became a bishop in the Catholic Church.
Went to study at the
Studied medicine, but discovered ancient
classics of math and astronomy
Summoned home by uncle
who had arranged for C. to take post as Canon of Frauenberg
Cathedral.
missed
getting the post by a few days because incumbent failed to die in an even
numbered month when the uncle had the power to appoint successors to such
positions. (The pope appointed in uneven months.)
Copernicus returned to his studies, but this
time went on to the universities at
Eventually he took a doctorate in Canon Law at
the
Even then he did not take up his post as Canon,
but instead lived at his uncle's castle as house physician (ostensibly) for six
years. During this time he formed his ideas about astronomy and made an outline
of them which was not published until centuries later (The Commentary).
When his uncle died in 1512, Copernicus finally
took up residence and duties as Canon at Frauenberg
where he remained the rest of his life.
Officially, Copernicus functioned as a
physician and church administrator, but had much leisure time and devoted much
of it to his interest in astronomy.
He completed a draft of On the Revolutions
of the Heavenly Spheres in 1530, but locked it away, making only occasional
corrections after that. In 1543, he was eventually persuaded to publish it. He
died in the same year.
Copernicus' interests:
Copernicus was a prototype Renaissance Man.
Studied widely in many subjects, but took a special interest in mathematics and
astronomy, as these seemed crucial and central to his philosophical
understanding.
He was especially the flaws perceived in the
current astronomical theory.
Julian Calendar
out by about 10 days.
Council of
To understand Copernicus' interests we need to
understand the classical tradition that he inherited and why astronomy was
crucial to it.
Ancient natural philosophy sought universal,
unchanging aspects of nature. These were eternal and worthy of attention. Other
events were random and not worthy.
For Plato in 4th century B.C., the
unchanging forms were the ultimate realities; their physical
manifestations were not important. Therefore abstract thinking was the only
kind of real value. This emphasis aided the development of mathematics a great
deal because it focused on abstract relations. Ancient Greeks were excellent
mathematicians. But Plato's appeal to the abstract was to
disembodied to gain general approval and understanding. His view remained a
very influential one among a certain segment of the educated society.
Plato's student, Aristotle, had much
more success in characterizing nature in a way that made sense to his culture
and to generations and generations after. Like Plato, Aristotle focussed
attention upon those aspects of Nature which were in some sense eternal. But
unlike Plato Aristotle's eternal forms existed only in physical manifestations.
These two outlooks provided philosophy with its
major contrasting viewpoints. The dissonance between the two views has been
responsible for much lack of communication among intelligent people for
centuries. Also it provided issues to focus the attention of thinkers where the
two points of view seemed to clash.
Such a clash is involved in the Copernican
Revolution.
What was eternal was what never changed, or
what repeated in a cycle. In antiquity there was nothing more obviously cyclic
than the constant east-west motion of the objects in the heavens.
General pattern of star motions
remained the same. As though a large ball was viewed from the inside with the
stars painted on its inner surface and it turned slowly and constantly.
Sun and moon also moved with
regularity, though not in step with the stars. They could be viewed as having a
circular motion of their own in addition to sharing the motion of the stars.
Circles were the
ideal, perfect pathways because they were eternal (endless) and unchanging.
Likewise, a sphere was the perfect shape because it had no sharp edges and was
the same everywhere.
Hence it seemed only fitting that the
eternal motions of the heavenly bodies were somehow composed of the motions of
circles and/or rotations of spheres.
In addition to the stars, which seemed
to be fixed on some large rotating sphere at the outer edge of the universe,
and the sun and moon which dominated the sky when visible, there were a handful
of other bodies which appeared regularly in the sky but were not so well
behaved.
These appeared to be stars, but stars
that wandered. The Greeks called them wandering stars, which in Greek was the
word planet. A planet was a star that did not remain in position
relative to the other stars. Planets seemed to have an irregular motion
in the sky, but one which repeated.
For a web site illustrating and
discussing the problem of the planets go to:
http://csep10.phys.utk.edu/astr161/lect/retrograde/retrograde.html
Another site, with extensive analysis of different ways of dealing with
planetary motion, from the ancients to the Renaissance is http://faculty.fullerton.edu/cmcconnell/Planets.html#7
This site has animations and
explanations of all aspects of this problem. Check this out by all means.
Irregular but repeating was a
self-contradiction to the ancient Greek mind. There must be something wrong
here.
