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CONNEXIONS
Rice University, Houston, Texas
This selection and arrangement of content as a collection is copyrighted by Joel Thierstein. It is licensed under the
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Collection structure revised: June 29, 2007
PDF generated: October 26, 2012
For copyright and attribution information for the modules contained in this collection, see p. 61.
Table of Contents
1 (Untitled)
2 Copernican System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Galileo's Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Johannes Kepler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 Ptolemaic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6 Satellites of Jupiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7 Saturn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
8 Sunspots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
9 The Biography of Galileo Galilei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
10 The Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Glossary
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Bibliography
Index
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Attributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
iv
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Chapter 1
(Untitled)
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1
2
CHAPTER 1. (UNTITLED)
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Chapter 2
Copernican System
Figure 2.1:
1
Copernicus
The rst speculations about the possibility of the Sun being the center of the cosmos and the Earth being
one of the planets going around it go back to the third century BCE. In his
Sand-Reckoner, Archimedes (d.
212 BCE), discusses how to express very large numbers. As an example he chooses the question as to how
many grains of sand there are in the cosmos. And in order to make the problem more dicult, he chooses not
the geocentric cosmos generally accepted at the time, but the heliocentric cosmos proposed by Aristarchus
of Samos (ca. 310-230 BCE), which would have to be many times larger because of the lack of observable
stellar parallax.
We know, therefore, that already in Hellenistic times thinkers were at least toying with
this notion, and because of its mention in Archimedes's book Aristarchus's speculation was well-known in
Europe beginning in the High Middle Ages but not seriously entertained until Copernicus.
1 This
content is available online at <http://cnx.org/content/m11938/1.3/>.
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3
CHAPTER 2. COPERNICAN SYSTEM
4
Figure 2.2:
Copernicus
European learning was based on the Greek sources that had been passed down, and cosmological and
astronomical thought were based on Aristotle and Ptolemy (Chapter 5). Aristotle's cosmology of a central
Earth surrounded by concentric spherical shells carrying the planets and xed stars was the basis of European thought from the 12th century CE onward. Technical astronomy, also geocentric, was based on the
constructions of excentric circles and epicycles codied in Ptolemy's
Almagest
(2d. century CE).
In the fteenth century, the reform of European astronomy was begun by the astronomer/humanist Georg
Peurbach (1423-1461) and his student Johannes Regiomontanus (1436-1476). Their eorts (like those of their
colleagues in other elds) were concentrated on ridding astronomical texts, especially Ptolemy's, from errors
by going back to the original Greek texts and providing deeper insight into the thoughts of the original
authors. With their new textbook and a guide to the
Almagest,
Peurbach and Regiomontanus raised the
level of theoretical astronomy in Europe.
Several problems were facing astronomers at the beginning of the sixteenth century. First, the tables (by
means of which to predict astronomical events such as eclipses and conjunctions) were deemed not to be
suciently accurate. Second, Portuguese and Spanish expeditions to the Far East and America sailed out
of sight of land for weeks on end, and only astronomical methods could help them in nding their locations
on the high seas. Third, the calendar, instituted by Julius Caesar in 44 BCE was no longer accurate. The
equinox, which at the time of the Council of Nicea (325 CE) had fallen on the 21st, had now slipped to
the 11th.
Since the date of Easter (the celebration of the dening event in Christianity) was determined
with reference to the equinox, and since most of the other religious holidays through the year were counted
forward or backward from Easter, the slippage of the calendar with regard to celestial events was a very
serious problem. For the solution to all three problems, Europeans looked to the astronomers.
Nicholas Copernicus (1473-1543) learned the works of Peurbach and Regiomontanus in the undergraduate
curriculum at the university of Cracow and then spent a decade studying in Italy.
Upon his return to
Poland, he spent the rest of his life as a physician, lawyer, and church administrator. During his spare time
he continued his research in astronomy.
The result was
De Revolutionibus Orbium Coelestium
("On the
Revolutions of the Celestial Orbs"), which was published in Nuremberg in 1543, the year of his death. The
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5
book was dedicated to Pope Paul III and initially caused litle controversy. An anonymous preface (added by
Andreas Osiander, the Protestant reformer of Nuremberg) stated that the theory put forward in this book
was only a mathematical hypothesis: the geometrical constructions used by astronomers had traditionally
had only hypothetical status; cosmological interpretations were reserved for the philosophers. Indeed, except
for the rst eleven chapters of Book I,
of the
Almagest.
Figure 2.3:
De Revolutionibus was a technical mathematical work in the tradition
Diagram of the Copernican system, from De Revolutions2
But in the rst book, Copernicus stated that the Sun was the center of the universe and that the
Earth had a triple motion
3 around this center. His theory gave a simple and elegant explanation of the
retrograde motions of the planets (the annual motion of the Earth necessarily projected onto the motions
of the planets in geocentric astronomy) and settled the order of the planets (which had been a convention
in Ptolemy's work) denitively. He argued that his system was more elegant than the traditional geocentric
system. Copernicus still retained the priviledged status of circular motion and therefore had to construct
his planetary orbits from circles upon and within circles, just as his predecessors had done. His tables were
perhaps only marginally better than existing ones.
The reception of
De Revolutionibus
was mixed. The heliocentric hypothesis was rejected out of hand
by virtually all, but the book was the most sophisticated astronomical treatise since the
Almagest,
and
for this it was widely admired. Its mathematical constructions were easily transferred into geocentric ones,
and many astronomers used them.
In 1551 Erasmus Reinhold, no believer in the mobility of the Earth,
Prutenic Tables, based on Copernicus's parameters. These tables came
accuracy. Further, De revolutionibus became the central work in a network of
published a new set of tables, the
to be preferred for their
astronomers, who dissected it in great detail.
Not until a generation after its appearance, however, can
we begin point to a community of practicing astronomers who accepted heliocentric cosmology.
the most remarkable early follower of Copernicus was Thomas Digges (c.
Description of the Coelestiall Orbes (1576)
Perhaps
A Pert
De Revolutionibus into
1545-c.1595), who in
translated a large part of Book I of
English and illustrated it with a diagram in which the Copernican arrangement of the planets is imbedded
in an innite universe of stars.
2 http://cnx.org/content/m11938/latest/copernican_universe.gif
3 A daily rotation about its center, an annual motion around the
Sun, and a conical motion of its axis of rotation. This
last motion was made necessary because Copernicus conceptualized the Earth's annual motion as the result of the Earth being
embedded in a spherical shell centered on the Sun. Its axis of rotation therefore did not remain parallel to itself with respect
to the xed stars. To keep the axis parallel to itself, Copernicus gave the axis a conical motion with a period just about equal
to the year. The very small dierence from the annual period accounted for the precesion of the equinoxes, an eect caused by
the fact that the Earth's axis (in Newtonian terms) precesses like a top, with a period of about 26,000 years. (Copernicus's
ideas about this precession were more cumbersome and based on faulty data.)
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CHAPTER 2. COPERNICAN SYSTEM
6
Figure 2.4:
Diagram of the universe by Thomas Digges4
The reason for this delay was that, on the face of it, the heliocentric cosmology was absurd from a
common-sensical and a physical point of view. Thinkers had grown up on the Aristotelian division between
the heavens and the earthly region, between perfection and corruption. In Aristotle's physics, bodies moved
to their natural places. Stones fell because the natural place of heavy bodies was the center of the universe,
and that was why the Earth was there.
Accepting Copernicus's system meant abandoning Aristotelian
physics. How would birds nd their nest again after they had own from them? Why does a stone thrown
up come straight down if the Earth underneath it is rotating rapidly to the east? Since bodies can only have
one sort of motion at a time, how can the Earth have several? And if the Earth is a planet, why should it
be the only planet with a moon?
