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Full text of "Copernicus Work Book"

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 
Position 25 

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 

Glossary 50 



The Almagest of Ptolemy 



Geocentric - 
Earth centered 



Heliocentric- 
Sun centered 



Almagest ■ 

"The 

Greatest" 



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 
Ptolemaic System 
-the Earth is at 
the Centre of the 
Universe 



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 
Exploration. 

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 
Poland. 



When 
Copernicus 
was 19 
Columbus 
sailed to the 
New World 



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 
astronomical theories. 



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. 



Copernicus 
published his 
book De 
Revolutionibus 
Orbium 
Coelestium in 
1543, the year 
he died 



Aristarchus of 
Samos had 
proposed a 
sun-centred 
model in 
ancient times 



After 

Aristarchus, 
Aristotle had 
proposed an 
earth-centred 
model in 350 
B.C. 



This earth- 
centred model 
was elaborated 
by Claudius 
Ptolemy of 
Alexandria 
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 



R 



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 
Newton(1642-1727). 

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 



Copernicus 
recognized that 
the paths of the 
planets could be 
explained by 
their own motion 
and that of the 
earth 



Galileo Galilei 
(1564-1642) 

Johannes Kepler 
(1571 -1630) 

Isaac Newton 
(1642-1727) 



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. 



in hoc 

remotissimo 
loco terrae 



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. 



Plato's Principle 
- only circular 
and uniform 
motion are 
appropriate for 
celestial bodies. 



deferens - the 
main circle of a 
Ptolemaic Orbit 



epicycle - the 
smaller, secondary 
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 
uniform. 

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 



8 



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 
about it. 



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 
bodies. 



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. 



Nicolai Copernici 
de hypothesibus 
motuum 
coelestium a se 
constitutes 
Commentariolus 



De 

Revolutionibus 

orbium 

coelestium 

- published in 

1543 



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 
myself. " 

(De rev., dedication letter). 



George Joachim 
Rheticus 
arranged the 
publishing of De 
Revolutionibus 
in Nurnberg 



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 
motionless centre 
of the Universe, it 
is subject to a 
triple motion 



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. 



10 



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 
processional motion. 

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 



Assumption of 
Greater 
Probability - 
This reasoning 
is a form of 
Bayesian 
reasoning 



The loops the 
planets describe 
through the sky 
are caused by 
the yearly 
motion of the 
Earth around the 
Sun. 



Copernicus 
assumed the 
Earth is 
spherical, as is 
the Universe 



Parallax - 
small shift of 
the distant 
stars due to 
Earth's orbit 
around the 
Sun 



Planet means 
"wanderer" in 
Greek. 

Planets appear to 
sometimes move 
forward across the 
sky, then stop and 
then move 
backwards 
(retrograde motion) 



11 



Copernicus writes - 
a Commentary on 
the hypothesis 
concerning celestial 
motion, around 
1515; de 
hypothesibus 
motuum coelestium 
a se constitutes 
Commentariolus 



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 
epicycle. 

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 
revolution. 

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 



12 



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 
hundred years. 

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 



Isaac Newton 

Philosophiae 

Naturalis 

Principia 

Mathematica 

1687 



13 



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 
not sufficient. 

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 
called astrophysics. 

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 
all mankind. 

From: Excerpt from a Copernicus Quincentennial Celebration 

presentation to the Royal Astronomical Society of 
Canada, 1973 



14 



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 
position. 

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. 



15 



They follow in this order: 

Axioms 

Copernicus' 

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 
heavens. 

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 



16 



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 
1515. 




Figure 2. The 
Copernican 
System with 
the Sun at the 
Centre of the 
Universe 



17 



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 



18 



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 



19 



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. 



20 



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 



21 



The titles to 
several of the 
chapters in 
Copernicus' 
book are 
borrowed from 
Ptolemy's 
Almagest 



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 



22 



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. 



23 



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; 



24 



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 
disposed bodies. 

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 
heavenly bodies. 

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 
consideration. 



25 



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. 



26 



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. 




27 



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 
are unequal. 

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 
Heavens. 

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 



28 



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 
Refutation 

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? 



29 



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. 



30 



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 



31 



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." 



32 



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 



33 



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. 



-<A 



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 
are related. 

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 



35 



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 
Creator! 



36 



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 



37 



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 
starting point. 



Patus Born*. 








Partes Auftr/nar. 



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 



38 



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 
motions. 

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. 



f-nm^-i 



wmmmx 




39 



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 
retina. 

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. 



40 



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 
are worlds." 

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 



41 



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- 
flame? 

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 
remained. 

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. 



4Z 



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 
Mercury." 

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 



43 



human aims and aspirations would be judged from a different 
standpoint. 

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 



TT 



Copernicus Discovered Nothing 

Max Planck 

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 
existence. 

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, 

45 



Apparent Motion and the Orbits of the 
Planets 

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 
(retrograde motion). 

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 
at midnight). 



46 



JT*~ ^ ^*^ P0flTtpNf OP t, AMD M 

\ OH UHt SV UNKNOWN 

wj8£fti» 



( 






SaKlwns nwnki 
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 
between them. 

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. 




Q 



\ K 






V. _ -* "^ 



One Marhim ytw mm'} ' >|c ^ 

Maes mm? k m same jmdm. 



47 



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 
orbit's shape. 




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). 







kngfari a 
k&c tU , e; 
0* rejsdm 
lamefi ju 
0* arxpgdi 
Gmmm 

imtia iffii 
&&>& &>. 

VIII. 



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. 



a» 



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 
accurately: 



Planet 


Distance from Sun (R) 
(10 6 km) 


Period (T) Earth 
Years 


Mercury 


57.9 


0.241 


Venus 


108.2 


0.615 


Earth 


149.6 


1.00 


Mars 


227.9 


1.88 


Jupiter 


778.3 


11.86 


Saturn 


1427 


29.5 


Uranus 


2870 


84.0 


Neptune 


4497 


165 


Pluto 


5900 


248 



From: "Physics for the Inquiring Mind" by E. Rogers, Princeton 
University Press, 1960. 



49 



Glossary 



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 
Bayesian reasoning. 

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 
celestial bodies. 

Ptolemaic System - a model of the Universe with the Earth at its 
Centre. 

Retrograde motion - reverse motion of a planet through the heavens 

Timaeus - Plato's most important dialogue about physics and 
cosmology. 



50 




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