topics: |  biography | history | astronomy |

A lavishly illustrated work, tracing the life and work of Nicolas Copernicus, and his influences. Of particular interest is the develeopment of the Islamic astronomers whose ideas were strongly present in the work of Copernicus.

The book traces the development of Copernicus's ideas during his student days in Krakow and Padua (when he wrote an initial draft of his ideas), and his occupation as a canon in the parish of Warmia, where he worked as a treasurer and a doctor (he had studied both law and medicine). These were unsettling times, with war displacing him several times. During this period, he kept refining his theory, and updating his calculations. He also made observations of the planets, using a few simple instruments (no telescope) that he had built in his backyard.

His main goal was to devise a system that was more harmonious with the principles of motion as defined by Aristotle. The idea of creating such a system had been present for centuries in Islamic astronomy (9th to 14th c.), many works from which had been translated into Latin and were widely influential in the European renaissance.

Gingerich and Maclachlan write in a very accessible style, with many period
woodcuts and other illustrations.  Simple and effective diagrams
explain the relevant astronomical concepts, such as the following:


    The dotted lines represent the path of the sun across the sky
    as seen from the latitudes of northern Poland at the summer and
    winter solstices and the equinox.

Aristotelean dynamics

	from http://csep10.phys.utk.edu/astr161/lect/history/aristotle_dynamics.html

... stripped to its essentials, Aristotle believed that a stone fell to the
ground because the stone and the ground were similar in substance (in terms
of the 4 basic elements, they were mostly "earth"). Likewise, smoke rose
away from the Earth because in terms of the 4 basic elements it was
primarily air (and some fire), and therefore the smoke wished to be closer
to air and further away from earth and water. 

By the same token, Aristotle held that the more perfect substance (the
"quintessence") that made up the heavens had as its nature to execute
perfect (that is, uniform circular) motion. He also believed that objects
only moved as long as they were pushed. Thus, objects on the Earth stopped
moving once applied forces were removed, and the heavenly spheres only
moved because of the action of the Prime Mover, who continually applied the
force to the outer spheres that turned the entire heavens. 

A notorious problem for the Aristotelian view was why arrows shot from a
bow continued to fly through the air after they had left the bow and the
string was no longer applying force to them. Elaborate explanations were
hatched; for example, it was proposed that the arrow creating a vacuum
behind it into which air rushed and applied a force to the back of the
arrow!

Islamic astronomy

[The Aristotelean view was the dominant mode of thinking in middle age
astronomy, primarily carried out among the Islamic astronomers
(who may also have been Jewish or Christian) with their bases across a
widespread culturally-connected region from Persia to Spain (Al-Andalus).

This group was largely critical of the Ptolemaic interventions that
deviated from aristotelian principles such as uniform circular motion for
celestial bodies, and proposed many mechanisms that would explain observed
motions in terms of a conjunction of the motion of spheres rolling on each
other.  For % example, the 13th century persian astronomer 
Nasir al-Din al-Tusi, combined two small circles that accomplished a
linear oscillating motion]:

	 
	the Tusi couple, devised by the 
	Persian astronomer Nasir al-Din al-Tusi,
	generates an oscillating motion from the
	combined motion of a large and a small sphere. 
	(image: wikimedia)
	al-Tusi (d. 1274) was the director of the 
	Maragheh (Maragha) observatory in present-day
	Azerbaijan. 


Copernicus was essentially carrying forward the ideas of this group of
astronomers, many of whom had been translated into Latin by the 13th-14th
centuries.

Science in Islamic Spain

(from http://www.islamicspain.tv/Arts-and-Science/The-Culture-of-Al-Andalus/Astronomy.htm):

Among the earliest Muslim astronomers was al-Faraghani (fl. 863 CE), who
summarized but questioned Ptolemy’s work and made many important
calculations. Columbus used his figures on the earth’s circumference, but
misunderstood the astronomer's unit of measurement. Al-Khwarizmi
(ca. 770-840 CE), the famous Persian mathematician, prepared astronomical
charts that were later translated and further developed in Spain.

Al-Battani (d. 929 CE), another critic of Ptolemy, contributed to solving
the puzzle of the heavens, and whose work was used for centuries. He
calculated astronomical tables (charts on the movement of bodies in the
sky), and helped to develop the branch of mathematics called trigonometry,
which he used to calculate accurate solar and lunar timekeeping.

