BE ' REVOLUTIONIBUS ORBIUM
COELESTIUM- ON THE REVOLUT
OF THE HEAVENLY SPHERES
Nicolaus Copernicus, 1543
the re sult which we hope to attain by the motion of
the Earth. We shall assume this motion as a hypothesis
and follow its consequence."
Nicolaus Copernicus, 1543
.... What if the Sun
Be Center to the World, and other Stars
By this attractive virtue and their own
Incited, dance about him various rounds?
Their wondering course now high, now low, then hid,
Progressive, retrograde, or standing still,'
In six thou seest, and what if seventh to these
The planet Earth, so stedfast though she seems,
Insensibly three different motions move?
- John Milton, Paradise Lost, Book VIII 1667
Table of Contents
The Almagest of Ptolemy 4
Nicolaus Copernicus (1473 - 1543) 5
The Concept of the Sphere 7
Nicolaus Copernicus and Modern Science 8
A Commentary on the Hypothesis Concerning Celestial Motion 15
Preface to De Revolutionibus 18
First Book, De Revolutionibus 22
1. That the Universe is Spherical 22
2. That the Earth also is Spherical 22
3. How Earth, with the Water on it, Forms one Sphere 23
4. That the Motion of the Heavenly Bodies is Uniform, Circular, and
Perpetual, or Composed of Circular Motion 24
5. Whether Circidar Motion Belongs to the Earth; and Concerning its
6. Of the Fastness of the Heavens Compared to the Size of the Earth. ...27
7. Why the Ancients Believed that the Earth is at Rest, like a Centre, in
the Middle of the Universe 28
8. The Insufficiency of these Arguments and Their Refutation 29
9. Whether More than one Motion can be Attributed to the Earth, and of
the Centre of the Universe 32
10. Of the Order of the Heavenly Bodies 33
11. Explanation of the Threefold Motion of the Earth 37
The Study of Astronomy 40
Copernicus Discovered Nothing 45
Apparent Motion and the Orbits of the Planets 46
The Almagest of Ptolemy
Ptolemy worked at the famous University of Alexandria in Egypt
around 150 A.D. Alexandria at that time was the most important city in
the Eastern part of the Mediterranean. Alexandra was built by
Alexander the Great (356 - 323 B.C.) in the 3 rd century B.C. The city
included not only an excellent University, but the famous library of
Alexandria which once held over a million folio and parchments.
The Earth centered, or geocentric, model of the solar system was
developed by Aristotle around 350 B.C. and elaborated by Claudius
Ptolemy of Alexandria around 150 A.D. There had been other
mathematicians like the Pythagorean Philolaus who argued for a Sun
centered, heliocentric, model of the solar system however the
Aristotelians prevailed and Sun centered models of the solar system
were forgotten for fifteen centuries.
Ptolemy outlined his system in a treatise which has become known as
the Almagest, meaning "the greatest". What Ptolemy established for
the first time was a working mathematical model by which the positions
of the planets could be predicted accurately.
In the Ptolemaic system, each planet moved in a small circle known as
an epicycle, whose centre was carried round the Earth in a larger orbit
known as the deferens. For fourteen centuries astronomers computed
planetary positions from tables based on this analysis.
Figure 1 . The
-the Earth is at
the Centre of the
Ptolemy's Almagest was
unknown in the early Middle
Ages. Its first appearance in
Western Europe is in a
translation made direct from the
Greek in Sicily in the year 1 160.
Translation direct from the
Greek was very unusual in the
12 th century.
About 1170 the Englishman
Daniel of Morley was studying
the Arabic text of Ptolemy at
Toledo in Moorish Spain with
the help of a native Arabic-speaking Christian, Ibn Ghalib. Daniel
recounts how he listened in as Ibn Ghalib worked with the famous
translator Gerard of Cremona (died 1 187). Gerard's translation of the
Almagest was completed about 1 1 75 and used in the Middle Ages.
Gerard's translation was from Arabic into Latin.
The Almagest was again translated from the Greek in the 15 th century
by George of Trezibond (1396-1486). Copies were made of the
Trezibond translation in Venice in 1528 and were distributed to libraries
across Italy, including the Medici Library in Florence. It is believed that
Copernicus used a Trezibond copy of the Ptolemy's Almagest.
Nicolaus Copernicus (1473 - 1543)
Copernicus was born on February 19 th , 1473, in Torun, Polish Prussia,
the son of a merchant, youngest child of four. He lost his father at age
ten and was adopted by his uncle.
For his time Copernicus was exceptionally educated. He studied
mathematics and geometry at Crakow, Greek at Bologna, medicine at
Padua in Italy and became Doctor of Canon Law at Ferrara in 1503.
It is worth noting that when Christopher Columbus sailed to the new
world in 1492 Copernicus was a student at the Jagiellonian University
in Crakow; and during his lifetime Magellan's expedition rounded the
world. Copernicus' new celestial investigations were part of this Age of
As a student, Copernicus followed the standard medieval curriculum,
inherited from Roman educational practice: the trivium - grammar,
dialectic, rhetoric - and the quadrivium - arithmetic, music, geometry
and astronomy. On completion of his university education he went on
to lecture in mathematics at Rome.
Cracow was the
ancient capital of
sailed to the
Copernicus was proficient in Greek and Latin, using his linguistic skills
to read, translate and in some cases transcribe several of the
important Greek and Latin books. He was, however not a believer in
Scholasticism. In his late twenties he returned home and was
appointed a canon of Warmia, in Prussian Poland. He retained this
position until his death in 1543; he never married.
Though today he is remembered as the father of modern astronomy, in
his own time he made his livelihood not as an astronomer, but as an
ecclesiastic. His position as canon of the cathedral of Fromback gave
him both financial security and freedom to continue his studies in
medicine, mathematics and astronomy. Copernicus used his medical
skill to help the poor, and his mathematical skills to develop his
It is evident that Copernicus was aware of the work of the ancient
Greek mathematicians and astronomers, including Aristarchus and
Philolaus. Shortly after 1508 Copernicus wrote a brief Commentary on
astronomy which contained the sentence:
"What appears to us as motion of the sun arises not from
its motion but from the motion of the earth."
This important theme occupied his thoughts for the next thirty years. It
was at Fromback in Prussia that Copernicus worked on his great book,
the De Revolutionibus Orbium Coelestium.
1543, the year
model in 350
around 150 A.D.
Although his mathematical and astronomical skills were quite admired
he published his De Revolutionibus reluctantly and only saw the first
printed copy on his deathbed on May 23 rd , 1543.
The accepted model of the structure of the universe before
Copernicus' time was earth-centred. The sun, the moon, the five
known planets, and the stars were thought to revolve about the earth in
endless, perfect circles.
This earth-centred model was developed by Aristotle around 350 B.C.
and elaborated by Claudius Ptolemy of Alexandria around 150 A.D.
Ptolemy's earth-centred model, for a number of reasons, pushed
Aristarchus of Samos' sun-centred model aside.
Ptolemy outlined his system in a treatise which has come to be known
as the Almagest, meaning "the Greatest." What Ptolemy established
for the first time was a working mathematical model by which the
positions of the planets could be accurately predicted.
While Aristarchus' sun-centred model is conceptually correct, neither
Aristarchus nor his successors could build a predictive model based on
the mathematics of the day.
Ultimately such a sun-centred predictive model relies on an in-depth
understanding of projective geometry, of the mathematics of conic
sections (circles, parabolas and ellipses) and of polynomial equations.
In the Ptolemaic system, each planet moved in a small circle
(something called an epicycle) whose centre was carried round the
earth in a larger orbit (or deferent). For fourteen centuries astronomers
computed planetary positions from tables based on this analysis.
Copernicus described an unfamiliar universe, with the sun, not the
earth, at its centre; he treated the earth as a planet amongst the other
planets, with a yearly orbit around the sun, a daily rotation on its axis,
and a conical precession.
Copernicus's great breakthrough is its recognition that the complex
paths which we see traced out in the sky by the planets could be
explained by a combination of their own motion and that of the earth
from which we observe them.
It is worth noting, however, that he arrived at his innovation using some
traditional assumptions, shared by Aristotle and Ptolemy, that the
motion of the heavenly bodies must be a compound of circles, the
major difference being in Copernicus' model the sun was at the centre
of these compound circles.
Copernicus's new model not only gave astronomical inquiry the
direction it still follows today, it also helped to define the beginning of
modern scientific inquiry.
Following closely in his footsteps were other great scientists like
Johannes Kepler (1571 -1630), Galileo Galilei (1564-1642) and Isaac
The Copernican model was not generally accepted until the
seventeenth century. Johannes Kepler working with the finest of
contemporary celestial measurements, found that the planets orbit the
sun in ellipses, and that we could describe these orbits mathematically.
Galileo, outspoken supporter of the Copernican model, used his
telescope to challenge the ancient earth-centered model. Building on
the work of predecessors, Isaac Newton in the 1660's discovered his
theory of Universal Gravitation, showing definitively the validity of the
sun-centered model proposed by Copernicus.
The Concept of the Sphere
The concept of circles and spheres being perfect dates back to the
time of Plato and his treatise Timaeus. The perfection of the sphere
became a central principle of Aristotelian thought and was henceforth
incorporated into the Ptolemaic system.
Aristotle's reasoning was the Heavens were perfect, as are circles and
spheres are perfect, therefore they must govern the motion of the
Heavenly Spheres. Aristotle's thoughts pervade the whole of
astronomy in the Middle Ages until Kepler. The perfection of the
sphere is accepted as a matter of course by Copernicus
the paths of the
planets could be
their own motion
and that of the
reasoning was the
perfect, as are
they must govern
the motion of the
Nicolaus Copernicus and Modern Science
By Wilhelmina Iwanowska
Director of the Astronomical Institute of Nicolaus Copernicus
University, Torun, Poland.
It is hard to believe that one very modest man, living in a remote place
of the Earth - "in hoc remotissimo loco terrae" as he defines his native
country - working not professionally in astronomy, was able to change
essentially the ways of human thought and living with his only book,
which was issued the day of his death.
Born in Torun, Poland in 1473, as a son of a rich merchant who came
to Torun from Cracow, he early lost his father and was educated by his
mother and his uncle, the bishop of Warmia, a northern province of
Poland at the time, and spent four years attending all available
courses, including mathematics and astronomy, for which Cracow
University was then renowned. Later he was sent by his uncle to Italy
for almost seven years of further study in canonical law in Bologna and
medical art in Padova. He obtained his doctoral degree in law at the
University of Ferrara and returned to Poland in 1503.
- only circular
deferens - the
main circle of a
epicycle - the
circle of the orbit
His main interest during his studies in Cracow, however, as well as in
Italy, was astronomy, to which he devoted then and later all his free
time. He considered astronomy the most important and attractive
science but he was conscious that the state of this science was at that
time unsatisfactory, needing some basic reform.
The most important astronomical work before Copernicus was
Almagest written by Ptolemy of Alexandria in the second century A.D.
This work stood at the high mathematical level for that time and
explained the motions of all celestial bodies on the assumption that the
Earth is motionless in the centre of the Universe with all other bodies
revolving around it once a day. In addition, the Sun, the Moon, and the
planets describe their orbits around the Earth.