For astronomical purposes, astronomers always assumed that the Earth is as a point with respect to the
◦
heavens. Only in the case of the Moon could one notice a parallactic displacement (about 1 ) with respect
to the xed stars during its (i.e., the Earth's) diurnal motion. In Copernican astronomy one now had to
assume that the orbit of the Earth was as a point with respect to the xed stars, and because the xed
stars did not reect the Earth's annual motion by showing an annual parallax, the sphere of the xed stars
had to be immense. What was the purpose of such a large space between the region of Saturn and that of
the xed stars?
4 http://cnx.org/content/m11938/latest/digges_universe.gif
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Parallax5
Figure 2.5:
These and others were objections that needed answers. The Copernican system simply did not t into
the Aristotelian way of thinking. It took a century and a half for a new physics to be devised to undegird
heliocentric astronomy. The works in physics and astronomy of Galileo and Johannes Kepler (Chapter 4)
were crucial steps on this road.
There was another problem. A stationary Sun and moving Earth also clashed with many biblical passages.
Protestants and Catholics alike often dismissed heliocentrism on these grounds. Martin Luther did so in one
of his "table talks" in 1539, before
De Revolutionibus
had appeared. (Preliminary sketches had circulated
in manuscript form.) In the long run, Protestants, who had some freedom to interpret the bible personally,
accepted heliocentrism somewhat more quickly.
Catholics, especially in Spain and Italy, had to be more
cautious in the religious climate of the Counter Reformation, as the case of Galileo clearly demonstrates.
6
Christoph Clavius , the leading Jesuit mathematician from about 1570 to his death in 1612, used biblical
arguments against heliocentrism in his astronomical textbook.
The situation was never simple, however.
7
For one thing, late in the sixteenth century Tycho Brahe
devised a hybrid geostatic heliocentric system in which the Moon and Sun went around the Earth but the
planets went around the Sun.
In this system the elegance and harmony of the Copernican system were
married to the solidity of a central and stable Earth so that Aristotelian physics could be maintained. Especially after Galileo's telescopic discoveries, many astronomers switched from the traditional to the Tychonic
cosmology.
For another thing, by 1600 there were still very few astronomers who accepted Copernicus's
8
cosmology. It is not clear whether the execution of Giordano Bruno , a Neoplatonist mystic who knew little
about astronomy, had anything to do with his Copernican beliefs. Finally, we must not forget that Copernicus had dedicated
De Revolutionibus
to the Pope. During the sixteenth century the Copernican issue was
not considered important by the Church and no ocial pronouncements were made.
Galileo's discoveries changed all that. Beginning with
Sidereus Nuncius in 1610, Galileo brought the issue
before a wide audience. He continued his eorts, ever more boldly, in his letters on sunspots, and in his letter
to the Grand Duchess Christina (circulated in manuscript only) he actually interpreted the problematical
biblical passage in the book of Joshua to conform to a heliocentric cosmology. More importantly, he argued
that the Bible is written in the language of the common person who is not an expert in astronomy. Scripture,
he argued, teaches us how to go to heaven, not how the heavens go. At about the same time, Paolo Antonio
9
Foscarini , a Carmelite theologian in Naples, published a book in which he argued that the Copernican
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6 "Christopher Clavius" <http://cnx.org/content/m11958/latest/>
7 "Tycho Brahe" <http://cnx.org/content/m11946/latest/>
8 "Giordano Bruno (1548-1600)" <http://cnx.org/content/m11935/latest/>
9 "Paolo Antonio Foscarini" <http://cnx.org/content/m11966/latest/>
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CHAPTER 2. COPERNICAN SYSTEM
8
theory did not conict with Scripture. It was at this point that Church ocials took notice of the Copernican
De Revolutionibus on the Index of Forbidden Books10 until corrected.
Dialogue Concerning the Two Chief World Systems of 1632 was a watershed in what had shaped
theory and placed
Galileo's
up to be the "Great Debate." Galileo's arguments undermined the physics and cosmology of Aristotle for
an increasingly receptive audience. His telescopic discoveries, although they did not prove that the Earth
moved around the Sun, added greatly to his argument. In the meantime, Johannes Kepler (Chapter 4) (who
had died in 1630) had introduced physical considerations into the heavens and had published his
Tables, based on his own elliptical theory and Tycho Brahe's11
Rudolphine
accurate observations, and these tables were
more accurate by far than any previous ones. The tide now ran in favor of the heliocentric theory, and from
the middle of the seventeenth century there were few important astronomers who were not Copernicans.
10 "The Congregation of the Index" <http://cnx.org/content/m11974/latest/>
11 "Tycho Brahe" <http://cnx.org/content/m11946/latest/>
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Chapter 3
1
Galileo's Telescope
Figure 3.1:
Johannes Hevelius observing with one of his telescopes.2 (Source: Selenographia, 1647)
The telescope was one of the central instruments of what has been called the Scientic Revolution of the
seventeenth century. It revealed hitherto unsuspected phenomena in the heavens and had a profound inuence
on the controversy between followers of the traditional geocentric astronomy (Chapter 5) and cosmology and
3
those who favored the heliocentric system of Copernicus . It was the rst extension of one of man's senses,
and demonstrated that ordinary observers could see things that the great Aristotle had not dreamed of. It
therefore helped shift authority in the observation of nature from men to instruments. In short, it was the
prototype of modern scientic instruments. But the telescope was not the invention of scientists; rather, it
was the product of craftsmen. For that reason, much of its origin is inaccessible to us since craftsmen were
by and large illiterate and therefore historically often invisible.
Although the magnifying and diminishing properties of convex and concave transparent objects was
known in Antiquity, lenses as we know them were introduced in the West
4 at the end of the thirteenth
century. Glass of reasonable quality had become relatively cheap and in the major glass-making centers of
Venice and Florence techniques for grinding and polishing glass had reached a high state of development.
Now one of the perennial problems faced by aging scholars could be solved. With age, the eye progressively
1 This content is available online at <http://cnx.org/content/m11932/1.4/>.
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3 "Introduction" <http://cnx.org/content/m11838/latest/>
4 They may have developed independently in China.
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CHAPTER 3. GALILEO'S TELESCOPE
10
loses its power to accommodate, that is to change its focus from faraway objects to nearby ones.
This
condition, known as presbyopia, becomes noticeable for most people in their forties, when they can no
longer focus on letters held at a comfortable distance from the eye. Magnifying glasses became common in
the thirteenth century, but these are cumbersome, especially when one is writing. Craftsmen in Venice began
making small disks of glass, convex on both sides, that could be worn in a framespectacles. Because these
little disks were shaped like lentils, they became known as "lentils of glass," or (from the Latin) lenses. The
earliest illustrations of spectacles date from about 1350, and spectacles soon came to be symbols of learning.
Figure 3.2:
The Spectacle Vendor by Johannes Stradanus, engraved by Johannes Collaert, 15825
These spectacles were, then, reading glasses. When one had trouble reading, one went to a spectaclemaker's shop or a peddler of spectacles (see Figure 3.2 and Figure 3.3) and found a suitable pair by trial and
error. They were, by and large, glasses for the old. spectacles for the young, concave lenses
6 that correct
the refractive error known as myopia, were rst made (again in Italy) in the middle of the fteenth century.
So by about 1450 the ingredients for making a telescope were there. The telescopic eect can be achieved
by several combinations of concave and convex mirrors and lenses. Why was the telescope not invented in
the fteenth century? There is no good answer to this question, except perhaps that lenses and mirrors of
the appropriate strengths were not available until later.