Plato called attention to the problem
and called upon philosophers to solve the paradox. He enjoined them to "save
the phenomena" by which he meant to find out how it is that the
motions of the planets which appear irregular really were some combination of
regular eternal motions, that is, were really circular and unchanging.
The first real elaborated attempt to work out
such a solution was made by Plato's student Eudoxus. Eudoxus' system was adopted by Plato's more famous student,
Aristotle, and then considerably elaborated. It became a cornerstone of
Aristotle's view of the cosmos, which itself came to dominate scientific
thought for nearly two thousand years.
Eudoxus proposed that the planets were really bright spots imbedded on
otherwise invisible spherical shells concentric with the earth. Each planet was
part of a system of 4 concentric shells, connected to each other by their axes
of rotation, which were all different. Each system was imbedded within the
inner sphere of the system of the next farther planet. The outermost planet's
system (Saturn) was imbedded in the sphere of the fixed stars.
Thus each planet had the possibility of
considerable apparent irregularity in motion while really moving only in
perfect circles within circles as the various spheres rotated, communicating
the motion of one to the other.
Eudoxus's system was adopted in an amended and expanded version by Aristotle.
Aristotle's great power and appeal as a thinker had to do with his determination
to have an answer for everything. For
virtually every philosophical question that might have been raised in his day,
Aristotle either had an answer, with arguments to support it, or had an
argument to assert that the question was of no importance.
Moreover Aristotle's answers were all readily
understandable. He appealed to the evidence of the senses and analysed them in
a straightforward way.
The two sphere universe
For Aristotle, the most obvious distinction
that could be made about the world around him was that in the heavens things
went on and on, repeating themselves apparently forever, whereas on earth the
general trend was for everything to have a single span of existence. Animals
and plants were born, lived, and died and that was the end of them. Likewise
motions all seemed to begin and then end. An object thrown in the air falls to
the ground and then stops. Anything that stayed in motion on earth did so
because something was pushing it along. But in the heavens, events went on
forever.
Aristotle reasoned that there were really two
different worlds visible to man. Everything below the moon existed
somewhere within a life span from generation to corruption (beginning to end),
while everything from the moon outwards was eternal.
In the sublunar
world, below the moon, the substance of the world was in the form of the four
elements, earth, air, fire, and water. Everything was imperfect and existing
for a finite time. Motion, unless it was forced otherwise, was in straight
lines (because straight lines had natural beginning and end points).
In the superlunar
world, above the moon, everything that was consisted of a different material
altogether, because it was perfect and could hardly be
made from the imperfect elements. Beyond the moon, the substance of the world
was another element, which Aristotle called simply the "fifth"
element. The name has stuck, but we know it by the Latin for
"fifth element," "quintessence." In the superlunar world, all motion was eternal and changless. To the Greek mind it therefore had to be circular
motion at constant velocity. Nothing else made philosophical sense, but
perhaps equally important, the mathematics of antiquity could not cope with
any other kind of motion.
Aristotle's system of the world beyond the moon
was essentially the system of Eudoxus, with each
planet having several spherical shells associated with it, communicating motion
from one to the other. Saturn nearest the outer sphere of the
fixed stars and the moon nearest the boundary to the inner world which included
the motionless earth. Aristotle determined, somehow, that more spheres
were needed than Eudoxus had proposed and fixed the
required number at 55.
Though Aristotle's views on most subjects
prevailed, after the conquest of the surrounding world by (Aristotle's former
pupil) Alexander the Great, Greek thinkers came into contact with the vast
astronomical records of ancient
CLAUDIUS PTOLEMY 150 AD --
mathematical representation only (Platonic)
eccentric
epicycle - deferent
retrograde motion
equant
Greek
math only handled stasis and regular motion
Ptolemy's system "impossible" to be
physically real
Not a problem if true reality is realm of ideas
A web site on the Aristotelian world view and
the Ptolemaic system:
http://csep10.phys.utk.edu/astr161/lect/retrograde/aristotle.html
Retained and elaborated by Arabs
("Almagest")
Attempts to reconcile
with Aristotle system.
Epicycles as ball bearings between shells
Efforts to update Ptolemy
and make more accessible.
Culminated in publication
in 1496 of The Epitome of the Almagest by Regiomontanus
(Johann Müller).
Copernicus took an interest in astronomy in
part because it was perceived as a critical subject (understanding the order of
the heavens = understanding the mysteries of nature = understanding God, etc.)
and one that was in need of attention.