Astronomy in Spain

In Córdoba, al-Zarqali (1029-1087 CE) prepared astronomical charts called
the Toledan Tables. He also built and improved on the astrolabe, a tool
with hundreds of uses in astronomy, navigation, surveying and timekeeping.

Jaber ibn Aflah (d. 1145 CE) is considered important for his advancements in
trigonometry. Using spherical trigonometry, he designed a portable celestial
sphere.  Al-Bitruji (d. 1204 CE) was a leading astronomer who was born in
Morocco and migrated to Seville, where he developed a new theory of the
movement of stars.

Translation of books on mathematics and astronomy in Spain from Arabic
through Hebrew and Castilian into Latin added to the contributions of
Al-Andalus to advancing astronomy in Europe. Historians of science have long
known about these translations, where they were published, and which
scientists owned these books. Recently, it has become known that some
European scientists had direct or indirect knowledge of Arabic, and we are
learning that there was more than one path by which learning was exchanged
between East and West.

[This was the view inherited and worked on by Copernicus.]

Working out the details

Over several decades, Copernicus worked out a detailed argument on how
placing the sun at the center simplified the circular motion of the heavenly
bodies.  His goal was to show that his model adhered better to the
aristotelean assumption that celestial (heavenly) bodies moved along spheres
in aether (a special heavenly element).

Simple spherical motion, however, did not tally with the observation of the
planets, which "moved" against the rest of the sky.  These motions were
crucial because astrology was deemed to be a "science" and calculating the
positions of the planets were a crucial element.

The dominant theory at the time, due to Ptolemy (Egypt, 150 AD), proposed
a complex set of circles (equators of spheres) rolling along other spheres,
but to tally with observations, these required a center other than that of
the earth (deferent), and a different point about which the velocity was
uniform (equant).  Ptolemy's model also required the distance to the moon
to become half at its perigee (which would have resulted in it appearing
nearly 2x its size), but this discrepancy didn't matter as much, since the
astrologers who depended on these tables mainly wanted to know the
positions, and were less bothered by the size or brightness.

Copernicus was almost not being published

Despite spending a lifetime collating and organizing this evidence, and
preparing a manuscript intended to replace the Almagest - Ptolemy's
original text which was used as a reference at the time, he was aware of the
possibly strong reactions these ideas would provoke among his
contemporaries.  In fact, despite the strength of his conviction, he had
resigned himself to not having the book printed.  However, a friend in the
church (later became the Bishop Giese), and an accidental pupil, Georg
Joachim Rheticus, who had heard of the work through friends in Germany,
convinced him in his final days to get it printed.  Copernicus was able
to work on the proofs, and Giese says that the final printed work
reached him the very day he died.

   

* Understanding the Heavens: Thirty Centuries of Astronomical Ideas
   by Jean-Claude Pecker (2001)

	Up to the time of Copernicus, al-Bitruji's book was the new gospel
 	and it was an anti-Ptolemaic one. ...Undoubtlessly, it made room
 	for the new and original thinking of Copernicus two centuries
 	later. p.154

* A More Perfect Heaven: How Copernicus Revolutionised the Cosmos
   by Dava Sobel (2011)

	Working at a remote outpost in Poland, often under the shadow of
	war from Albrecht of Prussia and others, Copernicus formulated the
	heliocentric theory that changed our vision of the universe. ...


* Indian astronomy: an introduction
   by S. Balachandra Rao (1994)

	Sometimes, the sun may remain in the same rAshi for more
	than a lunar month; in such situations, one has an extra month
	(adhikamAsa, chapters 5 & 6)

* Science and Civilisation in China: v.4
    Physics and Physical Technology, part I: Physics
    by Joseph Needham and Wang Ling and Kenneth G Robinson (1977)

	The Indian [trigonometry] was taken over by the Arabs and
	transmitted to Europe, while in the other direction Indian monks
	or lay mathematicians who took service with the Chinese bureau of
	astronomy spread the new development farther east.  ...