In the literature of white magic, so popular in the sixteenth century, there are several tantalizing references
to devices that would allow one to see one's enemies or count coins from a great distance. But these allusions
were cast in obscure language and were accompanied by fantastic claims; the telescope, when it came, was
a very humble and simple device. It is possible that in the 1570s Leonard and Thomas Digges in England
actually made an instrument consisting of a convex lens and a mirror, but if this proves to be the case, it
was an experimental setup that was never translated into a mass-produced device.
5 http://cnx.org/content/m11932/latest/spectacle_maker2.gif
6 Note that the word lens was used only to denote convex lenses until the end
7 The claim for an "Elizabethan telescope" has recently been made by Colin
based on the writings of Thomas Digges and William Bourne.
7
of the seventeenth century.
Ronin, who has demonstrated an instrument
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11
The earliest known illlustration of a telescope. Giovanpattista della Porta included this
sketch in a letter written in August 1609.8
Figure 3.3:
The telescope was unveiled in the Netherlands.
In October 1608, the States General (the national
9 of Middelburg, and
government) in The Hague discussed the patent applications rst of Hans Lipperhey
then of Jacob Metius of Alkmaar, on a device for "seeing faraway things as though nearby." It consisted of
a convex and concave lens in a tube, and the combination magnied three or four times.
10 The gentlemen
found the device too easy to copy to award the patent, but it voted a small award to Metius and employed
Lipperhey to make several binocular versions, for which he was paid handsomely. It appears that another
citizen of Middelburg, Sacharias Janssen had a telescope at about the same time but was at the Frankfurt
Fair where he tried to sell it.
Figure 3.4:
Galileo's telescopes11
The news of this new invention spread rapidly through Europe, and the device itself quickly followed. By
April 1609 three-powered spyglasses could be bought in spectacle-maker's shops on the Pont Neuf in Paris,
12 observed
and four months later there were several in Italy. (Figure 3.4) We know that Thomas Harriot
the Moon (Chapter 10) with a six-powered instrument early in August 1609. But it was Galileo who made
the instrument famous. He constructed his rst three-powered spyglass in June or July 1609, presented an
eight-powered instrument to the Venetian Senate in August, and turned a twenty-powered instrument to the
heavens in October or November. With this instrument (Figure 3.5) he observed the Moon, discovered four
satellites of Jupiter (Chapter 6), and resolved nebular patches into stars. He published
Sidereus Nuncius
in
March 1610.
Verifying Galileo's discoveries was initially dicult.
In the spring of 1610 no one had telescopes of
sucient quality and power to see the satellites of Jupiter, although many had weaker instruments with
which they could see some of the lunar detail Galileo had described in
Sidereus Nuncius.
Galileo's lead was
one of practice, not theory, and it took about six months before others could make or obtain instruments
good enough to see Jupiter's moons. With the verication of the phases of Venus by others, in the rst half
8 http://cnx.org/content/m11932/latest/porta_sketch.gif
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10 Their optical system and magnication was the same as our traditional
11 http://cnx.org/content/m11932/latest/g_telescope.gif
12 "Thomas Harriot" <http://cnx.org/content/m11979/latest/>
opera glasses.
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CHAPTER 3. GALILEO'S TELESCOPE
12
of 1611, Galileo's lead in telescope-making had more or less evaporated. The next discovery, that of sunspots
(Chapter 8), was made by several observers, including Galileo, independently.
Figure 3.5
A typical Galilean telescope with which Jupiter's moons could be observed was congured as follows. It
had a plano-convex objective (the lens toward the object) with a focal length of about 30-40 inches., and
a plano-concave ocular with a focal length of about 2 inches.
The ocular was in a little tube that could
be adjusted for focusing. The objective lens was stopped down to an aperture of 0.5 to 1 inch. , and the
eld of view was about 15 arc-minutes (about 15 inches in 100 yards). The instrument's magnication was
15-20.
The glass was full of little bubbles and had a greenish tinge (caused by the iron content of the
glass); the shape of the lenses was reasonable good near their centers but poor near the periphery (hence
the restricted aperture); the polish was rather poor.
The limiting factor of this type of instrument was
its small eld of viewabout 15 arc-minuteswhich meant that only a quarter of the full Moon could be
accommodated in the eld. Over the next several decades, lens-grinding and polishing techniques improved
gradually, as a specialized craft of telescope makers slowly developed. But although Galilean telescopes of
higher magnications were certainly made, they were almost useless because of the concomitant shrinking
of the eld.
As mentioned above, the telescopic eect can be achieved with dierent combinations of lenses and
mirrors. As early as 1611, in his
Dioptrice,
Johannes Kepler (Chapter 4) had shown that a telescope could
also be made by combining a convex objective and a convex ocular. He pointed out that such a combination
would produce an inverted image but showed that the addition of yet a third convex lens would make the
image erect again. This suggestion was not immediately taken up by astronomers, however, and it was not
until Christoph Scheiner
13 published his
Rosa Ursina in 1630 that this form of telescope began to spread.
In
his study of sunspots, Scheiner had experimented with telescopes with convex oculars in order to make the
image of the Sun projected through the telescope erect.
14 But when he happened to view an object directly
through such an instrument, he found that, although the image was inverted, it was much brighter and
the eld of view much larger than in a Galilean telescope. Since for astronomical observations an inverted
image is no problem, the advantages of what became known as the astronomical telescope led to its general
acceptance in the astronomical community by the middle of the century.
13 "Christoph Scheiner" <http://cnx.org/content/m12126/latest/>
14 The Galilean telescope produces an erect image of an object viewed
directly but an inverted image of a projected object;
by substituting a convex for the concave ocular, this situation is reversed.
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13
The Galilean telescope could be used for terrestrial and celestial purposes interchangeably. This was not
true for the astronomical telescope with its inverted image. Astronomers eschewed the third convex lens (the
erector lens) necessary for re-inverting the image because the more lenses the more optical defects multiplied.
In the second half of the seventeenth century, therefore, the Galilean telescope was replaced for terrestrial
purposes by the "terrestrial telescope," which had four convex lenses: objective, ocular, erector lens, and a
eld lens (which enlarged the eld of view even further).
(a)
(b)
Figure 3.6:
16
scope
(Machina Coelestis, 1673) (a) Hevelius's 60 foot telescope15 (b) Hevelius's 140 foot tele-
With the acceptance of the astronomical telescope, the limit on magnication caused by the small eld
of view of the Galilean telescope was temporarily lifted, and a "telescope race" developed.
Because of
optical defects, the curvature of lenses had to be minimized, and therefore (since the magnication of a
simple telescope is given roughly by the ratio of the focal lengths of the objective and ocular) increased
magnication had to be achieved by increasing the focal length of the objective. Beginning in the 1640s,
the length of telescopes began to increase.
From the typical Galilean telescope of 5 or 6 feet in length,
astronomical telescopes rose to lengths of 15 or 20 feet by the middle of the century. A typical astronomical
telescope is the one made by Christiaan Huygens, in 1656. It was 23 feet long; its objective had an aperture
15 http://cnx.org/content/m11932/latest/hevelius_telescope_60ft.gif
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CHAPTER 3. GALILEO'S TELESCOPE
14
of several inches, it magnied about 100 times, and its eld of view was 17 arc-minutes.
Figure 3.7:
Aerial telescope (Christiaan Huygensm Astroscopium Compendiaria,1684)17
Telescopes had now again reached the point where further increases in magnication would restrict the
eld of view of the instrument too much. This time another optical device, the eld lens came to the rescue.
Adding a third convex lensof appropriate focal length, and in the right placeincreased the eld signicantly,
thus allowing higher magnications. The telescope race therefore continued unabated and lengths increased
exponentially. By the early 1670s, Johannes Hevelius had built a 140-foot telescope.