Julian calendar out of date
General revival of interest in
classical theories & mathematics
Something clearly wrong with Ptolemy
that a clever person might discern
Big issue was the apparent conflict between
Ptolemy's strictly mathematical representation and the Aristotelian literalist
view.
Some devices of Ptolemy's did not appear to be
possible physically.
The equant
particularly troubled Copernicus because it was not possible for a sphere to
rotate with stability evenly around a point which was not its geometrical
centre.
In the Epitome of the Almagest, Regiomontanus had shown that the effect of the equant could be produced by the introduction of another
epicycle. However, calculations could be so complex as to render this
impractical.
(One epicycle is required to explain
retrograde. Another for uniform motion.)
However, it is possible to explain retrograde
differently if instead of having the planets revolve around the earth, they
revolve around the sun. (Also suggested by Regiomontanus).
Copernicus, seeking to get rid of the
philosophically repugnant equant, tried to revise the
Ptolemaic system by substituting the sun as the center
of motion of the planets. (But the earth is still motionless.) (This is the
same as the Tycho Brahe
system.)
Problem of Mars' orbit. If the planets circled the sun,
but the earth was stationary, then the orbit of Mars (1.5 x radius of orbit of
sun round earth) cuts into the orbit of the sun around the earth. Impossible if
the orbits are physical spheres.
If the sun were motionless and the earth moved
around it, that would solve this problem.
In the prevailing Aristotelian climate of
thought, putting the earth in motion was an absurdity, as it violated common
sense.
But Coppernicus was
influenced as well by a strong Neo-Platonist tradition which sought the meaning
of life in mysteries that may seem to defy common sense. Also the neo-platonist tradition (and the Hermetic tradition, which
Copernicus also learned about at
Copernicus ultimate theory hung on to the
physical reasoning of the Aristotelians in the construction of his model
(physically real spheres carrying planets), but discarded the common sense
perception of the motionless earth.
Copernicus realized his conception would make
little sense to the public. Being secretive, he kept it to himself (and a few
trusted colleagues) for 30 years, until finally urged to publish in the year of
his death, 1543.
COPERNICUS' SYSTEM
Earth a planet, like others, all circling the
sun (no longer a planet)
Moon circling earth (no longer a planet)
Earth has three motions:
Daily rotation -- replacing the
movement of the sphere of the fixed start
Annual revolution around sun --
accounting for retrograde motion
3rd motion -- an annual rotation about
an axis perpendicular to the ecliptic (to correct for change in earth's axis
relative to the sun -- seeking symmetry around a point instead of inertial
orientation relative to the stars)
Fixed stars truly fixed now. Sphere of the fixed stars motionless.
No equant.
A web site on the basics of the Copernican system:
http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html
1. moving earth -- no
answer, really. Copernicus said that it was okay for the earth to move because
it was a sphere and spherical motion was natural for spheres. Clouds and other
objects in the air do not rush off to the west because being earthly,
they partake of the earth's motion.
2. phases of Venus --
since Venus is held to orbit the sun in a smaller orbit than the earth, it will
be seen from the earth at different angles with respect to the sun and
therefore should exhibit phases, like the moon does. But Venus does not appear
to exhibit phases. -- Copernicus' answer is that Venus is not lit by the sun,
but has its own light.
3. stelar
parallax. -- if earth is not the centre of the sphere
of the fixed stars, but in orbit around the centre, it should see the stars at
varying angles at different times of year. Therefore there should be stellar
parallax seen. But none is seen. -- Copernicus' answer (actually correct, but
seemed preposterous at the time) is that stellar parallax was not visible
because the stars were too far away. (In relation to the heavens, the orbit of
the earth is but a point.) (Stellar parallax discovered in
1838 by Bessel.)
Everything about Copernicus's reasoning was
ancient. Difficulties solved by ad hoc arguments. His system
just as complex as Ptolemy's. Copernicus solved some problems in Ptolemy
but replaced them with others just as bad, perhaps. Orbits
all circular and at constant speed--as required by ancients.
Copernicus saved the phenomena in a Platonic fashion.
His original appeal was to Neo-Platonists
only. Too much defying
common sense.