[Opens on a fictionalized scene from his early years at Jagiellonian
University in Cracow, when a student is waving a pamphlet describing
Columbus's journey to the Indies, from where he had brought back some
natives who "looked very different from Africans."]

 
   map of the world printed in Germany in 1482, ten years before
   columbus's journey.  most of the information is based on
   ptolemy's map from the 2nd c. AD
Columbus had depended on scholars’ estimates of the westward distance from
Europe to Asia for his trip.  One of the major sources had been a work
written more than a thousand years before by the mathematician Ptolemy of
Alexandria (in present-day Egypt). His Geography is an atlas giving the
locations of cities all across the known world.[p.10]

	[In the above passage, Gingerich and Maclachlan fail to mention that
	the scholar whose results Columbus used was Al-Bitruji, mentioned
	above.  Indeed, this link is weakened by the immediate
	move to the work of Ptolemy.  ]


    The 70 years of Copernicus’s lifetime — from 1473 to 1543 — marked
    great changes in Europeans’ outlook on the world.  In 1473 most people
    supposed that the searing heat from the sun at the equator would
    prevent sailors from ever crossing into the Southern Hemisphere.They
    believed that a great ocean surrounded Europe, Africa, and Asia, and
    that the only way to the spices of the Orient was by an overland
    route.

1522: One ship of Portuguese explorer Ferdinand Magellan returns
after going completely around the globe
	 ==> better understanding of the structure of the world.

Rapid spread of knowledge via printing

New information could spread more rapidly owing to the nascent
printing industry (dating from only a few years before
Copernicus’s birth).

The new printing presses made possible less expensive textbooks, illustrated
encyclopedias, calendars, and prayer books. Nicolaus was a student in Italy
from 1496 to 1503, at a time when arts and literature were in full flower
during the Renaissance. The artists Raphael, Leonardo, and Michelangelo were
painting and sculpting for wealthy patrons in Rome and Florence. Numerous
scholars were translating Greek classics into Latin, to be spread across
Europe as printed books.


16th c. woodcut of a printing house.  At the left in the
foreground, a "puller" removes a printed sheet from the press. The
"beater" to his right is inking the forme. In the background,
compositors are setting type.  (image: wikimedia; a
version of this image is also given in the text)

Studies in Italy: Law at Bologna

the university organization at Bologna was very different from that at
Cracow. Students were placed in various "nations" according to their native
language. Nicolaus enrolled in the German nation.At the head of each nation
was a student, not a faculty member.The university, although founded before
1200, had no buildings of its own. It was composed of the professors the
student nations chose to hire.The professors taught in their own
homes. Bologna was the foremost university for legal instruction in all of
Europe. Its total student population was two or three times larger than
Cracow’s.
 
    A 1493 woodcut of the university town of Bologna, where
    Copernicus studied law.  The rivers and canals and the
    bustling river port with its salt wharves have largely
    disappeared beneath today's city.

Medicine at Padua

In the 1500s, medicine students had to learn "medical
astrology".  Here one determined appropriate "bleeding" points
guided by astrological signs.

[This may seem laughable today, but I wonder how many of today's
measures in medicine would appear almost as laughable in the
2500s.]

Here is a figure of the "blood-letting man" showing which part of the body
should be allowed to "bleed" depending on the present sign of the zodiac.


    The "blood-letting man" - a figure used by doctors trained in
    astrology could determine where on the body to "bleed" a patient
    depending on which sign of the zodiac was about to rise in the east.

The motion of Mars

The complicated motion of Mars provided a great challenge both to
Copernicus and to his ancient predecessor, Ptolemy. The most conspicuous
feature of Mars’s observed motion occurs approximately every two years,
when the planet becomes very bright, stops its normal eastward motion
against the starry background, and for several weeks moves westward or in
"retrograde."


The patterns of retrograde
motion for Mars during 17
years in Copernicus’s lifetime.
Showing a small part - about
20 days - of Mars's orbit.
(Horiz line = ecliptic of sun.)

Copernicus observed Mars in 1504 and wrote a cryptic comment in one of his books noting that "Mars is ahead of the tables by 2 degrees, and Saturn is behind by 1½ degrees." Modern calculations compared with the almanacs of his day show this was true in 1504. Two of Copernicus’s records of the positions of Mars from 1512 are noted his de Revolutionibus.

Mars goes into retrograde motion every 780 days — that is, slightly more than two years. Each time, the retrogression is approximately 55 degrees farther around the zodiac, the band of the sky where the planets move. Mars’s path was different each time. The longest retrogression, in 1506, was nearly twice as long as the shortest one, in 1514.The lengths and shapes came back to a similar pattern when the retrogressions had moved all the way around the sky, so that the pattern in 1518–19 was similar to the one in 1504.

[Ptolemy tried to handle Mars' retrograde motion using a epicycle whose center was offset by a distance d from the earth, and its angular speed was determined based on an equant point, at a distance d from the equant, away from earth - i.e. at distance 2d from the earth.