But such long telescopes were useless for observation: it was almost impossible to keep the lenses aligned
and any wind would make the instrument utter. After about 1675, therefore, astronomers did away with
the telescope tube. The objective was mounted on a building or pole by means of a ball-joint and aimed
by means of a string; the image was found by trial and error; and the compound eyepiece (eld lens and
ocular), on a little stand, was then positioned to receive the image cast by the objective. Such instruments
were called aerial telescopes.
Although some discoveries were made with these very long instruments, this form of telescope had reached
its limits. By the beginning of the eighteenth century very long telescopes were rarely mounted any more,
and further increases of power came, beginning in the 1730s, from a new form of telescope, the reecting
telescope.
Since it was known that the telescopic eect could be achieved using a variety of combinations of lenses
and mirrors, a number of scientists speculated on combinations involving mirrors. Much of this speculation
was fueled by the increasingly rened theoretical study of the telescope. In his Dioptrique, appended to his
Discourse on Method of 1637, Renè Descartes addressed the problem of spherical aberration, already pointed
out by others. In a thin spherical lens, not all rays from innityincident parallel to the optical axisare
united at one point. Those farther from the optical axis come to a focus closer to the back of the lens than
those nearer the optical axis. Descartes had either learned the sine law of refraction from Willebrord Snell
(Snell's Law)
18 or had discovered it independently, and this allowed him to quantify spherical aberration. In
order to eliminate it, he showed, lens curvature had to be either plano-hyperboloidal or spherico-ellipsoidal.
His demonstration led many to attempt to make plano-hyperboloidal objectives,
19 an eort which was
doomed to failure by the state of the art of lens-grinding. Others began considering the virtues of a concave
paraboloidal mirror as primary receptor: it had been known since Antiquity that such a mirror would bring
parallel incident rays to a focus at one point.
17 http://cnx.org/content/m11932/latest/aerial_telescope.gif
18 The ratio of the sines of the angles of incidence and refraction is constant.
19 The eect is most apparent for the objective; spherical aberration in the ocular
aects the image much less.
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15
Figure 3.8:
Newton's reecting telescope (1671)20
A second theoretical development came in 1672, when Isaac Newton published his celebrated paper on
light and colors. Newton showed that white light is a mixture of colored light of dierent refrangibility: every
color had its own degree of refraction. The result was that any curved lens would decompose white light into
the colors of the spectrum, each of which comes to a focus at a dierent point on the optical axis. This eect,
which became known as chromatic aberration, resulted in a central image of, e.g., a planet, being surrounded
by circles of dierent colors. Newton had developed his theory of light several years before publishing his
paper, when he had turned his mind to the improvement of the telescope, and he had despaired of ever
ridding the objective of this defect.
He therefore decided to try a mirror, but unlike his predecessors he
was able to put his idea into practice. He cast a two-inch mirror blank of speculum metal (basically copper
with some tin) and ground it into spherical curvature. He placed it in the bottom of a tube and caught the
reected rays on a 45
◦
secondary mirror which reected the image into a convex ocular lens outside the tube
(see Figure 3.8). He sent this little instrument to the Royal Society, where it caused a sensation; it was the
rst working reecting telescope. But the eort ended there. Others were unable to grind mirrors of regular
curvature, and to add to the problem, the mirror tarnished and had to be repolished every few months, with
the attending danger of damage to the curvature.
Figure 3.9:
Hevelius's rooftop observatory, (Machina Coelestis, 1673)21
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CHAPTER 3. GALILEO'S TELESCOPE
16
The reecting telescope therefore remained a curiosity for decades. In second and third decades of the
eighteenth century, however, the reecting telescope became a reality in the hands of rst James Hadley
and then others. By the middle of the century, reecting telescopes with primary mirrors up to six inches
in diameter had been made.
It was found that for large aperture ratios (the ratio of focal length of the
primary to its aperture, as the f-ratio in modern cameras for instance), f/10 or more, the dierence between
spherical and paraboloidal mirrors was negligible in the performance of the telescope. In the second half of
the eighteenth century, in the hands of James Short and then William Herschel, the reecting telescope with
parabolically ground mirrors came into its own.
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Chapter 4
Johannes Kepler
Figure 4.1:
1
Johannes Kepler
Johannes Kepler was born in Weil der Stadt in Swabia, in southwest Germany. His paternal grandfather,
Sebald Kepler, was a respected craftsman who served as mayor of the city; his maternal grandfather, Melchior
Guldenmann, was an innkeeper and mayor of the nearby village of Eltingen. His father, Heinrich Kepler, was
"an immoral, rough and quarrelsome soldier," according to Kepler, and he described his mother in similar
unattering terms. From 1574 to 1576 Johannes lived with his grandparents; in 1576 his parents moved to
nearby Leonberg, where Johannes entered the Latin school. In 1584 he entered the Protestant seminary at
Adelberg, and in 1589 he began his university education at the Protestant university of T\x{00FC}bingen.
Here he studied theology and read widely. He passed the M.A. examination in 1591 and continued his studies
as a graduate student.
Kepler's teacher in the mathematical subjects was Michael Maestlin (1580-1635). Maestlin was one of
the earliest astronomers to subscribe to Copernicus's heliocentric theory, although in his university lectures
he taught only the Ptolemaic system. Only in what we might call graduate seminars did he acquaint his
students, among whom was Kepler, with the technical details of the Copernican system (Chapter 2). Kepler
stated later that at this time he became a Copernican for "physical or, if you prefer, metaphysical reasons."
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CHAPTER 4. JOHANNES KEPLER
18
In 1594 Kepler accepted an appointment as professor of mathematics at the Protestant seminary in Graz
(in the Austrian province of Styria).
He was also appointed district mathematician and calendar maker.
Kepler remained in Graz until 1600, when all Protestants were forced to convert to Catholicism or leave the
province, as part of Counter Reformation measures. For six years, Kepler taught arithmetic, geometry
(when there were interested students), Virgil, and rhetoric. In his spare time he pursued his private studies
in astronomy and astrology. In 1597 Kepler married Barbara Muller. In that same year he published his
rst important work,
The Cosmographic Mystery, in which he argued that the distances of the planets from
the Sun in the Copernican system were determined by the ve regular solids, if one supposed that a planet's
orbit was circumscribed about one solid and inscribed in another.
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19
Kepler's model to explain the relative distances of the planets from the Sun in the Copernican System.
Figure 4.2:
Except for Mercury, Kepler's construction produced remarkably accurate results. Because of his talent
2 to Prague to become his
as a mathematician, displayed in this volume, Kepler was invited by Tycho Brahe
2 "Tycho
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CHAPTER 4. JOHANNES KEPLER
20
assistant and calculate new orbits for the planets from Tycho's observations. Kepler moved to Prague in
1600.
Kepler served as Tycho Brahe's assistant until the latter's death in 1601 and was then appointed Tycho's
successor as Imperial Mathematician, the most prestigious appointment in mathematics in Europe.
He
occupied this post until, in 1612, Emperor Rudolph II was deposed. In Prague Kepler published a number of
important books. In 1604
Astronomia pars Optica ("The Optical Part of Astronomy") appeared, in which he
treated atmospheric refraction but also treated lenses and gave the modern explanation of the workings
of the eye; in 1606 he published
appeared in 1604; and in 1609 his
De Stella Nova ("Concerning the New Star") on the new star that had
Astronomia Nova ("New Astronomy") appeared, which contained his rst
two laws (planets move in elliptical orbits with the sun as one of the foci, and a planet sweeps out equal
areas in equal times). Whereas other astronomers still followed the ancient precept that the study of the
planets is a problem only in kinematics, Kepler took an openly dynamic approach, introducing physics into
the heavens.