Osiander's preface
A web site from a course that covers much the same ground on Copernicus as my lectures. These are also lecture notes, but with a few good illustrations, especially of retrograde motion as explained by Copernicus. This is one of the sites pointed to by the site for the astronomy course listed at the bottom of this document.
http://www-astro.mps.ohio-state.edu/~pogge/Ast161/Unit3/copernicus.html
(1571-1630)
One of the few converts to Copernicus' theory
in next 70 years was Johannes Kepler, a Lutheran
mathematics professor in
Kepler had achieved fame as an astrologer early in his career by correctly
predicting a cold winter one year, and also the Turkish invasion of
Kepler was obsessed with numerical and geometrical relationships and invested
them with great mystical meaning. (Pythagorean)
Kepler found Copernicus' more mystical arguments amenable.
Kepler believed he too had found order in the heavens -- a particular
geometrical symmetry.
Kepler's 5 solids:
At the age of 25 Kepler
had a great insight:
According to Copernicus, there were
now six planets:
Mercury, Venus,
Earth, Mars, Jupiter, Saturn
Each planet was a blip on the surface
of an invisible spherical shell
concentric with the sun.
What determined the relative size of
the spherical shells? (Or what amounts
to the same, the spaces between each?
A regular solid
can be inscribed and circumscribed in a sphere.
cube -- between Saturn and Jupiter
tetrahedron -- between Jupiter and Mars (4 triangles)
dodecahedron -- between Mars and Earth (12 pentagons)
icosahedron -- betwen
Earth and Venus (20 triangles)
octohedron -- between Venus and
Mercury (8 triangles)
The cosmic mystery is solved: the
planetary orbs are separated by the distances required to fit the five regular
solids between them as shown.
The answer seemed right to Kepler,
but to prove it he needed to consult the most accurate observations of the
planetary positions available. He sought out Tycho Brahe.
Tycho Brahe
(1546-1601), like Copernicus, thought astronomy immensely important, but saw
the problem with its state not with inadequate theory, but with innacurate observations. Gave his life to getting the
positions right. Adopted a system much like Regiomontanus with earth stationary but planets revolving
around sun.
A web site on Tycho Brahe:
http://csep10.phys.utk.edu/astr161/lect/history/brahe.html
Kepler came to Tycho's attention because of his Cosmographic
Mystery and other achievements that gave Kepler
some reputation. When Kepler sought out Tycho, Tycho hired him as an
assistant to work out the mathematics involved in his observations (and thereby
help Tycho prove that Tycho's
own system was correct).
Kepler went to work for Tycho in
Kepler wanted the data to prove his own system, with the 5 regular solids. In
working with Tycho's data, especially on Mars which has a very irregular orbit, Kepler
uncovers several other mathematical mysteries of the heavens, which he
publishes.
Three of these mysteries have survived,
primarily because
We know these as Kepler's
laws:
1. Planets travel in elliptical
orbits, with the sun at one focus.
2. Planets sweep out equal areas in
equal times (line from sun to planet sweeps out)
3. T2 = k d3
(square of time of revolution proportional to cube of mean distance from sun).
A web
site discussing and illustrating Kepler’s laws:
http://csep10.phys.utk.edu/astr161/lect/history/kepler.html
Another site on Kepler’s laws. The main (only?) virtue of this site is that it has another visual
demonstration of the three laws if you want another look at them.
http://www.cvc.org/science/kepler.htm
And
another: http://www-astro.mps.ohio-state.edu/~pogge/Ast161/Unit3/watershed.html
Point is, these were all magical numerological hocus pocus, the appeal of which
was purely their elegance. Note also the sun's magnetic power of drawing the
planets closer and infusing the planets with the ability to move more quickly
as the sun is neared. Action at a distance -- an occult
quality.
Kepler no more than Copernicus could have brought about a sea change in public
opinion about astronomy and the place of the earth.
GALILEO GALILEI (1564-1642)
Born in
Son of musician
Studied medicine (to earn
a good living) at the
Got interested in mathematics and began
studying it privately.
Left university without a degree, but was
appointed professor of mathematics at
(Paid 1/10 of what a philosophy professor was
paid.)
Galileo detested philosophers. Thought they
merely mouthed dogma. Their dogma was Aristotle, who was a great empiricist,
but the philosophers no longer used their eyes to gain first hand experience of
the world, they only learned what Aristotle and his commentators said. Galileo
liked nothing better than to show up philosophers to be fools.