These orbits were composed of circles: a main one called the
deferens and a secondary one called epicycle, whose centre moved on
the deferens with the planet circling the epicycle. The Earth was not
strictly in the centre of the deferens and the motion was not strictly
Thus Ptolemy disobeyed, to some extent, the principles expressed by
Plato that only circular and uniform motions are appropriate to celestial
bodies. Adjusting the sizes of circles and the periods of revolution for
different planets, Ptolemy achieved with his model a relatively good
agreement between the predicted and observed positions of celestial
bodies and was able to predict their positions several centuries in
advance. With time, however, the discrepancies between the tables
and observations grew bigger and bigger. Astronomers of the Middle
Ages modified the theory by adding new circles to the Ptolemaic model
and changed the assumed values of the parameters.
There were, however, some aspects of the Ptolemaic system which
contradicted the observed facts in an obvious way from the beginning.
For example, the Moon should show its diameter at the quarters to be
twice as great as at Full Moon, which was never observed. To prove
this, while he was in Bolgna, Copernicus and his professor of
astronomy, Maria Domenico Novara, observed the occultation of the
star alpha Taura by the Moon. They did not find any considerable
difference between the Moon's distance at different phases. This and
some other contradictions were probably obvious to Ptolemy himself
and surely to his successors. Nobody worried, however, very much
In error, Ptolemy
predicted that the
Moon should show
its diameter at the
quarters to be
twice as great as
at Full Moon.
Although astronomy was one of the oldest sciences, for some twenty
centuries from antiquity to the time of Copernicus it was nothing more
than a practical tool for measuring time and assisting navigation.
Moreover, astronomy was a domain of myths and legends and served
to cast horoscopes. It was not a means to provide knowledge of the
real world since nobody asked: how is it really? It was sufficient to
have a formal scheme enabling one to predict the positions of celestial
After his return from Italy, Copernicus took a position as canon at the
chapter in Frombork, Warmia, prepared for him by his uncle.
Copernicus was soon involved in many administrative and medical
duties in the unsettled environment of the day, since Warmia and other
northern Polish provinces were under constant attack by the Teutonic
Knights who held the neighbouring region. Copernicus had many
conflicts with them and even organized the military defence of Olsztyn,
asking the Polish King for help. Al these duties did not prevent him
from continuing his astronomical work.
Before 1515 he wrote a booklet in Latin Nicolai Copernici de
hypothesibus motuum coelestium a se constitutes Commentariolus - a
Commentary on the hypothesis concerning celestial motion
established by Nicolaus Copernicus. In this booklet he presented a
first sketch of his heliocentric system, still as a hypothesis. This
booklet was not printed, since printing was a newly discovered art, but
was distributed in handwritten copies to some selected persons.
coelestium a se
- published in
Copernicus needed thirty more years to prove his hypothesis and to
turn it into a scientific theory. The results of these mathematical
elaborations, supported by observations made by himself and by his
predecessors were written in his major work De Revolutionibus orhium
coelestium - On the Revolutions of Celestial Spheres.
Copernicus hesitated to publish his work because of a double fear: that
it was not perfect and that it would be opposed by
"those who basing on some places in the Holy Scriptures,
interpreted badly and perversedly according to their
intentions, will dare to condemn this my theory and
(De rev., dedication letter).
publishing of De
Literally at the last moment, a few years before his death, Copernicus
decided to deliver his work to be printed in Nuremberg, persuaded by
his intellectual friends and his only student George Joachim Rheticus,
a young professor of mathematics at the University of Wittemberg, who
came to Frombork to learn the new theory from Copernicus himself.
Rheticus helped his master to prepare the work for printing and took it
to Nuremberg. The first copies of the printed book arrived in Frombork
when Copernicus was on his deathbed.
The Earth is not a
of the Universe, it
is subject to a
Let us now review what this book contains. Precede by a remarkable
letter dedicating the work to Pope Paul III and by a poetical
introduction glorifying astronomy, the first chapter, called "book"
presents the basic assumptions of the new theory: The Earth is not a
motionless centre of the world, it is subject to a triple motion;
• a daily motion around its axis,
• a yearly revolution around the Sun, and finally,
• the Earth's axis changes slowly its orientation in
space (describing a cone in 26,000 years). The result
of this last motion is a slow drift, called procession, of
the position of the equinoxes relative to the stars.
The Sun, says Copernicus, stays in the centre of the system with the
planets revolving around it in the order of their distances, following the
lengths of their periods of revolution: Mercury, Venus, Earth, Mars,
Jupiter and Saturn. The Earth, with the Moon revolving around it, is
the third planet from the Sun. No planets beyond Saturn were known
at that time.
The arguments for these assumptions were those of greater
probability. It is more probable, says Copernicus, that the Earth
rotates around its axis than that all remaining bodies, including stars,
revolve around the Earth once a day - stars should then have
enormous linear velocities. It is also more probable that the Earth
revolves around the Sun in a year than vice versa, and that the other
planets also revolve around the Sun.
The observed motion of planets can then be interpreted much more
simply, and the loops which they apparently describe reflect simply the
yearly motion of the Earth. The big epicycles introduced by Ptolemy in
order to take account of these loops are no longer necessary.
Furthermore, the Sun is physically distinguished from the planets as
the only shining body. Copernicus also considers it as more probable
that the Earth's axis is swinging than the whole heavens suffer
In addition to these assumptions, Copernicus says in the first book that
the Earth is spherical and the Universe is spherical. He mentions
gravity as a natural property keeping all celestial bodies in their
spherical volumes. He argues that the distance to the stars are
incomparably greater than the dimensions of the planetary system.
This last statement was necessary in order to refute the most serious
criticism raised against his theory; namely, if the Earth orbits the Sun,
why then do not stars reflect this motion in their yearly oscillations
similar to the loops described by planets?
Copernicus' answer was: stars do oscillate, reflecting Earth's yearly
motion, but the amplitude of these oscillations are immeasurably small
because of the enormous stellar distances. As we now know, these
parallactic oscillations were discovered three hundred years later in the
nineteenth century, but they were less than one second of arc. The
fundamental method of determining stellar distances is based on
measuring parallactic motions of stars. Whether the Universe is finite
or infinite Copernicus considers to be an open question.
After such a descriptive outline of his theory, presented in the first book
of the Revolutions, the following five books contain a laborious
mathematical development of the heliocentric model. Assuming the
Earth's triple motion and the orbital revolutions of the planets around
the Sun, Copernicus derives from these assumptions how an observer
on the moving Earth should see the motions of all the other bodies. He
then compares these predicted motions with those observed by his
predecessors and by himself. There are records of about 60
observations made by Copernicus during his life up to the second to
last year before his death. His instruments were very primitive, made
is a form of
The loops the
through the sky
are caused by
motion of the
Earth around the
spherical, as is
small shift of
stars due to
Planets appear to
forward across the
sky, then stop and
Copernicus writes -
a Commentary on
a se constitutes
by himself. They had no lenses, for these were not yet known. What
he could do with these instruments was to measure the angular
distances between planets and stars and the elevations of celestial
bodies above the horizon, he also observed solar and lunar eclipses.
He planned his observations in such a way as to get crucial tests for
his theory, as far as possible. The mathematical tools of Copernicus
were mainly Euclidean geometry and the elements of trigonometry.
Copernicus tried to conform to the Platonic principle of uniform circular
motions, and in Commentariolus he adheres to it strictly, placing the
Sun in the common centre of circular orbits for all the planets. In order
to take account of the non-uniformity of planetary motions, which
Kepler later accomplished by introducing elliptical orbits, Copernicus
introduced small double epicycles, thus keeping all motions uniform
and circular. This resembles very much the development of a periodic
function into a Fourier series, applied so often nowadays. In the
Revolutions Copernicus changes this model, pushing the Sun slightly
out of the centres of the planetary orbits and leaving a single small
It is well known that the Copernican theory was received in a variety of
ways. Some brilliant scientists, like the famous Italian physicist Galileo
Galilei, who lived in both the sixteenth and seventeenth centuries, or
his contemporary, the famous German astronomer, Johannes Kepler,
accepted the new theory with enthusiasm. Galileo realized that it could
not be otherwise, for with his lens telescope, which he was the first to
turn on the sky, he had observed the succession of phases of the
planets Venus, which indicated that it revolved around the Sun. not
around the Earth.
Kepler analyzed long lists of observations of planetary positions made
by his master, Tycho Brahe, and could find the relations, called
Kepler's laws, only by placing the Sun in the centre of the planetary
system. We know that Kepler improved the model of Copernicus by
introducing elliptical orbits and placing the Sun in their common focus.
The planets move with constant areal velocity and their distances to
the Sun are proportional to some power (2/3) of their periods of
But the great majority of people, as well as official organizations such
as the universities and the churches, rejected the theory of
Copernicus. Why? Because it contradicted the common sense of
immobility and of the importance of the Earth, and because it
surpassed the limitations of human senses and of the human brain,
which are anthropocentric in their nature. This opposition reached its
peak at the beginning of the seventeenth century when the Holy
Inquisition forced Galileo to deny and to condemn the Copernican
theory. The work of Copernicus, De Revolutionibus, was put on the list
of prohibited books in 1616 and remained there for more than two
These sad events hindered the acceptance of Copernican theory and
the development of science, but they could not stop it. In the second
half of the seventeenth century we find Isaac Newton, the founder of
mechanics and a pioneer in other branches of physics. In 1687 he
published his major work, Philosophiae Naturalis Principia
Mathematica, in which he formulated the basic principles of dynamics,
defining force as being connected with acceleration, not with velocity
as his predecessors tried to do.
In this same work Newton formulated the law of universal gravitation,
stating that every two masses attract each other with a force
proportional to the mass values and inversely proportional to the
square of their distance. Newton discovered and proved this law, as
well as his principle of dynamics, using planetary motions referred to
the heliocentric system. Kepler's Laws appear as a direct
consequence of Newton's dynamics.
Since the days of Newton it has frequently been found that the
discovery and proof of new laws of nature have required a great
laboratory than those which are available on Earth. In the case of
Newton a laboratory at least as big as the planetary system was
needed and it was Copernicus who brought this laboratory into order.
It was by no means an accident, then, that the development of modern
science began with astronomy. It could not be otherwise.
In order to use Newtonian mechanics for calculating celestial and
terrestrial motions, more sophisticated mathematics than the
elementary one available at the time was needed. It is known that
Newton himself, invented the differential and integral calculus, which
was also established independently by Leibnitz and Descartes, and
had previously invented analytical geometry . Thus, astronomy,
physics and mathematics, helping each other, began their progress
which has continued as an ever-increasing rate up to the present time.