In 1610 Kepler heard and read about Galileo's discoveries with the spyglass.
a long letter of support which he published as
Dissertatio cum Nuncio Sidereo
He quickly composed
("Conversation with the
Sidereal Messenger"), and when, later that year, he obtained the use of a suitable telescope, he published
his observations of Jupiter's satellites (Chapter 6) under the title
Satellitibus ("Narration about Four Satellites of Jupiter observed").
Narratio de Observatis Quatuor Jovis
These tracts were an enormous support
to Galileo, whose discoveries were doubted or denied by many. Both of Kepler's tracts were quickly reprinted
in Florence. Kepler went on to provide the beginning of a theory of the telescope in his
Dioptrice, published
in 1611.
During this period the Keplers had three children (two had been born in Graz but died within months),
Susanna (1602), who married Kepler's assistant Jakob Bartsch in 1630, Friedrich (1604-1611), and Ludwig
(1607-1663).
Kepler's wife, Barbara, died in 1612.
In that year Kepler accepted the position of district
mathematician in the city of Linz, a position he occupied until 1626.
In Linz Kepler married Susanna
Reuttinger. The couple had six children, of whom three died very early.
In Linz Kepler published rst a work on chronology and the year of Jesus's birth, In German in 1613 and
De Vero Anno quo Aeternus Dei Filius Humanam Naturam in Utero Benedictae
Virginis Mariae Assumpsit (Concerning the True Year in which the Son of God assumed a Human Nature in
more amply in Latin in 1614:
the Uterus of the Blessed Virgin Mary"). In this work Kepler demonstrated 0 Kepler heard and read about
Galileo's discoveries with the spyglass. He quickly composed a long letter of support which he published as
Dissertatio cum Nuncio Sidereo ("Conversation with the Sidereal Messenger"), and when, later that year, he
obtained the use of a suitable telescope, he published his observations of Jupiter's satellites under the title
Narratio de Observatis Quatuor Jovis Satellitibus ("Narration about Four Satellites of Jupiter observed").
These tracts were an enormous support to Galileo, whose discoveries were doubted or denied by many. Both
of Kepler's tracts were quickly reprinted in Florence. Kepler went on to provide the beginning of a theory
of the telescope in his Dioptrice, published in 1611.that the Christian calendar was in error by ve years,
and that Jesus had been born in 4 BC, a conclusion that is now universally accepted. Between 1617 and
1621 Kepler published
Epitome Astronomiae Copernicanae
("Epitome of Copernican Astronomy"), which
became the most inuential introduction to heliocentric astronomy; in 1619 he published
Harmonice Mundi
("Harmony of the World"), in which he derived the heliocentric distances of the planets and their periods
from considerations of musical harmony. In this work we nd his third law, relating the periods of the planets
to their mean orbital radii.
In 1615-16 there was a witch hunt in Kepler's native region, and his own mother was accused of being a
witch. It was not until late in 1620 that the proceedings against her ended with her being set free. At her
trial, her defense was conducted by her son Johannes.
1618 marked the beginning of the Thirty Years War, a war that devastated the German and Austrian
region.
Kepler's position in Linz now became progressively worse, as Counter Reformation measures
put pressure on Protestants in the Upper Austria province of which Linz was the capital.
Because he
was a court ocial, Kepler was exempted from a decree that banished all Protestants from the province,
but he nevertheless suered persecution.
During this time Kepler was having his
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Tabulae Rudolphinae
21
("Rudolphine Tables") printed, the new tables, based on Tycho Brahe's accurate observations, calculated
according to Kepler's elliptical astronomy. When a peasant rebellion broke out and Linz was besieged, a re
destroyed the printer's house and shop, and with it much of the printed edition. Soldiers were garrisoned
in Kepler's house. He and his family left Linz in 1626. The
Tabulae Rudolphinae
were published in Ulm in
1627.
Kepler now had no position and no salary.
He tried to obtain appointments from various courts and
returned to Prague in an eort to pry salary that was owed him from his years as Imperial Mathematician
from the imperial treasury.
He died in Regensburg in 1630.
Besides the works mentioned here, Kepler
published numerous smaller works on a variety of subjects.
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CHAPTER 4. JOHANNES KEPLER
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Chapter 5
1
Ptolemaic System
Figure 5.1:
In his
Ptolemaic System
Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican
of 1632, Galileo
attacked the world system based on the cosmology of Aristotle (384-322 BCE) and the technical astronomy
of Ptolemy (ca. 150 CE).
In his books
On the Heavens,
and
Physics,
Aristotle put forward his notion of an ordered universe or
cosmos. It was governed by the concept of place , as opposed to space, and was divided into two distinct
parts, the earthly or sublunary region, and the heavens. The former was the abode of change and corruption,
where things came into being, grew, matured, decayed, and died; the latter was the region of perfection,
where there was no change. In the sublunary region, substances were made up of the four elements, earth,
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CHAPTER 5. PTOLEMAIC SYSTEM
24
water, air, and re. Earth was the heaviest, and its natural place was the center of the cosmos; for that
reason the Earth was situated in the center of the cosmos. The natural places of water, air, and re, were
concentric spherical shells around the sphere of earth.
Things were not arranged perfectly, and therefore
areas of land protruded above the water. Objects sought the natural place of the element that predominated
in them. Thus stones, in which earth predominated, move down to the center of the cosmos, and re moves
straight up. Natural motions were, then, radial, either down or up. The four elements diered from each
other only in their qualities. Thus, earth was cold and dry while air was warm and moist. Changing one or
both of its qualities, transmuted one element into another. Such transmutations were going on constantly,
adding to the constant change in this sublunary region.
Figure 5.2:
Ptolemy
The heavens, on the other hand, were made up of an entirely dierent substance, the aether
quintessence (fth element), an immutable substance.
2 The
2 or
Heavenly bodies were part of spherical shells of
traditional English spelling, aether, is used here to distinguish Aristotle's heavenly substance from the modern chemical
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25
aether. These spherical shells t tightly around each other, without any spaces between them, in the following order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, xed stars. Each spherical shell (hereafter,
simply, sphere) had its particular rotation, that accounted for the motion of the heavenly body contained
in it. Outside the sphere of the xed stars, there was the prime mover (himself unmoved), who imparted
motion from the outside inward. All motions in the cosmos came ultimately from this prime mover. The
natural motions of heavenly bodies and their spheres was perfectly circular, that is, circular and neither
speeding up nor slowing down.
It is to be noted about this universe that everything had its natural place, a privileged location for bodies
with a particular makeup, and that the laws of nature were not the same in the heavenly and the earthly
regions. Further, there were no empty places or vacua anywhere. Finally, it was nite: beyond the sphere
of the xed stars and the prime mover, there was nothing, not even space.
The cosmos encompassed all
existence.
Figure 5.3:
Christian Aristotelian Cosmos. From Peter Apian, Cosmographia3
Now, ingenious as this cosmology was, it turned out to be unsatisfactory for astronomy. Heavenly bodies
did, in fact, not move with perfect circular motions: they speeded up, slowed down, and in the cases of
the planets even stopped and reversed their motions. Although Aristotle and his contemporaries tried to
account for these variations by splitting individual planetary spheres into component spheres, each with
a component of the composite motion, these constructions were very complex and ultimately doomed to
failure. Furthermore, no matter how complex a system of spheres for an individual planet became, these
spheres were still centered on the Earth. The distance of a planet from the Earth could therefore not be
varied in this system, but planets vary in brightness, a variation especially noticeable for Venus, Mars, and
Jupiter. Since in an unchangeable heaven variations in intrinsic brightness were ruled out, and since spheres
did not allow for a variation in planetary distances from the Earth, variations in brightness could not be
accounted for in this system.