Mathematician = engineer in XVI -- a person
good with instruments and calculations
Galileo became a fine instrument maker
and inventor of instruments (e.g. one like a slide rule)
Moved to the
A web site on Galileo’s early work. Same topics as above. Good pictures.
http://www-astro.mps.ohio-state.edu/~pogge/Ast161/Unit3/
Galileo became interested in Copernicus to
explain Galileo's theory of the tides.
Galileo believed the tides were
explained by mechanical motion -- the sloshing of water due to the changes in
speed of the earth as the daily and annual motion would be combined and opposed
at different times of day.
A spyglass was invented in
Used his telescope to
spots ships at sea coming into harbor. Sold the telescopes to merchants who wanted to get a
jump on the competition.
After a while, he got the idea to turn the
telescope on the heavens. There, what he saw astounded him. He realized that he
saw so much more clearly with a telescope than with the naked eye that he was
seeing things no one had ever seen before.
It seemed to Galileo that what he saw proved
the general correctness of Copernicus, or, more to the point, proved the
incorrectness of the philosophers, who were all committed to the
Aristotelian-Ptolemaic earth-centered view.
In 1610, Galileo published a slim volume
recounting his observations, The Starry Messenger.
Moon he found rocky and uneven.
Had mountains as large as on earth. Its craters he
thought were seas. Therefore, the earth was not different in kind from the
heavenly bodies, as Aristotle had thought, but instead the heavenly bodies were
like the earth.
Earthshine on the
moon. Therefore irregular bodies can reflect light.
Venus did indeed have phases.
But they could only be seen with the greater resolution of the telescope.
Jupiter has moons. Galileo saw
four satellites of Jupiter. Therefore the earth is not an anomaly in having a
moon.
Milky way
was not just a blur, but a conglomerate of stars. Indeed many more stars were
visible than with the naked eye.
Galileo invited the public to make their own
telescopes and see for themselves.
Galileo became famous. Moved to
Galileo began to undermine Aristotle as the
privileged interpreter of the Bible.
In letter to the Grand Duchess
Christina, Galileo suggests that the Bible needs to be interpreted
figuratively. Viz: when Joshua commands the sun to
stand still (to prolong the day indefinitely), Galileo
argues that this must be taken merely as a convenient way to express the
thought to ordinary people who knew nothing of astronomy. (Because
in Aristotelian-Ptolemaic astronomy, the explanation would actually be more
complex.)
Galileo was playing with fire by suggesting
that the authority of the Church needed to be re-examined. This was the middle
of the Counter-Reformation. Those who opposed any aspect of Church authority
were on thin ice.
In 1616 Galileo was forbidden by the
But the temptation is too great. Galileo itches
to show that the Aristotelians are wrong, and that his
theory of the tides is right (or at least might be). He decides that discussing
the Copernican view is not the same as holding and defending it as true.
In 1632 he completes a dialogue, in the style
of Plato, which discusses the explanation of the tides. After some trouble he
obtains no less than 4 imprimateurs giving permission
of the censors for it to be published. He planned to call it the Dialogue on
the Tides, but perhaps realizing that it really was about much more, dropped
the reference to tides, and the work appeared under the simple title, Dialogue.
History has come to know it better by the expanded title that was appended to
later editions and translations: Dialogue Concerning the Two Chief World
Systems--Ptolemaic and Copernican.
Dialogue has 3 characters:
Salviati =
Galileo = Copernican
Sagredo =
impartial observer, converted to Copernican view
Simplicio =
Aristotelian = fool = pope
The Dialogue systematically refutes every tenet
of Aristotelian cosmology. And upsets the authority of the
Church, which was based upon Aristotelian authority.
Galileo was called before the Inquisition.
Convicted of vehemently suspected heresy, and sentenced to house arrest for the
rest of his life.
A web site on Galileo’s astronomical work:
http://csep10.phys.utk.edu/astr161/lect/history/galileo.html
The Dialogue was banned, of course, which made
it immensely popular, and Galileo had made Copernican astronomy understandable
and reasonable (by simplifying it) and also made a shambles of the
Aristotelian/Ptolemaic world view.
Galileo caused the Copernican Revolution (or
completed it).
Galileo died in the year
Here is a web site from a course in the history of astronomy that pretty well encapsulates everything covered here. This link takes you to the beginning of a unit on Renaissance astronomy with links to all the people mentioned above.
http://www-astro.mps.ohio-state.edu/~pogge/Ast161/Unit3/