Newton's dynamics together with the law of universal gravitation
served astronomers during the next several centuries as the key to the
solution of all problems of celestial mechanics, especially for the
calculations of the orbits of planets, comets, satellites, natural and
artificial bodies. These orbits are not strictly Keplerian ellipses,
parabolas or hyperbolas because the mutual attraction of all these
bodies perturb the simple orbits. The same Newtonian laws enabled
astronomers to calculate the orbits of double and multiple stars, stellar
orbits in the Galaxy and the motions of the galaxies. The system
worked well until astronomers encountered very large masses and
very large velocities, when it was found that Newtonian mechanics was
At the beginning of the twentieth century Albert Einstein established
the special and general theories of relativity which were
generalizations of Newton's mechanics. These theories were tested
and are still being proven using celestial observations. The successes
attained in mechanics encouraged physicists to perform experiments in
other branches of physics, and during the eighteenth and nineteenth
centuries these other branches, such as optics, magnetism, electricity,
thermodynamics and chemistry, made their appearance. In their turn,
they were successfully applied to astronomy, opening a new field
A common approach to problems, called "the scientific method", first
introduced by Copernicus, was followed in all these investigations.
The method begins with an idea called, "a working hypothesis," but
then needs strict and thorough mathematical consideration of all its
consequences and a confrontation of these consequences with
experiment or observation.
Let us remember that science is still very young, being less than five
hundred years old. It is on its ascending branch, progressing at an
exponential rate. What its progress will be in the next five hundred
years is difficult to predict. One might wish only that it serves to benefit
From: Excerpt from a Copernicus Quincentennial Celebration
presentation to the Royal Astronomical Society of
A Commentary on the Hypothesis
Concerning Celestial Motion
By Nicolaus Copernicus
Our ancestors assumed, I observe, a large number of celestial spheres
for this reason especially, to explain the apparent motion of the planets
by the principle of regularity. For they thought it altogether absurd that
a heavenly body, which is a perfect sphere, should not always move
uniformly. They saw that connecting and combining regular motions in
various ways they could make any body appear to move to any
Callipps and Eudoxus, who endeavored to solve the problem by use of
concentric spheres, were unable to account for all the planetary
movements; they had to explain not merely the apparent revolutions of
the planets but also the fact that these bodies appear to us sometimes
to mount higher in the heavens, sometimes to descend; and this fact is
incompatible with the principle of concentricity. Therefore it seemed
better to employ eccentrics and epicycles, a system which most
scholars finally accepted.
Yet the planetary theories of Ptolemy and most other astronomers,
although consistent with the numerical data, seemed likewise to
present no small difficulty. For these theories were not adequate
unless certain equants were also conceived; it then appeared that a
planet moved with uniform velocity neither on its deferent nor about the
centre of its epicycle. Hence a system of this sort seemed neither
sufficiently absolute nor sufficiently pleasing to the mind.
Having become aware of these defects, I often considered whether
there could perhaps be found a more reasonable arrangements of
circles, from which every apparent inequality would be derived and in
which everything would move uniformly about its proper centre, as the
rule of absolute motion requires.
After I had addressed myself to this very difficult and almost insoluble
problem, the suggestion at length came to me how it could be solved
with fewer and much simpler constructions then were formerly used, if
some assumptions (which are called axioms) were granted me.
They follow in this order:
Seven Axioms 1 ■ There is no one centre of all the celestial circles or spheres.
2. The centre of the Earth is not the centre of the Universe, but
only of gravity and of the lunar sphere.
3. All the spheres revolve about the Sun as their mid-point, and
therefore the Sun is the centre of the Universe.
4. The ratio of the Earth's distance from the Sun to the height of
the firmament is so much smaller than the ratio of the Earth's radius to
its distance from the Sun that the distance from the Earth to the Sun is
imperceptible in comparison with the height of the firmament.
5. Whatever motion appears in the firmament arises not from any
motion of the firmament, but from the Earth's motion. The Earth
together with its circumjacent elements performs a complete rotation
on its fixed poles in a daily motion, while the firmament and highest
heaven abide unchanged.
6. What appear to us as motions of the Sun arise not from its
motions but from the motion of the Earth and our sphere, with which
we revolve about the Sun, like any other planet. The Earth has, then,
more than one motion.
7. The apparent retrograde and direct motion of the planets arise
not from their motion but from the Earth's motion. The motion of the
Earth alone, therefore, suffices to explain so many inequalities in the
Having set forth these assumptions, I shall endeavour briefly to show
how uniformity of the motions can be saved in a systematic way.
However, I have thought it well, for the sake of brevity, to omit from this
sketch mathematical demonstrations, reserving these for my larger
work. But in the explanation of the circles I shall set down here the
lengths of the radii; and from these the reader who is unacquainted
with mathematics will readily perceive how closely this arrangement of
circles agrees with numerical data and observations.
Accordingly, let no one suppose that I have gratuitously asserted, with
the Pythagoreans, the motion of the Earth; strong proof will be found in
my exposition of the circles. For the principal arguments by which the
natural philosophers attempt to establish the immobility of the Earth
rest for the most part on the appearances; it is particularly such
arguments that collapse here, since I treat the Earth's immobility as
due to an appearance.
from: Nicolai Copernici de hypothesibus motuum coelestium a se
constitutes Commentariolus - a Commentary on the hypothesis
concerning celestial motion established by Nicolaus Copernicus, circa
Figure 2. The
the Sun at the
Centre of the
Preface to De Revolutionibus
By Nicolas Copernicus, 1543
To the Most Holy Lord, Pope Paul III
I may well presume, most Holy Father, that certain people, as soon as
they hear that in this book On the Revolutions of the Spheres of the
Universe I ascribe movement to the earthly globe, will cry out, that
holding such views, I should at once be hissed off the stage. For I am
not so pleased with my own work that I should fail duly to weight
judgment which others may pass thereon: and though I know that the
speculations of a philosopher are far removed from the judgment of the
multitude - for his aim is to seek the truth in all things as far as God
has permitted human reason so to do - yet I hold that opinions which
are quite erroneous are to be avoided.
Thinking therefore within myself that to ascribe movement to the Earth
must indeed seem an absurd performance on my part to those who
know that many centuries have consented to the establishment of the
contrary judgment, namely that the Earth is placed immovably at the
central point in the middle of the Universe, I hesitated long whether, on
the one hand, I should give light these my written Commentaries
written to prove the Earth's motion, or whether, on the other hand, it
were better to follow the example of the Pythagoreans and others who
were wont to impart their philosophic mysteries only to intimates and
friends, and then not in writing but by word of mouth, as the letter of
Lysis to Hipparchus witnesses.
In my judgment they did so not, as some would have it, through
jealousy of sharing their doctrines, but as fearing lest these so noble
and hardly won discoveries of the learned should be despised by such
as either care not to study aught save for gain, or, - if by the
encouragement and example of others they are stimulated to
philosophical liberal pursuits - yet by reason of the dullness of their
wits are in the company of philosophers as drones amongst bees.
Reflecting thus, the thought of the scorn which I have to fear on
account of the novelty and incongruity of my theory, well-nigh induced
me to abandon my project.
These misgivings and actual protests have been overcome by my
friends. First among these was Nicolaus Schonberg, Cardinal of
Capua, a man renowned in every department of learning. Next was
one who loved me well, Tiedemann Giese, Bishop of Kulm, a devoted
student of sacred and all other good literature, who often urged and
even importuned me to publish this work which I have kept in store not
for nine years only, but to a fourth period of nine years. The same
request was made to me by many other eminent and learned men.
They urged that I should not, on account of my fears, refuse any longer
to contribute the fruits of my labours to the common advantage of
those interested in mathematics. They insisted that, though my theory
of the Earth's movement might at first seem strange, yet it would
appear admirable and acceptable when the publication of my
elucidatory comments should dispel the mists of paradox. Yielding
then to their persuasion I at last permitted my friends to publish that
work which they have so long demanded.
That I allow the publication of these my studies may surprise your
Holiness the less in that, having been at such travail to attain them, I
had already not scrupled to commit to writing my thoughts about the
motion of the Earth. How I came to dare to conceive such motion of
the Earth, contrary to the received opinion of the Mathematicians and
indeed contrary to the impression of the sense, is what your Holiness
will rather expect to hear. So I should like your Holiness to know that I
was induced to think of a method of computing the motions of the
spheres by nothing else than the knowledge that the Mathematicians
are inconsistent in their investigations.
For, first, the mathematicians are so unsure of the movements of the
Sun and the Moon that they cannot even explain or observe the
constant length of the seasonal year. Secondly, in determining the
motions of these and of the other five planets, they do not even use the
same principles and hypotheses as in their proofs of seeming
revolutions and motions. So some use only concentric circles while
others use eccentrics and epicycles. Yet even by these means they do
completely attain their ends. Those who rely on concentrics, though
they have proven the some different motions can be compounded
therefrom, have not thereby been able fully to establish a system which
agrees with the phenomena. Those again who devised eccentric
systems, though they appear to have well-nigh established the
seeming motions by calculations agreeable to their assumptions, have
yet made any admissions which seem to violate the first principle of
uniformity in motion. Nor have they been able thereby to discern or
deduce the principal thing - namely the shape of the Universe and the
unchangeable symmetry of its parts.
With them it is as though an artist were to gather the hands, feet, head
and other members from his images from divers models, each part
excellently drawn, but not related to a single body, and since they in no
way match each other, the result would be monster rather than man.
So in the course of their exposition, which the mathematicians cal their
system we find that they have either omitted some indispensable detail
or introduced something foreign and wholly irrelevant. This would of a
surety not have been so had they followed fixed principles; for if their
hypotheses were not misleading, all inferences based thereon might
be surely verified. Though my present assertions are obscure, they
will be made clear in due course.
I pondered long upon this uncertainty of mathematical tradition in
establishing the motions of the systems of the spheres. At last I began
to chafe that philosophers could by no means agree on any one certain
theory of the mechanism of the Universe, wrought for us by the
supremely good and orderly Creator, though in other respects they
investigated with meticulous care the minutest points relating to its
orbits. I therefore took pains to read again the works of all the
philosophers on whom I could lay hand to seek out whether any of
them had ever supposed that the motions of the spheres were other
than those demanded by the mathematical schools.
I found first in Cicero that Hicetas had realized that the Earth moved.
Afterwards I found in Plutarch that certain others had held the like
opinion. I think fit here to add Plutarch's own words, to make them
accessible to all:
"The rest hold the Earth to be stationary, but Philolaus
the Pythagorean says that she moves around the
(central) fire on an oblique circle like the Sun and the
Moon. Heraclides of Pontus and Ecphantus the
Pythagorean also make the Earth to move, not indeed
through space but by rotating round her own centre as a
wheel on an axle from west to East."
Taking advantage of this I too began to think of the mobility of the
Earth; and though the opinion seemed absurd, yet knowing now that
others before me had been granted freedom to imagine such circles as
they chose to explain the phenomena of the stars, I considered that I
also might easily be allowed to try whether, by assuming some motion
of the Earth, sounder explanations than theirs for the revolution of the
celestial spheres might also be discovered.
Thus assuming motions, which in my work I ascribe to the Earth, by
long and frequent observations I have at last discovered that, if the
motions of the rest of the planets be brought into relation with the
circulation of the Earth and be reckoned in proportion to the orbit of
each planet, not only do their phenomena presently ensue, but the
order and magnitudes of all stars and spheres, nay the Heavens
themselves, become so bound together that nothing in any part thereof
could be moved from its place without producing confusion of all the
other parts and of the Universe as a whole.