Thus, although Aristotle's spherical cosmology had a very long life, mathematicians who wished to make
geometrical models to account for the actual motions of heavenly bodies began using dierent constructions
within a century of Aristotle's death.
These constructions violated Aristotle's physical and cosmological
principles somewhat, but they were ultimately successful in accounting for the motions of heavenly bodies.
It is in the work of Claudius Ptolemy, who lived in the second century CE, that we see the culmination of these
eorts. In his great astronomical work,
Almagest,
4 Ptolemy presented a complete system of mathematical
substance, ether.
3 http://cnx.org/content/m11943/latest/ptolematic_universe.gif
4 The title is one given to this book by Islamic translators in the ninth century. Its original Greek title is Mathematical
Syntaxis.
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CHAPTER 5. PTOLEMAIC SYSTEM
26
constructions that accounted successfully for the observed motion of each heavenly body.
Ptolemy used three basic constructions, the eccentric, the epicycle, and the equant. An eccentric construction is one in which the Earth is placed outside the center of the geometrical construction. Here, the
Earth, E, is displaced slightly from the center, C, of the path of the planet.
Although this construction
violated the rule that the Earth was the center of the cosmos and all planetary motions, the displacement
was minimal and was considered a slight bending of the rule rather than a violation. The eccentric in the
gure below is xed; it could also be made movable. In this case the center of the large circle was a point
that rotated around the Earth in a small circle centered on the Earth. In some constructions this little circle
was not centered in the Earth.
The second construction, the epicycle, is geometrically equivalent to the simple movable eccentric.
In
this case, the planet moved on a little circle the center of which rotated on the circumference of the large
circle centered on the on theEarth. When the directions and speeds of rotation of the epicycle and large
circle were chosen appropriately, the planet, as seen from the Earth, would stop, reverse its course, and then
move forward again. Thus the annual retrograde motion of the planets (caused, in heliocentric terms by the
addition of the Earth's annual motion to the motion of the planet) could roughly be accounted for.
(a)
(b)
(c)
From Michael J. Crowe, Theories of the World from Antiquity to the Copernican Revolution. (a) Eccentric5 (b) Epicycle6 (c) Equant7
Figure 5.4:
But these two constructions did not quite bring the resulting planetary motions within close agreement
with the observed motions.
Ptolemy therefore added yet a third construction, the equant.
In this case,
the center of construction of the large circle was separated from the center of motion of a point on its
circumference, as shown below, where C is the geometrical center of the large circle (usually called in these
constructions the excentric circle) but the motion of the center of the epicycle, P (middle of Figure 5.4), is
uniform about Q, the equant point (righthand side of Figure 5.4).
Ptolemy combined all three constructions in the models of the planets, Sun, and Moon.
A typical
construction might thus be as in the picture below, where E is the Earth, C the geometric center of the
eccentric circle, Q the equant point, F the center of the epicycle, and P the planet. As mentioned before,
the eccentric was often not xed but moved in a circle about the Earth or another point between the Earth
and the equant point.
5 http://cnx.org/content/m11943/latest/eccentric_p.gif
6 http://cnx.org/content/m11943/latest/epicycle_p.gif
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Typical Ptolemaic planetary model (From Michael J. Crowe, Theories of the World from
Antiquity to the Copernican Revolution.)8
Figure 5.5:
With such combinations of constructions, Ptolemy was able to account for the motions of heavenly bodies
within the standards of observational accuracy of his day. The idea was to break down the complex observed
planetary motion into components with perfect circular motions. In doing so, however, Ptolemy violated the
cosmological and physical rules of Aristotle. The excentric and epicycle meant that planetary motions were
not exactly centered on the Earth, the center of the cosmos. This was, however, a "fudge" that few objected
to. The equant violated the stricture of perfect circular motion, and this violation bothered thinkers a good
deal more. Thus, in
De Revolutionibus
(see Copernican System (Chapter 2)), Copernicus tells the reader
that it was his aim to rid the models of heavenly motions of this monstrous construction.
Aristotelian cosmology and Ptolemaic astronomy entered the West, in the twelfth and thirteenth centuries, as distinct textual traditions. The former in Aristotle's
commentaries on these works; the latter in the
Almagest
Physics and On the Heavens
and the many
and the technical astronomical literature that had
grown around it, especially the work of Islamic astronomers working in the Ptolemaic paradigm. In the world
of learning in the Christian West (settled in the universities founded around 1200 CE), Aristotle's cosmology
gured in all questions concerned with the nature of the universe and impinged on many philosophical and
theological questions. Ptolemy's astronomy was taught as part of the undergraduate mathematical curriculum only and impinged only on technical questions of calendrics, positional predictions, and astrology.
Copernicus's innovations was therefore not only putting the Sun in the center of the universe and working
out a complete astronomical system on this basis of this premise, but also trying to erase the disciplinary
boundary between the textual traditions of physical cosmology and technical astronomy.
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CHAPTER 5. PTOLEMAIC SYSTEM
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Chapter 6
Satellites of Jupiter
Figure 6.1:
1
Jupiter's moons
Jupiter has a large number of satellites.
Of these, four are comparable to the Earth's Moon in size; the
rest are orders of magnitude smaller. When Jupiter is at opposition and closest to the Earth, the stellar
2
magnitude of its four large moons is between 5 and 6.
This means that, were it not for the shielding
brightness of Jupiter, these bodies would be visible with the naked eye. The aperture of the telescope used
by Galileo in 1610 and its magnication thus brought these four "Galilean" satellites within his grasp.
But rst Galileo had to make adjustments to the instruments. When viewing bodies that are very bright
and very small, the optical defects of the telescope (Chapter 3) can be crippling. By trial and error Galileo
learned to stop down the aperture of his instrument until he could begin to make useful observations. At
the end of 1609, as he was nishing his series of observations of the Moon (Chapter 10), Jupiter was at
opposition and the brightest object in the evening sky (not counting the Moon). When he had made the
new adjustment to his instrument, he turned his attention to Jupiter. On 7 January 1610 he observed the
1 This content
2 In Antiquity
is available online at <http://cnx.org/content/m11971/1.2/>.
a rough numerical brightness rating for stars and planets was developed. Stars of the rst magnitude were
brightest; the dimmest celestial objects visible (to the naked eye) were assigned the sixth magnitude. This system is the basis
of the modern system of stellar magnitudes bases on instrumental readings.
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CHAPTER 6. SATELLITES OF JUPITER
30
planet and saw what he thought were three xed stars near it, strung out on a line through the planet. This
formation caught his attention, and he returned to it the following evening.
Galileo's expectation was that Jupiter, which was then in its retrograde loop,
3 would have moved from
east to west and had left the three little stars behind. Instead, he saw all three stars to the west of Jupiter.
It appeared as though Jupiter had not moved to the west but rather to the east.
This was an anomaly,
and Galileo returned to this formation again and again. Over the next week he found out several things.
First, the little stars never left Jupiter; they appeared to be carried along with the planet. Second, as they
were carried along, they changed their position with respect to each other and Jupiter. Third, there were
not three but four of these little stars. By the 15th of January he had gured it out: these were not xed
stars but rather planetary bodies that revolved around Jupiter. Jupiter had four moons. His book, Sidereus
Nuncius, in which his discovery was described, came o the press in Venice in the middle of March 1610 and
made Galileo famous.