[Thus, Mars was moving on an epicycle (a circle rolling around another), whose center was eccentric (not at the earth). However, explaining the details of Mars's motion required greater ingenuity. In Ptolemy's system introduced a peculiarity, whereby the speed of the planet was determined based on the distance from a third point, called the equant. The arrangement, while unusual, was very clever, and though complex, it permitted computation of the entire cycle of Mars's motion. However, as Copernicus observed, it could be off by one or two degrees. ]

Later astronomers were not always so satisfied with Ptolemy’s solution, not because it was inaccurate, but because they violated some of the accepted ideas about how eternal, celestial motions should be circular and uniform, (whereas terrestrial motions should be linear). In order to conform as much as possible to such Aristotelian principles, Ptolemy had confined his models to various combinations of circular motions, and devised the equant mechanism to produce non-constant speed on the epicycle. Some scholars - and later Copernicus - felt that this was cheating, or at least it was not philosophically pleasing.

[In the 13th century, the astronomer Nasir al-Din al-Tusi, working at the Maragha Observatory (in present-day Iran), combined two small circles that accomplished a linear oscillating motion. Later, in Damascus, Ibn al-Shatir arranged the circles (called epicyclets) somewhat differently to explain Mars's retrograde motion without an equant device.]

 
The diagram shows to scale the deferent and epicycle that produces
Mars’s retrograde loop.  The same epicycle is shown here in
two positions as it carries Mars around from M1 into its
retrograde loop at M2.


Because these little circles were not independent in their motion but
were locked into a particular angle depending on where they moved on the
larger circle, the planetary tables did not become more complicated. 47

It was one of these arrangements that Copernicus would incorporate into his
own cosmological system.



    The equant model of Ptolemy that Copernicus sought to replace.
    The epicycle center must move from A to B in the same time it
    takes to go from B to C - so the epicycle with its planet
    moves faster near C and slower near A.

Note that the main objective of the calculations was to predict the
positions of the planets (including the moon) - at a given time.  If a
theory managed to predict the position well, though it had other side
effects (e.g. the Moon should appear nearly twice as large) - then these
side effects could be ignored.  (see motion of the moon below).

Here is an animated image showing how Mars's retrograde motion may be
accounted for in a copernicus-like heliocentric model.


Mars's retrograde motion in the Copernican model.
from http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html

Motion of the Moon

Ptolemy’s method for getting the correct angles at which the moon is seen
made it appear to change its distance to the earth quite drastically. The
moon’s distance from the center of the earth is about 60 times the radius
of the earth.  At certain times of the month, Ptolemy’s model put this
distance at only about 34 earth radii. If the moon actually came that much
closer, it would appear nearly twice as wide. But the moon’s apparent size
never changes that much (or very much at all).  Copernicus improved the
model considerably.

Perhaps unwittingly, he used one of the revisions made by Muslim
astronomers many years before. Whether he learned about their model while
in Italy, or invented it independently, we simply do not know.

In his de Revolutionibus, Copernicus replaced Ptolemy’s clumsy
trigonometry with the more up-to-date version that had
been developed by the Islamic mathematicians. 76

Alfonsine tables

In the centuries immediately preceding Copernicus, the most common way
to calculate the positions of planets was to use the Alfonsine Tables. These
tables gave starting positions at specified dates for each of the planets, plus
information about how far each planet moved per day.There were also extensive
tables of corrections, because the speed of each planet as seen from Earth
was far from uniform. Copernicus obtained a set printed in 1492 while he was
a student at Cracow.

Copernicus’s other main argument for placing all the planets in orbit
around the sun was that it put their distances and periods of revolution
into a regular order.  Copernicus’s calculations showed that Mercury in the
smallest orbit moves about the sun most swiftly, while distant Saturn is
the slowest. And the earth, with its period of one year, has its natural
place between Venus and Mars.

		Distance from the sun 	Period of revolution
		(astronomical units)
Mercury 	0.39			88 days
Venus 		0.72 			225 days
Earth 		1.00 			365 days or 1 year
Mars 		1.52 			687 days or nearly 2 years
Jupiter 	5.2 			12 years
Saturn 		9.5 			30 years

"Only in this way," Copernicus wrote, "do we find a sure harmonious
connection between the size of the orbit and the planet’s period of
revolution."


    page from manuscript of de revolutionibus, in Copernicus's
    own handwriting and images of the planets.

the above image is not from the book, but it also contains similar
handwritten notes by Copernicus, such as calculations in some blank pages
at the back of a astronomy text that he had bought during his college days
in Krakow.