In the course of the work the order which I have pursued is as here
follows: In the first book I describe the position of the spheres together
with such movements as I ascribe to Earth; so that this book contains,
as it were, the general system of the Universe. Afterwards, in the
remaining books, I relate the motions of the other planets and all the
spheres to the mobility of the Earth that we may gather thereby how far
the motions and appearances of the rest of the planets and spheres
may be preserved, if related to all the motions of the Earth.
I doubt not that gifted and learned mathematicians will agree with me if
they are willing to comprehend and appreciate, not superficially but
thoroughly, according to the demands of this science, such reasoning
as I bring to bear in support of my judgment. But that learned and
unlearned alike may see that I shrink not from any man's criticism, it is
your Holiness rather than anyone else that I have chosen to dedicate
these studies of mine, and since in this remote corner of Earth in which
I live you are regarded as the most eminent by virtue alike of the
dignity of your Office and of your love of letters and science.
You by your influence and judgment can readily hold the slanderers
from biting, though the proverb hath it that there is no remedy against
the sycophant's tooth. It may fall out, too, that idle babblers, ignorant
of mathematics, may claim a right to pronounce a judgment on my
work, by reason of a certain passage of Scripture basely twisted to suit
their purpose. Should any such venture to criticize and carp at my
project, I make no account of them; I consider their judgment rash, and
utterly despise it. I well know that even Lactantius, a writer in other
ways distinguished but in no sense a mathematician, discourses in a
most childish fashion touching the shape of the Earth, ridiculing even
those who have stated the Earth to be a sphere. Thus my supporters
need not be amazed if some people of like sort ridicule me too.
Mathematics is for mathematicians, and they, if I be not wholly
deceived, will hold that these my labours contribute somewhat even to
the Commonwealth of the Church, of which your Holiness is now
Prince. For not long since, under Leo X, the question of correcting the
ecclesiastical calendar was debated at the Council of the Lateran. It
was left undecided for the sole cause that the lengths of the years and
months and motions of the Sun and Moon were not held to have been
yet determined with sufficient exactness.
From that time on I have given thought to their more accurate
observation, by the advice of the eminent Paul, Lord Bishop of
Sempronia, sometime in charge of that business of the calendar. What
results I have achieved therein, I leave to the judgment of learned
The titles to
several of the
mathematicians and of your Holiness in particular. And now, not to
seem to promise your Holiness more than I can perform with regard to
usefulness of the work, I pass to my appointed task.
First Book, De Revolutionibus
By Nicolas Copernicus 1543
1 . That the Universe is Spherical
In the first place we must observe that the Universe is spherical. This
is either because that figure is the most perfect, as not being
articulated but whole and complete in itself; or because it is most
capacious and therefore best suited for that which is to contain and
preserve all things; or again because all the perfect parts of it, namely,
Sun, Moon and Stars, are so formed; or because all things tend to
assume this shape, as is seen in the case of drops of water and liquid
bodies in general if freely formed. No one doubts that such a shape
has been assigned to Heavenly bodies.
2. That the Earth also is Spherical
The Earth also is spherical, since on all sides it inclines towards the
centre. At first sight, the Earth does not appear absolutely spherical,
because of the mountains and valleys; yet these make but little
variation in its general roundness, as appears with what follows. As
we pass from any point northward, the North Pole of the daily rotation
gradually rises, while the other pole sinks correspondingly and more
stars near the North Pole cease to set, while certain stars in the South
do not rise. Thus, Canopus, invisible in Italy, is visible in Egypt, while
the last star of Eradinus, seen in Italy, is unknown in our colder zone.
On the other hand, as we go southward, these stars appear higher,
while those which are high for us appear lower. Further, the change in
altitude of the pole is always proportional to the distance traversed on
the Earth, which could not be save on a spherical figure. Hence the
Earth must be finite and spherical.
Furthermore, dwellers in the East do not see eclipses of the Sun and
Moon which occur in the evening here, nor do they in the West see
those which occur here in the morning. Yet mid-day eclipses here are
seen later in the day by the eastward dwellers, earlier by the
westerners. Sailors too have noted that the sea also assumes the
same shape, since land invisible from the ship is often sighted at the
mast-head. On the other hand, if some shining object at the mast-
head be observed from the shore, it seems gradually to sink as the
vessel leaves the land. It is also a sure fact that water free to flow
always seeks a lower level, just as the Earth does, nor does the sea
come higher up the shore than the convexity of the Earth allows. It
therefore follows the land, rising above the level of Ocean, is by so
much further removed from the centre.
3. How Earth, with the Water on it, Forms one Sphere
The waters spread around the Earth form the sea and fill the lower
declivities. The volume of the waters must be less than that of the
Earth, else they would swallow up the land (since both, by their weight,
press towards the same centre). Thus, for the safety of living things,
stretches of the Earth are left uncovered, and also numerous islands
widely scattered. Nay, what is a continent, and indeed the whole of the
Mainland, but a vast island?
We must pass by certain Peripatetics who claim the volume of the
waters to be ten times that of the Earth. They base themselves on a
mere guess that in the transmutation of the elements, one part of Earth
is resolved into ten parts of water. They say, in fact, that the Earth
rises to a certain height above the water because, full of cavities, it is
not symmetrical as regards weight and therefore the centre of weight
does not accord with the geometrical centre. Ignorance of geometry
prevents them from seeing that the waters cannot be even seven times
as great if some parts of the Earth is to be left dry, unless the Earth, as
being heavier, be quite removed from the centre of gravity to make
room for the waters. For spheres are to each other as the cubes of
their diameters. If, therefore, there have been seven parts of water to
one of Earth, the Earth's diameter could not be greater than the radius
of the waters. Even less is it possible that the waters could be ten
times as great as the Earth.
There is, in fact, no difference between the Earth's centre of gravity
and its geometric centre, since the height of the land above the ocean
does not increase continuously - for so it would utterly exclude the
waters and there would be no great gulfs of seas between parts of the
Mainland. Further, the depth of the ocean would constantly increase
from the shore outwards, and so neither island or rock nor anything of
the nature of land would be met by sailors, how far soever they
ventured. Yet, we know that between the Egyptian Sea and the
Arabian Gulf, well-nigh in the middle of the great land-mass, is a
passage barely 15 stades wide. On the other hand, in his
Cosmography Ptolemy would have it that the habitable land extends to
the middle circle with a terra incognita beyond where discovery has
added Cathay and a very extensive region as far as 60° of longitude.
Thus we know now that the Earth is inhabited to a greater longitude
than is left for Ocean.
This will more evidently appear if we add the islands found in our own
time under the Princes of Spain and Portugal, particularly America, a
land named after the Captain who discovered it and, on account of its
unexplored size, reckoned as another Mainland - besides many other
islands hitherto unknown. We thus wonder the less at the so-called
Antipodes or Antichthones. For geometrical arguments demands that
the Mainland of America on account of its postion be diametrically
opposite to the Ganges basin in India.
From such considerations then, it is clear that Land and Water have
the same centre of gravity, which coincides with the centre of Earth's
volume, yet since Earth is heavier, and its chasms filled with water,
therefore the quantity of water is moderate as against Earth, though,
as to the surface, there may perhaps be more water. Moreover, the
Earth, with the waters around it, must have a shape conformable with
its shadow. Now at the Moon's eclipse we see a perfect arc of a circle;
the Earth therefore is not flat as Empedocles and Anaxagoras would
have it, nor drum shape as Leucippus held, nor bowl shape as
Heraclitus said, nor yet concave in some other way as Democritus
believed; nor again cylindrical as Anaximander maintained, nor yet
infinitely thick with roots extending below as Xenophanes represented;
but perfectly round, as the Philosophers rightly held.
4. That the Motion of the Heavenly Bodies is Uniform,
Circular, and Perpetual, or Composed of Circular Motion
We now note that the motion of the heavenly bodies is circular.
Rotation is natural to a sphere and by that very act is its shape
expressed. For here we deal with the simplest kind of body, wherein
neither beginning nor end may be discerned nor, if it rotate ever in the
same place, may the one de distinguished from the other.
Now in the multitude of heavenly bodies various motions occur. Most
evident to sense is the diurnal rotation, marking day and night. By this
motion the whole Universe, save Earth alone, is thought to glide from
East to West. This is the common measure of all motions, since time
itself is measured in days. Next we see other revolutions in contest, as
it were, with this daily motion and opposing it from West to East. Such
opposing motions are those of Sun and Moon and the five planets. Of
these the Sun portions out the year, the Moon the month, the common
measures of time. In like manner the five planets define each of his
own independent period.
But these bodies exhibit various differences in their motion. First their
axes are not that of diurnal rotation, but of the Zodiac, which is oblique
thereto. Secondly, they do not move uniformly even in their own orbits;
for are not Sun and Moon found now slower, now swifter in their
courses? Further, at times the five planets become stationary at one
point and another even go backward. While the Sun ever goes
forward unswerving on his own course, they wander in divers ways,
straying southward, now northward. For this reason they are named
Planets. Furthermore, sometimes they approach Earth, being there in
Perigee, while at other times receding they are in Apogee.
Nevertheless, despite these irregularities, we must conclude that the
motions of these bodies are ever circular or compounded of circles.
For the irregularities themselves are subject to a definite law and recur
at stated times, and this could not happen if the motions were not
circular, for a circle alone can thus restore the place of a body as it
was. So with the Sun which, by a compounding of circular motions,
brings ever again the changing days and nights and the four seasons
of the year. Now therein it must be that divers motions are conjoined,
since a simple celestial body cannot move irregularly in a single orbit.
For such irregularity must come of unevenness either in the moving
force (whether inherent or acquired) or in the form of the revolving
body. Both these alike the mind abhors regarding the most perfectly
It is then generally agreed that the motions of the Sun, Moon and
Planets do but seem irregular either by reason of the divers directions
of their axes of revolution, or else by reason that Earth is not the centre
of the circles in which they revolve, so that to us on Earth the
displacements of these bodies when they seem greater than when
they are more remote, as is shown in the Optics. If then we consider
equal arcs in the paths of the planets we find that they seem to
describe differing distances in equal period of time. It is therefore
above all needful to observe carefully the relation of the Earth toward
the Heavens, lest, searching out the things on high, we should pass by
those nearer at hand, and mistakenly ascribe earthly qualities to
5. Whether Circular Motion Belongs to the Earth; and
Concerning its Position
Since it has been shown that Earth is spherical, we now consider
whether her motion is conformable to her shape and her position in the
Universe. Without these we cannot construct a proper theory of the
heavenly phenomena. Now authorities agree that Earth holds firm her
place at the centre of the Universe, and they regard the contrary as
unthinkable, nay as absurd. Yet if we examine more closely it will be
seen that this question is not so settled, and needs wider
A seeming change of place may come of movement either of object or
of observer, or again of unequal movements of the two (for between
equal and parallel motions no movement is perceptible). Now it is
Earth from which the rotation of the Heavens is seen. If then some
motion of Earth is assumed it will be reproduced in external bodies,
which will seem to move in the opposite direction.