(a)
Figure 6.2:
(b)
Galileo's observations of Jupiter's moon (a) large version4 (b) large version5
The moons of Jupiter had a major impact on cosmology. In 1610 the traditional Aristotelian cosmology
had come under attacks from Copernican astronomers. Aristotelians had a number of arguments against
the Copernican System (Chapter 2), one of which was now made obsolete. In traditional cosmology, there
was only one center of motion, the center of the universe which was the place of the Earth. The motions of
all heavenly bodies centered on the Earth. But according to the Copernican theory, the Earth went around
the Sun while the Moon went around the Earth. There were thus two centers of motion, which seemed an
absurdity. Moreover, if the Earth was a planet, like Mercury, Venus, Mars, Jupiter, and Saturn, why was
it the only planet to have a Moon? Galileo's discovery answered this question. The Earth was, in fact, not
the only planet to have a moon, Jupiter had four. And no matter what cosmological system one believed in,
there were now at least two centers of motion in the universe, the Earth or Sun and Jupiter. Thus, although
the satellites (the term was rst used by Johannes Kepler (Chapter 4)) of Jupiter were by no means proof
of the truth of the Copernican system, they certainly added ammunition on that side of the argument.
3 When Jupiter is near opposition, it is on the same side of the Sun as the Earth, but the Earth is moving much faster than
Jupiter. It therefore appears that Jupiter is moving backward with respect to the xed stars.
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31
In the purely astronomical realm, the satellites of Jupiter posed a new problem for astronomers. It had
taken centuries in Antiquity to arrive at adequate geometrical modes for the motions of the known planets.
Now there was a new system of planetary bodies in miniature, and astronomers had to develop models that
could predict their motions. There was a great incentive to come up with good mathematical models, for
6
the satellites oered some hope for the solution of the problem of longitude at sea .
It took almost two
centuries, however, before the models and tables based on them reached satisfactory accuracy.
The naming of the satellites provides an interesting example of how such matters were handled before the
foundation of the International Astronomical Union in the twentieth century. As their discoverer, Galileo
claimed the right to name the satellites. He wanted to name them after his patrons and asked whether they
7
would prefer "Cosmic Stars" (after Cosimo II ) or "Medicean Stars." They opted for the latter, and through
much of the seventeenth century they were known by that name. In his notebooks, Galileo referred to them
individually by number, starting with the satellite closest to Jupiter, but he never had occasion to refer to
them in this way in print.
In Provence, Nicholas Claude Fabri de Peiresc tried to dierentiate between the Medicean Stars by
assigning them the names of individual members of the family, but this system was not published and thus
was never used by others. In his Mundus Iovialis ("Jovian World") of 1614, Simon Marius
naming problem in some depth.
8 went into the
First, he himself used the numerical system beginning with the satellite
closest to Jupiter. Second, he thought that he might call them after his patron, the Duke of Brandenburg
a suggestion followed by no one. Third, he suggested naming the farthest satellite the Saturn of Jupiter,
the next one the Jupiter of Jupiter, the third one the Venus of Jupiter, and the one nearest the planet the
Mercury of Jupiter.
This cumbersome system never caught on.
Finally, Marius related a suggestion by
Kepler (Chapter 4):
Jupiter is much blamed by the poets on account of his irregular loves. Three maidens are
especially mentioned as having been clandestinely courted by Jupiter with success. Io, daughter
of the River, Inachus, Callisto of Lycaon, Europa of Agenor. Then there was Ganymede, the
handsome son of King Tros, whom Jupiter, having taken the form of an eagle, transported to
heaven on his back, as poets fabulously tell . . . . I think, therefore, that I shall not have done
amiss if the First is called by me Io, the Second Europa, the Third, on account of its majesty of
light, Ganymede, the Fourth Callisto . . . .
This fancy, and the particular names given, were suggested to me by Kepler, Imperial Astronomer,
when we met at Ratisbon fair in October 1613. So if, as a jest, and in memory of our friendship
then begun, I hail him as joint father of these four stars, again I shall not be doing wrong. [3]
None of these suggestion caught on because with Jupiter's satellites, there was no confusion in the
numbering system. Following Galileo and Marius, astronomers simply referred to them by number. With
the satellites of Saturn, however, a problem developed. In 1655 Huygens discovered the rst and largest; then
in 1671-72 Giandomenico Cassini discovered two more, and in 1684 yet another two. These ve satellites were
numbered like their Galilean counterparts. But when in 1789 William Herschel discovered two additional
satellites internal to the rst, confusion followed. Did one now renumber them all (thus causing confusion for
those who consulted older works), refer to the two new ones as nos. 6 and 7 (thus making the order of the
satellites confusing), or refer to them by order of discovery (equally confusing as to order)? Herschel's son,
John Frederick William, suggested in 1847 that Saturn's satellites be given individual names of mythological
gures associated with Saturn after the suggestion made by Marius for Jupiter's satellites.
When, the
following year, William Lassel and George Bond independently discovered an eighth satellite of Saturn, they
agreed to adopt the naming system proposed by Herschel, in which Saturn's satellites were named after his
brothers and sisters, the Titans.
This system and the now revived suggestion by Kepler and Marius for
Jupiter quickly became the convention for naming the satellites of the superior planets.
6 "Longitude at Sea" <http://cnx.org/content/m11963/latest/>
7 "The Medici Family" <http://cnx.org/content/m11975/latest/>
8 "Simon Marius" <http://cnx.org/content/m11973/latest/>
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CHAPTER 6. SATELLITES OF JUPITER
32
Modern Images of the Galilean Satellites
(a)
(e)
Figure 6.3:
16
(h) Callisto
(b)
(f)
(c)
(g)
(d)
(h)
(a) Io9 (b) Io10 (c) Europa11 (d) Europa12 (e) Ganymede13 (f) Ganymede14 (g) Callisto15
9 http://cnx.org/content/m11971/latest/io1.gif
10 http://cnx.org/content/m11971/latest/io2.gif
11 http://cnx.org/content/m11971/latest/europa1.gif
12 http://cnx.org/content/m11971/latest/europa2.gif
13 http://cnx.org/content/m11971/latest/ganymede1.gif
14 http://cnx.org/content/m11971/latest/ganymede2.gif
15 http://cnx.org/content/m11971/latest/callisto1.gif
16 http://cnx.org/content/m11971/latest/callisto2.gif
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Chapter 7
Saturn
Figure 7.1:
1
Saturn
To all serious observers of the heaven, it was known that stars move in a xed formation around the Earth
except for seven bodies that moved through the xed stars in a wide band, the zodiac. To the Greeks, all
heavenly bodies were stars; most were xed but some wandered. These seven wandering stars, or planets,
were (in the conventional order), Moon (Chapter 10), Mercury, Venus, Sun, Mars, Jupiter, Saturn. Mercury
was the most dicult to observe because it was always close to the Sun, Venus, as morning or evening star,
was the brightest body in the heavens.
Mars had a distinctive red color, Jupiter at opposition was very
bright, and the straw-colored Saturn, the slowest of all planets (sidereal period 30 years), was the dimmest.
The planets were identied with gods by the Mesopotamians, and the Greeks copied this system, assigning
planets the names of their gods. The planets were also associated with the seven known metals: Moon/silver,
Mercury/mercury, Venus/copper, Sun/gold. Mars/iron, Jupiter/tin, and Saturn/lead. In accordance with
their gods, the planets were assigned astrological meanings still used by the astrologers who write daily
columns in many of our newspapers.
1 This
content is available online at <http://cnx.org/content/m11972/1.2/>.