Consider first the diurnal rotation. By it the whole Universe, save Earth
alone and its contents, appears to move very swiftly. Yet grant that
Earth revolves from West to East, and you will find, if you ponder it,
that my conclusion is right. It is the vault of Heavens that contains all
things, and why should not mention be attributed rather the contained
than to the container, to the located than the locater? The later view
was certainly that of Heraclides and Ecphantus the Pythogorean and
Hicetas of Syracuse (according to Cicero). All of them made the Earth
rotate in the midst of the Universe, believing that the Stars set owing to
the Earth coming in the way, and rise again when it has passed on.
There is another difficulty, namely, the position of the Earth. Nearly all
have hitherto held that Earth is at the centre of the Universe. Now,
grant that Earth is not at the exact centre but at a distance from it
which, while small compared to the starry sphere, is yet considerable
compared to the orbits of Sun and the other planets. Then calculate
the consequent variations in their seeming motions, assuming these to
be really uniform and about the some centre other than the Earth's.
One may then perhaps adduce a reasonable cause for these variable
motions. And indeed since the Planets are seen at varying distances
from the Earth, the centre of the Earth is surely not the centre of their
orbits. Nor as it certain whether the Planets move toward and away
from Earth, or Earth toward or away from them. It is therefore
justifiable to hold that the Earth has another motion in addition to
diurnal rotation. That the Earth, besides rotating, wanders with several
motions and is indeed a Planet, is a view attributed to Philolaus the
Pythagorean, no mean mathematician, and one whom Plato is said to
have eagerly sought out in Italy.
Many, however, have thought that Earth could be shown by geometry
to be at the centre and like a mere point in the vast Heavens. They
have thought too that Earth, as centre, remains unmoved, since if the
whole system move the centre must remain at rest, and the parts
nearest the centre must move slowly.
6. Of the Vastness of the Heavens Compared to the
Size of the Earth
That the size of the Earth is insignificant in comparison with the
Heavens, may be inferred thus.
The bounding Circles (interpreting the Greek word horizons) bisect the
Celestial Sphere. This could not be if the size of the Earth or its
distance from the centre were considerable compared with the
Heavens - for a circle to bisect a sphere must pass through its centre
and be in fact a "great circle."
Let the circle ABCD represent the
celestial horizon, and E the point of
the Earth from which we observe.
The "horizon" or boundary line
between bodies visible and bodies
31 [ •).-,.-... g£ i i In invisible has its centre at this point.
Suppose that from point E we
observe with Dioptra or Astrolabe or
Chorobates the first point of the sign
Cancer rising at C and at the same
moment the first point of Capricorn
setting at A. AEC, since it is
observed as a straight line through Dioptra, is a diameter of the
Ecliptic, for six Zodiacal Signs from a semicircle and its centre E
coincides with that of the horizon. Next, suppose that after some time
the first point of Capricorn rises at B; then Cancer will be seen setting
at D, and BED will be a stright line, again a diameter of the ecliptic.
Hence, it is clear that E, the point of intersection of the two lines, is the
centre of the horizon. Therefore the horizon always bisects the
ecliptic, which is a great circle on the sphere. But a circle that bisects
a great circle must itself be a great circle. Therefore the horizon is a
great circle and its centre is that of the ecliptic.
It is true that a line from the surface of Earth cannot coincide with the
one from its centre. Yet owing to their immense length compared to
the size of the Earth these lines are practically parallel. Moreover,
owing to the great distance of their meeting point they are practically
one line - for the distance between them is immeasurably small in
comparison with their length - as is shown in Optics. It therefore
follows that the Heavens are immeasurable in comparison with the
Earth. Thus the Earth appears as a mere point compared to the
Heavens, as a finite thing to the infinite.
Yet it does not follow that the Earth must be at rest at the centre of the
Universe. Should we not be more surprised if the vast Universe
revolved in twenty-four hours, then the little Earth should do so? For
the idea that the centre is at rest and the parts nearest it moves least
does not imply that Earth remains still. It is merely as one should say
that the Heavens revolve, but the poles are still, and the parts nearest
them move the least (as Cynosura moves slower than Aquila or
Procyon because, being near the pole, it describes a smaller circle).
These all belong to the same sphere, whose motion becomes zero at
the axis. Such motion does not admit that all the parts have the same
rate of motion, since the revolution of the whole brings back each point
to the original position in the same time, though the distances moved
So too, it may be said, Earth, as part of the celestial sphere, shares in
the motion thereof, though being at the centre she moves but little.
Being herself a body and not a mere point, she will therefore move
through the same angle as the Heavens but with a smaller radius in
any given period of time. The falsity of this is clear, for if true it would
always be mid-day in one place and mid-night in another, and the daily
phenomena of rising and setting could not occur, for the motion as a
whole and the part are one and inseparable. A quite different theory is
required to explain the various motions observed, namely the bodies
moving in smaller paths revolve more quickly than those moving in
larger paths. Thus Saturn, most distant of the Planets, revolves in 30
years, and Moon, nearest Earth, compasses her circuit in a month.
Lastly, then, the Earth must be taken to go round in the course of a day
and a night, and so doubt is again cast on the diurnal rotation of the
Besides we have not yet fixed the exact position of the Earth, which as
shown above, is quite uncertain. For what was proved is only the vast
size of the Heavens compared with the Earth, but how far this
immensity extends is quite unknown.
7. Why the Ancients Believed that the Earth is at
Rest, like a Centre, in the Middle of the Universe.
The ancient Philosophers tried by divers other methods to prove Earth
fixed in the midst of the Universe. The most powerful argument was
drawn by the doctrine of the heavy and the light. For, they arguer,
Earth is the heaviest element, and all things of weight move towards it,
tending to its centre. Hence, since the Earth is spherical, and heavy
things more vertically to it, they would all rush together to the centre if
not stopped at the surface. Now these things which move towards the
centre must, on reaching it, remain at rest. Much more then will the
whole Earth remain at rest at the centre of the Universe. Receiving all
falling bodies, it will remain immovable by its won weight.
Another argument is based on the supposed nature of motion.
Aristotle says that the motion of a single and simple body is simple. A
simple motion may be either straight, or circular. Again a straight
motion may be either up or down. So every simple motion must be
either toward the centre, namely downward, or away from the centre,
namely upward, or round the centre, namely circular. Now it is a
property only of the heavy elements earth and water to move
downward, that is to seek the centre. But the light elements air and fire
move upward away from the centre. Therefore we must ascribe
rectilinear motion to these four elements. The celestial bodies
however have circular motion. So far Aristotle.
If then, says Ptolemy, Earth moves at least with a diurnal rotation, the
result must be reverse of that described above. For the motion must
be of excessive rapidity, since in 24 hours it must impart a complete
rotation to the Earth. Now things rotating very rapidly resist cohesion
or, if united, are apt to disperse, unless firmly held together. Ptolemy
therefore says that Earth should have been dissipated long ago, and
(which is the height of absurdity) would have destroyed the Heavens
themselves; and certainly all living creatures and other heavy bodies
free to move could not have remained on its surface, but must be
shaken off. Neither could falling objects reach their appointed place
vertically beneath, since in the meantime the Earth would have moved
swiftly from under them. Moreover clouds and everything in the air
would continually move westward.
8. The Insufficiency of these Arguments and Their
For these and like reasons, they say that Earth surely rests at the
centre of the Universe. Now if one should say that the Earth moves,
that is as much as to say that the motion is natural, not forced; and
things which happen according to nature produce the opposite effects
to those due to force. Things subjected to any force, gradual or
sudden, must be disintegrated, and cannot long exit. But natural
processes being adapted to their purpose work smoothly.
Idle therefore is the fear of Ptolemy that Earth and all thereon would be
disintegrated by natural rotation, a thing far different from an artificial
act. Should he not fear even more for the Universe, whose motion
must be as much more rapid as the Heavens are greater than the
Earth? Have the Heavens become so vast because of the centrifugal
force of their violent motion, and would they collapse if they stood still?
If this were so the Heavens must be of finite size. For the more they
expand by centrifugal force of their motion, the more rapid will become
the motion because of the ever increasing distance to be traversed in
24 hours. And in turn, as the motion waxes, must the immensity of the
Heavens wax. Thus velocity and size would increase each the other to
infinity - and as the infinite neither be traversed nor moved, the
Heavens must stand still!
They say too that outside the Heavens is no body, no space nay not
even void, in fact absolutely nothing, and therefore no room for the
Heavens to expand. Yet surely it is strange that something can be
held by nothing. Perhaps indeed it will be easier to understand this
nothingness outside the Heavens if we assume them to be infinite, and
bounded internally only by their concavity, so that everything, however
great, is contained in them, while the Heavens remains immovable.
For the fact that it moves is the principal argument by which men
inferred that the Universe is finite.
Let us then leave to Physicists the question whether the Universe be
finite or no, holding only to this that Earth is finite and spherical. Why
then hesitate to grant Earth that power of motion natural to its shape,
rather than suppose a gliding round of the whole Universe, whose
limits are unknown and unknowable? And why not grant that the
diurnal rotation is only apparent in the Heavens but real in the Earth?
It is but as the saying of Aeneas in Virgil - "We sail forth from the
harbour, and lands and cities retire." As the ship floats along in the
calm, all external things seem to have the motion that is really that of
the ship, while those within the ship feel that they and all its contents
are at rest.
It may be asked what of the clouds and other objects suspended in the
air, or sinking and rising in it? Surely not only the Earth, with the water
on it, moves thus, but also a quantity of air and all things associated
with the Earth. Perhaps the contiguous air contains an admixture of
earthy and watery matter and so follows the same natural law as the
Earth, or perhaps the air acquires motion from the perpetually rotating
Earth by propinquity and absence of resistance. So the Greeks
thought that the higher regions of the air follow the celestial motion, as
suggested by those swiftly moving bodies, the "Comets," or "Pogoniae"
as they called them, for whose origin they assign this region, for these
bodies rise and set like other stars. We observe that because of the
great distance from the Earth that part of the air is deprived of
terrestrial motion, while the air nearest the Earth, with objects
suspended in it, will be stationary, unless disturbed by the wind or
other impulse which moves with them this way or that - for a wind in
the air is as a current in the sea.
We must admit the possibility of a double motion of objects which fall
and rise in the Universe, namely the resultant of rectilinear and circular
motion. Thus heavy falling objects, being specially earthy, must
doubtless retain the nature of the whole to which they belong. So also
there are objects which by their fiery force can carry into the higher
regions. This terrestrial fire is nourished particularly by earthy matter,
and flame is simply burning smoke. Now it is the property of fire to
expand that which it attacks, and this so violently that it cannot in any
wise be restrained from breaking its prison and fulfilling its end. The
motion is one of extension from the centre outward, and consequently
any earthy parts set on fire are carried to the upper region.
That the motion of a simple body must be simple is true then primarily
of circular motion, and only so long as the simple body rests on its own
place and state. In that state no motion save circular is possible, for
such motion is wholly self-contained and similar to being at rest. But if
objects move or are moved from their natural place rectilinear motion
supervenes. Now it is inconsistent with the whole order and form of the
Universe that it should be outside its own place. Therefore there is no
rectilinear motion save of objects out of their right place, nor is such
motion natural to perfect objects, since they would be separated from
the whole to which they belong and thus would destroy its unity.
Moreover, even apart from circular motion, things moving up and down
do not move simply or uniformly; for they cannot avoid the influence of
their lightness or weight. Thus all things which fall begin by moving
slowly, but their speed is accelerated as they go. On the other hand
earthly fire (the only kind we can observe) when carried aloft loses
energy, owing to the influence of the earthy matter.
A circular motion must be uniform for it has a never falling cause of
motion; but other motions have always a retarding factor, so that
bodies having reached their natural place cease to be either heavy or
light, and their motion too ceases.
Circular motion then is of things as a whole, parts may possess
rectilinear motion as well. Circular motion, therefore may be combined
with rectilinear - just as a creature may be at once animal and horse.
Aristotle's method of dividing simple motion into three classes, from the
centre, to the centre, and round the centre, is thus merely abstract
reasoning; just as we form separate conceptions of a line, a point, and
a surface, thought they cannot exist without another, and none can
exist without substance.
Further, we conceive immobility to be nobler and more divine than
change and inconstancy, which latter is thus more appropriate to Earth
than to the Universe. Would it not then seem absurd to ascribe motion
to that which contains or locates, and not rather to the contained and
located, namely the Earth?
Lastly, since the planets approach and recede from the Earth, both
their motion around the centre, which is held to be the Earth, and also
their motion outward and inward are the motion of one body.
Therefore we must accept this motion around the centre in a more
general sense, and must be satisfied that every motion has a proper
centre. From all these considerations it is more probable that the Earth
moves that that it remains at rest. This is especially the case with the
diurnal rotation, as being particularly a property of the Earth,
9. Whether More than one Motion can be Attributed to
the Earth, and of the Centre of the Universe.
Since then there is no reason why the Earth should not possess the
power of motion, we must consider whether in fact it has more motions
than one, so as to be reckoned as a Planet.
That Earth is not the centre of all revolutions is proved by the
apparently irregular motions of the planets, and the variations in their
distances from the Earth. These would be unintelligible if they moved
in circles concentric with Earth. Since, therefore, there are more
centres than one, we may discuss whether the centre of the Universe
is or is not the Earth's centre of gravity.
Now it seems to me gravity is but a natural inclination, bestowed on the
parts of bodies by the Creator so as to combine the parts in the form of
a sphere and thus contribute to their unity and integrity. And we may
believe this property present even in the Sun, Moon and Planets, so
that thereby they retain their spherical form notwithstanding their
various paths. If, therefore, the Earth also has other motions, these
must necessarily resemble the many outside motions having a yearly
period. For if we transfer the motion of the Sun to the Earth, taking the
Sun to be at rest, then morning and evening settings of Stars will be
unaffected, while the stationary points, retrogressions, and
progressions of the Planets are due not to their own proper motions,
but to that of the Earth, which they reflect. Finally we shall place the
Sun himself at the centre of the Universe. All this is suggested by the
systematic procession of events and harmony of the whole Universe, if
only we face the facts, as they say, "with both eyes open."
10. Of the Order of the Heavenly Bodies
No one doubts that the Sphere of the Fixed Stars is the most distant of
visible things. As for the planets, the early Philosophers were inclined
to believe that they form a series in order of magnitude of their orbits.
They adduce the fact that of objects moving with equal speed, those
further distant seem to move more slowly (as is proved in Euclid's
Optics). They think that the Moon describes her path in the shortest
time, because, being nearest to the Earth, she revolves in the smallest
circle. Furthest they place Saturn, who in the longest time describes
the greatest orbit. Nearer than this is Jupiter, and then Mars.
Opinions differ as to Venus and Mercury which, unlike the others, do
not altogether leave the Sun. Some place them beyond the Sun, as
Plato in his Timaeus, others nearer the Sun, as Ptolemy and many of
the moderns. Alpetragius makes Venus nearer and Mercury further
than the Sun. If we agree with Plato in thinking that the planets are
themselves dark bodies that do but reflect the light from the Sun, it
must follow, that if nearer than the Sun, on account of their proximity to
him they would appear as half or partial circles; for they would
generally reflect such light as they receive, upwards, that is toward the
Sun, as with the waxing and waning Moon. Some think that since no
eclipse even proportional to their size is ever caused by these planets
they can never be beween us and the Sun.
On the other hand, those who place Venus and Mercury nearer the
Sun adduce in support the great distance which they posit between
Sun and Moon. For the maximum distance of Moon from Earth,
namely 64 1/6 times Earth's radius, they calculate is about 1/18 of the
minimum distance from the Sun to Earth, which is 1160 times Earth's
radius. So the distance between the Sun and the Moon is 1096 such
units. So vast a space must not remain empty. By calculating the
widths of the paths of these planets from their greatest and least
distances from the Earth they find that the sum of the widths is
approximately the same as the whole distance. Thus the perigee of
Mercury comes immediately beyond the apogee of the Moon and the
apogee of the Mercury is followed by the perigee of Venus, who finally,
at her apogee practically reaches the perigee of the Sun. For they
estimate that the difference between the greatest and least distances
of Mercury is nearly 177 Vz of the aforesaid units, and the remaining
space is very nearly filled up by the difference between the maximum
and minimum distances of Venus, reckoned at 910 units.
They therefore deny that the planets are opaque like the Moon, but
think that they either shine by their own light or that their bodies are
completely pervaded by the light of the Sun. They also claim that the
Sun is not obstructed by them for they are very rarely interposed
between our eyes and the Sun since they usually differ from him in
latitude. They are small, too, compared with the Sun. According to
Albategni Aratenis even Venus, which is greater than Mercury, can
scarcely cover a hundredth part of the Sun. He estimates the Sun's
diameter to be ten times that of Venus; and, therefore, so small a spot
to be almost invisible in so powerful a light. Averroes indeed, in his
Paraphrases of Ptolemy, records that he saw a kind of black spot when
investigating the numerical relations between the Sun and Mercury.
This is the evidence that these two planets are nearer than the Sun.
But this reasoning is weak an uncertain. Whereas the least distance of
the Moon is 38 times Earth's radius, according to Ptolemy, but
according to a truer estimate, more than 52 yet we are not aware of
anything in all that space except air, and, if you will, the so called "fiery"
element." Besides, the diameter of the orbit of Venus, but which she
passes to a distance of 45 degrees more or less on either side of the
Sun, must be six times the distance from the Earth's centre to her
perigee. What then will they say is contained in the whole of that
space, which is so much bigger than that which could contain the
Earth, the Air, the Aether, the Moon and Mercury, in addition to the
space that the huge epicycle of Venus would occupy if it revolved
round the resting Earth?
Unconvincingly too is Ptolemy's proof that the Sun moves between the
bodies that do and those that do not recede from him completely.
Consideration of the case of the Moon, which does so recede, exposes
his falseness. Again, what cause can be alleged, by those who place
Venus nearer than the Sun, and Mercury nest, or in some other order?
Why should not these planets also follow separate paths, distinct from
that of the Sun, as do the other planets? and this might be said even if
their relative swiftness and slowness does not belie their alleged order.
Either then the Earth cannot be the centre to which the order of the
planets and their orbits are related, or certainly their relative order is
not observed, nor does it appear why a higher position should be
assigned Saturn than Jupiter, or any other planet.
Therefore I think we must seriously consider the ingenious view held
by Martianus Capella the author of the Encyclopedia and certain other
Latins that Venus and Mercury do not go round the Earth like the other
planets but run their courses with the Sun as centre, and so do not
depart from him further than the size of their orbits allows. What else
can they mean than that the centre of these orbits is near the Sun? So
certainly the orbit of Mercury must be within that of Venus, which, it is
agreed, is more than twice as great.
We may now extend this hypothesis to bring Saturn, Jupiter and Mars
also into relation with this centre, making their orbits great enough to
contain those of Venus and Mercury and Earth; and their proportional
motions according to the Table demonstrate this. These outer planets
are always nearer to the Earth about the time of their evening rising,
that is, when they are in opposition to the Sun, and the Earth between
them and the Sun. They are more distant from the Earth at the time of
their evening setting, when they are in conjunction with the Sun and
the Sun between them and the Earth. These indications prove that
their centre pertains rather to the Sun than to the Earth, and that this is
the same centre as that to which the revolutions of Venus and Mercury
But since all these have one centre it is necessary that the space
between the orbit Venus and the orbit of Mars must be viewed as a
Sphere concentric with the others, capable of receiving the Earth with
her satellite the Moon and whatever is contained within the Sphere of
the Moon - for we must not separate the Moon from the Earth, the
former being beyond all doubt nearer to the latter, especially as in that
space we find suitable and ample room for the Moon.
We therefore assert that the centre of the Earth, carrying the Moon's
path, passes in a great orbit among the other planets in an annual
revolution round the Sun; that near the Sun is the centre of the
Universe; and that whereas the Sun is at rest, any apparent motion of
the Sun can be explained by motion of the Earth. Yet so great is the
Universe that though the distance of the Earth from the Sun is not
insignificant compared with the size of any other planetary path, in
accordance with the ratios of their sizes, it is insignificant compared
with the distance of the Sphere of Fixed Stars.
I think it is easier to believe this than to confuse the issue by assuming
a vast number of Spheres, which those who keep Earth at the centre
must do. We thus rather follow Nature, who producing nothing vain or
superfluous often prefers to endow one cause with many effects.
Though these views are difficult, contrary to expectation, and certainly
unusual, yet in the sequel we shall, God willing, make them abundantly
clear at least to mathematicians.
Given the above view - and there is none more reasonable - that the
periodic times are proportional to the sizes of their orbits, then the
order of the Spheres, beginning from the most distant, is as follows.
Most distant of all is the Sphere of the Fixed Stars, containing all
things, and being therefore immovable. It represents that to which the
motion and position of all the other bodies must be referred. Some
hold that it too changes in some way, but we shall assign another
reason for this apparent change, as will appear in the account of the
Earth's motion. Next is the planet Saturn, revolving in 30 years. Next
comes Jupiter, moving in a 12 year circuit; then Mars, who goes
around in 2 years, the fourth place is held by the annual revolution in
which the Earth is contained, together with the orbit of the Moon as on
an epicycle. Venus, whose period is 9 months, is in the fifth place,
and sixth is Mercury, who goes around in the space of 80 days.
In the middle of all sits Sun enthroned. In this most beautiful temple
could we place this luminary in any better position from which he can
illuminate the whole at once? He is rightly called the Lamp, the Mind,
the Ruler of the Universe; Hermes Trismegistus named him the Visible
God, Sophocles' Electra calls him the All-seeing. So the Sun sits as
upon a royal throne ruling his children the planets which circle round
him. The Earth has the Moon at her service. As Aristotle says, in his
de Animalibus, the Moon has its closest relationship with the Earth.
Meanwhile the Earth conceives by the Sun, and becomes pregnant
with an annual rebirth.
So we find underlying this ordination an admirable symmetry in the
Universe, and a clear bond of harmony in their motion and magnitude
of the orbits such as can be discovered in no other wise. For here we
may observe why the progression and retrogression appear greater for
Jupiter than for Saturn, and less for Mars, but again greater for Venus
than in Mercury; moreover why Saturn, Jupiter and Mars are nearer to
the Earth at opposition to the Sun than when they are lost in or emerge
from the Sun's rays. Particularly Mars, when he shines all night,
appears to rival Jupiter in Magnitude, being only distinguishable by his
ruddy colour; otherwise he is scarce equal to a star of second
magnitude, and can be recognized only when his movements are
carefully followed. All these phenomena proceed from the same
cause, namely Earth's motion.
That there are no such phenomena for the Fixed Stars proves their
immeasurable distance, compared to which even the size of the
Earth's orbit is negligible and the parallactic effect unnoticeable. For
every visible object has a certain distance beyond which it can no
longer be seen (as is proved in the Optics). The twinkling of the stars,
also, shows that there is still a vast distance between the furthest of
the planets, Saturn, and the Sphere of the Fixed Stars, and it is chiefly
by this indication that they are distinguished from the planets. Further,
there must necessarily be a great difference between moving and non-
moving bodies. So great is the divine work of the Great and Noble
1 1 . Explanation of the Threefold Motion of the Earth
Since then planets agree in witnessing to the possibility that Earth
moves, we shall now briefly discuss the motion itself, in so far as the
phenomena can be explained by this hypothesis. This motion was
must take to be threefold. The first defines the cycle of night and day.
It is produced by the rotation of the Earth on its axis from West to East,
corresponding to the opposite motion by which the Universe appears
to move round the equinoctial circle, that is the equator, which some
call the "equidial" circle. The second is the annual revolution of the
centre of the Earth, together with all things on the Earth. This
describes the ecliptic round the Sun, also from West to East, that is,
backwards, between the orbits of Venus and Mars. So it comes about
that the Sun himself seems to traverse the ecliptic with a similar
motion. For instance, when the centre of the Earth passes over
Capricorn, as seen from the Sun, the Sun appears to pass over
Cancer as seen from Earth; but seen from Aquarius, he would seem to
pass over Leo, and so on. The equator and Earth's axis are variably
inclined to this circle, which passes through the middle of the Zodiac,
and to its plane, since if they were fixed and followed simply the motion
of the Earth's centre there would be no inequality of days and nights.
Then there is a third motion, of declination, which is also an annual
revolution, but forwards, that is, tending in opposition to the motion of
the Earth's centre; and thus, as they are nearly equal and opposite, it
comes about that the axis of the Earth, and its greatest parallel, the
equator, point in an almost constant direction, as if they are fixed. But
meantime the Sun is seen to move along the oblique direction of the
Ecliptic with that motion which is really due to the centre of the Earth
(just as if the Earth were the centre of the Universe, remembering that
we see the line joining the Sun and Earth projected on the Sphere of
the fixed Stars).
To express it
graphically, draw a
circle ABCD to
represent the annual
path of the Earth's
centre in the plane of
the Ecliptic. Let E near
its centre be the Sun.
Divide this circle into
four equal parts by the
diameters AEC and
BED. Let the first point
of Cancer be at A, of
Libra at B, of Capricorn
at C and of Aries at D. Now let the centre of the Earth be first at A and
round it draw the terrestrial equator FGHI. This circle FGHI however is
not in the same plane as the Ecliptic but its diameter GAI is the line of
intersection with the ecliptic. Draw the diameter FAH, at right angles to
GAI, and let F be the point of the greatest declination to the South, H to
the north. This being so the inhabitants of the Earth will see the Sun
near the centre E at its winter solstice in Capricorn, owing to the
turning towards the Sun of the point of greatest Northern declination H.
Hence in the diurnal rotation the inclination of the equator to AE makes
the Sun move along the Tropic of Capricorn, which is distant from the
Equator by an angle equal to EAH.
Now let the centre of the Earth travel forwards and let F, the point of
greatest declination, move to the same extent backwards until both
have completed quadrants of their circles at B. During this time the
angle EAI remains always equal to the angle AEB, on account of the
equality of the motions. The diameters FAH, FBH, and GAI, GBI are
also always parallel each to each, and the Equator remains parallel to
itself. These parallel lines appear coincident in the immensity of the
Heavens as has often been mentioned. Therefore, from the first point
of Libra, E will appear to be in Aires, and the intersection of the planes
will be the line GBIE, so that the diurnal rotation will give no
declination, and all the motion of the Sun will be lateral (in the plane of
the Ecliptic). The Sun is now at the vernal equinox. Further, suppose
that the centre of the Earth continues its course. When it has
completed a semi-circle at C, the Sun will appear to be entering
Cancer. F, the point of greatest southern declination of the Equator, is
now turned towards the Sun, and he will appear to be running along
the Tropic of Cancer, distant from the Equator by an angle equal to
ECF. Again, when F has turned through it third quadrant, the line of
intersection Gl will once more fall along the line ED, and from this
position the Sun will be seen in Libra at the autumnal equinox. As the
process continues and HF gradually turns towards the Sun, it will
produce a return of the same phenomena as we observed at the
We can explain it otherwise as follows. Take the diameter AEC in the
plane of the page. AEC is the line of intersection by this plane of a
circle perpendicular to it. At points A and C, that is at Cancer and
Capricorn respectively, describe in this plane a circle of longitude of
the Earth DFGI. Let DF be the axis of the Earth, D the north pole, F
the south, and Gl a diameter of the equator. Since then F turns
towards the Sun at E, and the northern inclination of the equator is the
angle IAE, the rotation round the axis will describe a parallel south of
the equator with diameter KL and at a distance from the equator equal
to LI, the apparent distance from the equator of the Sun in Capricorn.
Or better, by this rotation round the axis the line of sight AE describes
a conical surface, with vertex at Earth's centre and as base a circle
parallel to the equator. At the opposite point C the same phenomena
occur, but conversely. Thus the contrary effects of the two motions,
that of centre and that of declination, constrain the axis of the Earth to
remain in a constant direction, and produce all the phenomena of solar
We were saying that the annual revolution of the centre and of
declination were almost equal. If they tallied exactly the equinoctial
and solstitial points and the whole obliquity of the Ecliptic with
reference to the Sphere of the Fixed Stars would be unchangeable.
There is, however, a slight discrepancy, which has only become
apparent as it accumulated in the course of the ages. Between
Ptolemy's time and ours it has reached nearly 21°, the amount at which
the equinoxes have precessed. For this reason some thought that the
Sphere of the Fixed Stars also moves, and they have therefore
postulated a ninth sphere. This being found insufficient, modern
authorities now add a tenth. Yet they have still not attained the result
which we hope to attain by the motion of the Earth. We shall assume
this motion as a hypothesis and follow its consequence.
The Study of Astronomy
Sir James Jeans
On the evening of January 7, 1610, a fateful day for the human race,
Galileo Galilei, Professor of Mathematics in the University of Padua,
sat in front of a telescope he had made with his own hands.
More than three centuries previously, Roger Bacon, the inventor of
spectacles, had explained how a telescope could be constructed so as
"to make the stars appear as near as we please." He had shown how
a lens could be so shaped that it would collect all the rays of light
falling on it from a distant object, bend them until they met in a focus,
and then pass them on through the pupil of the eye and on to the
Such an instrument would increase the power of the human eye just as
an ear trumpet increases the power of the human ear by collecting all
the waves of sound which falls on a large aperture, bending them, and
passing them through the orifice of the ear on to the ear drum.
Yet it was not until 1608 that the first telescope had been constructed
by Lippershey, a Flemish spectacle-maker. On hearing of this
instrument, Galileo had set to work to discover the principles of its
construction and had soon made himself a telescope far better than
the original. His instrument had created no small sensation in Italy.
Such extraordinary stories had been told of its powers that he had
been commanded to take it to Venice and exhibit it to the Doge and
Senate. The citizens of Venice had then seen the most aged of their
Senators climbing the highest bell-towers to spy through the telescope
at ships which were too far out to sea to be seen at all without its help.
The telescope admitted about a hundred times as much light as the
unaided eye, and Galileo claimed that it showed objects fifty miles
distant as clearly as though they were only five miles away. The
absorbing interest of his new instrument had almost driven from
Galileo's mind a problem to which he had once given much thought.
Over two thousand years previously, Pythagorus and Philolaus had
taught that the earth is not fixed in space but rotates on its axis every
twenty-four hours, thus causing the alternation of day and night.
Aristarchus of Samos, perhaps the greatest of all Greek
mathematicians, had further maintained that the earth not only turned
on its axis, but it also described a yearly journey round the sun, this
being the cause of the cycle of the seasons.
Then these doctrines had fallen in disfavour. Aristotle had pronounced
against them, asserting that the earth formed a fixed centre of the
universe. At a later date Ptolemy had explained the tracks of the
planets across the sky in terms of a complicated system of cycles and
epicycles; this explanation had again supposed the planets moved
around an immoveable earth. The Church had given its sanction and
active support to these doctrines.
Yet, even in the Church, the doctrine had not gained universal
acceptance. Oresme, Bishop of Lisieux, and Cardinal Nicholas of
Cusa had both declared against it, the latter writing in 1440:
"I have long considered that this earth is not fixed, but
moves as do the other stars. To my mind the earth turns
upon its axis once every day and night."
At a later date such views incurred the active hostility of the Church,
and in 1600 Giordano Bruno was burned at the stake, one of the
counts against him being his insistence on the doctrine of the plurality
of worlds. He had written:
"It has seemed to me unworthy of the divine goodness
and power to create a finite world, when able to produce
beside it another and others infinite; so that I have
declared that there are endless particular worlds similar
to this of the earth; with Pythagoras I regard it as a star,
and similar to it are the moon, the planets and other
stars, which are infinite in number, and all these bodies
The most weighty attack on orthodox doctrine had, however, been
delivered by the Polish ecclesiastic and astronomer, Nicolaus
Copernicus (1473 - 1543). In his great work De Revolutionibus
Orbium Coelestium Copernicus had shown most of Ptolemy's
elaborate structure of cycles and epicycles to be unnecessary,
because the tracks of the planets across the sky could be explained in
a much simpler manner by supposing that the earth and the planets all
moved round a fixed central sun.
The sixty-six years which had elapsed since this book was published
had seen these theories hotly debated, but they were still neither
proved nor disproved. And although Galileo found himself powerfully
attracted to them, he had hitherto though it the more prudent course to
keep his opinions to himself. Galileo had already found that his new
telescope provided a means of testing astronomical theories. As soon
as he had turned it on to the Milky Way, a whole crowd of legends and
fables as to their nature and structure of this object had vanished into
thin air; it proved to be nothing more that a swarm of faint stars
scattered like golden dust on the black background of the sky.
Another glance through the telescope had disclosed the true nature of
the moon. On it were mountains which cast shadows, so that it proved
to be a world like our own, as Giordano Bruno had maintained. What if
the telescope should now in some way prove able to decide between
the orthodox doctrine that the earth formed the hub of the universe,
and the revolutionary new doctrine that the earth was only one of a
number of bodies, all circling round the sun like moths round a candle-
And now Galileo catches Jupiter in the field of his telescope and sees
four small bodies circling around the great mass of the planet - like
moths round a candle-flame. What he sees is an exact replica of the
solar system, as imagined by Copernicus, and it provides direct visual
proof that such systems are at least not alien to the architectural plan
of the universe.
On January 30 th he writes to Belisario Vinta that these small bodies
move round the far greater mass of Jupiter "just as Venus and
Mercury, and perhaps the other planets, move round the sun."
Any lingering doubts that Galileo may have felt as to the significance of
his discovery were removed nine months later when he observed the
phases of Venus; the shining surface of the planet was seen to pass
through the same cycle of shapes as the moon - from crescent
through semicircle to a full circle, and then, reversing the paths, back
through semicircle to crescent. This of course showed at once that the
planet was not self-luminous, since had it been so, its surface would
always have appeared as a full circle of light. But even when it was
known that the planet was not self-luminous, two distinct alternatives
If Venus moved round the earth in a Ptolemaic epicycle, then, as
Ptolemy had himself pointed out, should never show more than half
her surface illuminated. If, on the other hand, she moved round the
sun in a large circle, as the new Copernican view required, then the
shining surface of Venus ought to exhibit the complete sequence of
phases shown by the moon, the surface of the planet appearing
completely dark at the moment when it passed between the earth and
the sun. And the same ought to be true also of Mercury. It had indeed
urged as an objection to the Copernican theory that neither Venus nor
Mercury exhibited this full cycle of phases.
Galileo's telescope now showed that, precisely as Copernicus had
foretold, Venus passed through the full cycle of phases, so that, in
Galileo's own words:
"we are now supplied with a determination most conclusive, and
appealing to the evidence of our senses, of two very important
problems, which up until this day have been discussed by the greatest
of intellects with different conclusions. One is that the planets are not
self-luminous. The other is that we are absolutely compelled to say
that Venus, and Mercury also, revolve around the sun, as do also all
the rest of the planets, a truth believed indeed by the Pythagorean
school, by Copernicus and by Kepler, but never proved by the
evidence of our sense, as is now proved in the case of Venus and
These discoveries of Galileo made it clear that Aristotle, Ptolemy and
the majority of those who had thought about these things in the past
2000 years had been utterly and hopelessly wrong.
In estimating his position in the universe, man had up to now been
guided mainly by his own desires, and his self-esteem; long fed on
boundless hope, he had spurned the simpler fare offered by patient
scientific thought. Inexorable facts now dethroned him from his self-
arrogated station at the centre of the universe; henceforth he must
reconcile himself to the humble position of the inhabitant of a speck of
dust, and adjust his views as to the significance and importance of
human life accordingly.
The adjustment was not made at once. Human vanity, reinforced by
the authority of the Church, contrived to make a rough road for those
who dared draw attention to the earth's insignificant position in the
universe. Galileo was forced to abjure his beliefs.
Well on into the eighteenth century the ancient University of Paris was
teaching that the motion of the earth round the sun was a convenient
but false hypothesis, while the newer American Universities of Harvard
and Yale taught the Ptolemaic and Copernican systems of astronomy
side by side as if they were equally tenable.
Yet men could not keep their heads buried in the sand for ever, and
when at last its full implications were accepted, the revolution of
thought initiated by Galileo's observation of January 7, 1610, proved to
be the most catastrophic in the history of the race.
The cataclysm was not confined to the realms of abstract thought;
henceforth human existence itself was to appear in a new light, and
human aims and aspirations would be judged from a different
This oft-told story has been told once again, in the hope it might
explain some of the interest taken in astronomy today. The more
mundane sciences prove their worth by adding to the amenities and
pleasures of life, or by alleviating pain or distress, but it may well be
asked what reward astronomy has to offer. Why does the astronomer
devote arduous nights, and even more arduous days, to studying the
structure, motions and changes of bodies so remote that they can have
no conceivable influence on human life?
In part at least the answer would seem to be that many have begun to
suspect that the astronomy of today, like that of Galileo, may have
something to say on the enthralling question of human life in the
universe in which it is placed, and on the beginnings, meaning and
destiny of the human race.
Bede records how, some twelve centuries ago, human life was
compared in poetic simile to the flight of a bird through a warm hall in
which men sit feasting, while the winter storms rage without:
"The bird is safe from the tempest for a brief moment, but
immediately passes from winter to winter again. So
man's life appears for a little while, but of what is it to
follow, or of what went before, we know nothing. If,
therefore, a new doctrine tells us something certain, it
seems to deserve to be followed."
Man wishes to probe farther into the past and the future than his brief
span of life permits. He wishes to see the universe as it existed before
man was, as it will be after the last man has passed again into the
darkness from which he came.
The wish does not originate solely in mere intellectual curiosity, in the
desire to see the next range of mountains, the desire to attain a
summit commanding a wide view, even if it be only of a promised land
which he may never hope himself to enter; it has deeper roots and a
more personal interest. Before he can understand himself, man must
first understand the universe from the dust of which his body has been
formed, and from the events of which all his sense perceptions are
drawn. He wishes to explore the universe, both in space and time,
because he himself forms part of it, and it forms part of him.
Except from: The Universe Around Us, Cambridge University Press,
1938, Sir James Jeans
Copernicus Discovered Nothing
Suppose we say, with Ptolemy, that the earth is the fixed centre of the
universe and that the sun and all the stars move around it; or
supposing we say, with Copernicus, that the earth is a small particle of
matter which is relatively insignificant in relation to the whole universe,
turning on its axis once every 24 hours and revolving around the sun
once every twelve months on the positivist principle the one theory is
as good as the other, when considered from the scientific viewpoint.
They are merely two different ways of making a mental construction
out of sensory reactions to some outer phenomena; but they have no
more right to be looked upon as scientifically significant than the
mental construction which the mystic or poet may make out of his
sensory impressions when face to face with nature.
It is true that the Copemican theory of astronomy is more widely
accepted; but that is because it is a simpler way of formulating a
synthesis of sensory observations and it does not give rise to so many
difficulties about astronomical laws as would arise from the acceptance
of the Ptolemaic theory. Therefore Copernicus is not to be judged as a
pioneer discoverer in the realms of science, no more than a poet is to
be judged as a pioneer discoverer when he gives fanciful and attractive
expression to sentiments that are known to every human breast.
Copernicus discovered nothing. He only formulated, in the shape of a
fanciful mental construction, a mass of facts that were already known.
He did not add anything to the store of scientific knowledge already in
A tremendous mental revolution was caused by this theory and bitter
battles were waged around it. For the logical consequence of it was to
give an entirely different account of man's place in the universe from
that generally held at the time by religion and philosophy of Europe.
But for the positivist scientist all the fuss and trouble made over the
Copernican theory were quite as senseless, from the scientific point of
view, as if one were to quarrel with the rapture of a contemplative poet
who gazes at the Milky Way and ponders over the fact that each star in
the Milky Way is a sun somewhat like ours and that each spiral nebula
is again a Milky Way from which the light has taken many millions of
years to reach our earth, while the earth itself, with its human race on
it, sinks away into an insignificant speck which is hardly discernible in
the boundless space.
From: Where is Science Going? George Allen & UnWin, London, 1933,
Apparent Motion and the Orbits of the
The planets all orbit the sun in the same direction, but orbit at different
speeds. As a result planets seen from earth will display apparent
motion. Apparent motion is when a planet viewed against the
background of "fixed stars" (stars very far in the distance),
accelerates, decelerates and changes direction.
For instance Mars as seen from Earth displays apparent motion:
Against the distance stars planets like Mars trace out a strange motion,
sometimes moving forward and sometime moving backwards
Mapping a planet's orbit is very difficult and involves complicated
mathematics and trigonometry. To map a planet's orbit, for instance
the Earth's orbit, around the sun we need many sets of measurements,
each giving the Earth's bearing from two fixed points.
Johannes Kepler (1571-1630) took the fixed Sun for one of these
points, and for the other he took Mars at a series of times when it was
in the same position in its orbit. He started by marking the "position" of
Mars in the star pattern at one opposition (opposite the Sun, overhead
JT*~ ^ ^*^ P0flTtpNf OP t, AMD M
\ OH UHt SV UNKNOWN
d "vppMi&m'^ Mm
That gave him the direction of a base line Sun - (Earth) - Mars, SEiM.
Then he turned the pages of Tycho Brahe's records to a time exactly
one Martian year later (the time of Mar's motion around its orbit was
known accurately, from records over centuries). Then he knew that
Mars was in the same position, M so that SM had the same direction.
By now Earth had moved on to E2 in its orbit.
Tycho's record of the position of Mars in the star pattern gave him the
new apparent direction of Mars, E2M; and the Sun's position gave him
the direction E2S. Then he could calculate the angles of the triangle
SE 2 M from the record thus; since he knew the direction E1M and E2M
(marked on the celestial sphere of stars) he could calculate the angle A
Since he knew the direction E1S and E 2 S he could calculate the angle
B, between them. Then on a scale diagram he could choose two
points to represent S and M and locate the Earth's position, E 2 , as
follows: at the ends of the fixed baseline SM, draw lines making angles
A and B and mark their intersection E2.
V. _ -* "^
One Marhim ytw mm'} ' >|c ^
Maes mm? k m same jmdm.
One Mars year later, you find the directions E3M and E3S from the
records and mark E 3 on this diagram. Thus Kepler could start with the
points S and M and locate E2, E 3 , E 4l ... and enough points to show the
Then, knowing the Earth's true orbit, he could invert the investigation
and plot the shape of Mars' orbit. He found he could treat the Earth's
orbit either as an eccentric circle or as slightly oval; but Mars' orbit was
far from circular.
By plotting the orbits or the Earth and Mars Kepler was able to show
that these two planets orbit the Sun in ellipses with the Sun in one
focus. This proof was the basis of his First Law.
By plotting the location and dates of the Earth and Mars in their orbits
he discovered his Second law (Equal Areas in Equal Times).
k&c tU , e;
Si circulus dividatur in
tas partes; & punchi divifion
Kepler was so proud of his
achievements that he added
a sketch of a victorious
astronomer to his diagram of
elliptic orbits in his book on
the orbit of planets.
Today we know the distances from the sun of the different planets and
the time it takes the planets to orbit the sun (in earth years) very
Distance from Sun (R)
(10 6 km)
Period (T) Earth
From: "Physics for the Inquiring Mind" by E. Rogers, Princeton
University Press, 1960.
Almagest - astronomy book by Claudius Ptolemy of Alexandria
published around 150 AD.
Assumption of Greater Probability - reasoning used by Copernicus ...
"given the evidence it is more likely that ...". This reasoning is a form of
Concept of the Sphere - Aristotle's reasoning was the Heavens were
perfect, as are circles and spheres are perfect, therefore they must
govern the motion of the Heavenly Spheres
Deferens - the main circle of a Ptolemaic Orbit.
Epicycle - the smaller, secondary circle of the orbit.
Geocentric - Earth centered model of the Universe (geo : Earth).
Heliocentric- Sun centered model of the Universe (Helios: Sun).
Plato's Principle - only circular and uniform motion are appropriate for
Ptolemaic System - a model of the Universe with the Earth at its
Retrograde motion - reverse motion of a planet through the heavens
Timaeus - Plato's most important dialogue about physics and
Mathematics, Physics and Astronomy
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