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CHAPTER 7. SATURN
34
Figure 7.2:
Saturn as the grim reaper2
Saturn, associated with time and the grim reaper, was usually depicted with a scythe. According to the
prevailing cosmology of Aristotle, Western astronomers knew that, like all other heavenly bodies, the planet
Saturn was perfect and spherical. The telescope therefore gave them a surprise. After publishing Sidereus
Nuncius, in March 1610, Galileo continued scrutinizing the heavens, especially the planets, in the hope of
3
making further discoveries. In July, as Saturn was bright in the evening sky and approaching opposition,
4
he turned his telescope toward it and made a new discovery. On 30 July he wrote to his Medici patron:
I discovered another very strange wonder, which I should like to make known to their Highnesses
. . . , keeping it secret, however, until the time when my work is published . . . . the star
of Saturn is not a single star, but is a compsite of three, which almost touch each other, never
change or move relative to each other, and are arranged in a row along the zodiac, the middle
one being three times larger than the lateral ones, and they are situated in this form: oOo.
Galileo no doubt planned to publish this new discovery in his next book, but in the meantime, how could
he preserve his priority and prevent others from claiming the discovery as their own? His solution was to
circulate an anagram, s m a i s m r m i l m e p o e t a l e u m i b u n e n u g t t a u i r a s.
Others
would know that he had discovered something and when he had discovered it, but they would not known
what the discovery was. The number of letters in the anagram, 37, was too small to allow him later to fudge
and change the solution to describe a discovery made by someone else in the meantime. Before the days of
scientic papers (invented in the 1660s) this was an eective (if not always foolproof ) method of claiming
priority.
Galileo sent his correspondents the solution of the anagram,
Altissimum planetam tergeminum observavi,
or "I have observed the highest planet tri-form." And the newly congured Saturn now took its place in
Galileo's Hall of Fame. But there was something very strange about this planet. For one thing, after being
notied other observers often saw the planet oval shaped, but Galileo argued that this was due to inferior
telescopes. For another, if these lateral bodies were satellites, they were very dierent from the satellites of
Jupiter for they were much larger with respect to the planet and never moved with respect to it. Or did
they?
2 http://cnx.org/content/m11972/latest/saturn_manuscript-t.gif
3 At opposition, Saturn is 180 degrees removed from the Sun and
crosses the meridian at midnight. It is then closest to the
Earth and therefore at its brightest.
4 "The Medici Family" <http://cnx.org/content/m11975/latest/>
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
35
In his third sunspot (Chapter 8) letter, dated December 1612, Galileo revealed another mystery about the
planet: the lateral bodies had disappeared. Although Galileo condently predicted that they would return,
which they did, Saturn's appearances remained an enigma. If Saturn was sometimes seen oval (denied by
Galileo), sometimes with two lateral bodies, and at other times round and solitary, how could one explain
all these appearances? And the mystery grew deeper as time went on. In 1616 Galileo announced to his
patrons that he had now observed Saturn in yet another shape, and he published this without commentary
in his Asayer of 1623.
(a)
Figure 7.3:
(b)
Galileo's sketch of 1616 and engraving in The Assayer of 1623.
Although the planet had again appeared solitary in 1626, few noticed this.
But by the next solitary
appearance in 1642, there was a growing community of telescopic astronomers who now made observation
of the planet a central part of their research programs.
Pierre Gassendi and Johannes Hevelius played
central roles in this quest, but there were a number of others. Astronomers now routinely published gures
of the shapes in which they had observed Saturn, a sampling of which can be seen in g.
3.
Near the
solitary appearances, virtually all astronomers still saw the planet triple-bodied as Galileo had rst seen it;
at other times, however, they saw two arms, or handles (Latin, ansae) attached to the central body and,
representations of this handled appearance varied greatly.
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CHAPTER 7. SATURN
36
Figure 7.4:
The composite gure from Huygens's Systema Saturnium5
If in 1642 there was a lack of information about Saturn's appearances, by 1655 when the handles had
again shrunk into little disks and the planet was approaching its solitary appearance, there was a plethora of
information. What was needed now was a model or theory that would make sense out of all these divergent
observations. In 1656 Hevelius pubished
De Nativa Saturni Facie
(On the Real Appearance of Saturn"), in
which he proposed that Saturn's body was ellipsoidal in shape with two crescents attached to its extremeties.
Rotation about the minor axis in the plane of the crescents would, according to Hevelius, explain all the
planet's appearances.
Figure 7.5:
Hevelius's Theory6
5 http://cnx.org/content/m11972/latest/huygens_phases1.gif
6 http://cnx.org/content/m11972/latest/hevelius_phases.gif
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37
His book convinced few. In 1658 Christopher Wren (remembered more for his later architecture) proposed
a model in which a "corona" so thin it could be considered a mere surface was attached to the planet; the
entire formation rotated or librated about its major axis.
In the meantime, Christiaan Huygens had discovered a satellite of Saturn, now named Titan. In 1656 he
published a brief tract on the discovery and included an anagram containing his own theory about Saturn's
appearances.
He unveiled his theory in 1659, in a substantial book entitled
Systema Saturnium
("The
Saturnian System"). Huygens's theory was that the planet was surrounded by a thin at ring that nowhere
touched it. Although Huygens did think that the ring had an appreciable thickness, this was basically the
modern solution of the problem.
Figure 7.6:
Wren's Theory7
But Huygens's solution was a geometrical one. The question now facing astronomers was how such a
ring could be stable. Huygens thought the ring was a solid structure; others opined that it was made up of
a huge swarm of minute satellites. The argument went on for several centuries until James Clerk Maxwell
published his mathematical analysis of the ring structure in 1858, proving that the ring had to be made up
of particles no larger than a few inches. At the end of the nineteenth century, spectrographic studies showed
that the angular rotation of the inside of the ring was greater than that of the outside of the ring, and that
the ratio obeyed Kepler's third law. The problem was now solved, although Saturn's ring system still held
surprises, as can be seen from the results of the recent ybys of the planet.
7 http://cnx.org/content/m11972/latest/wren_phases.gif
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CHAPTER 7. SATURN
38
Figure 7.7:
Huygen's Theory8
8 http://cnx.org/content/m11972/latest/huygens_phases2.gif
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
Chapter 8
Sunspots
Figure 8.1:
1
The Sun2
Sunspots are dark areas of irregular shape on the surface of the Sun. Their short-term and long-term cyclical
nature has been established in the past century. Spots are often big enough to be seen with the naked eye.
While direct observation of the Sun in a clear sky is painful and dangerous, it is feasible when the Sun is
close to the horizon or when it is covered by a thin veil of clouds or mist. Records of naked-eye sunspot
observations in China go back to at least 28 BCE. In the West, the record is much more problematical. It is
possible that the Greek philosopher Anaxagoras observed a spot in 467 BCE, and it appears that there are
a few scattered mentions in the ancient literature as well. However, in the dominant Aristotelian cosmology,
the heavens were thought to be perfect and unchanging.
A spot that comes and goes on the Sun would
mean that there is change in the heavens. Given this theoretical predisposition, the diculty of observing
the Sun, and the cyclic nature of spots, it is little wonder that records of sunspots are almost non-existent
in Europe before the seventeenth century.
A very large spot seen for no less than eight days in 807 was
simply interpreted as a passage of Mercury in front of the Sun. Other mentions of spots seen on the Sun
were ignored by the astronomers and philosophers. In 1607 Johannes Kepler (Chapter 4) wished to observe
a predicted transit of Mercury across the Sun's disk, and on the appointed day he projected the Sun's image
through a small hole in the roof of his house (a camera obscura) and did indeed observe a black spot that
he interpreted to be Mercury. Had he been able to follow up on his observation the next day, he would still
1 This content is available online at <http://cnx.org/content/m11970/1.4/>.
2 http://cnx.org/content/m11970/latest/sun.gif
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39
CHAPTER 8. SUNSPOTS
40
have seen the spot. Since he knew that Mercury takes only a few hours to cross the Sun's disk during one
of its infrequent transits, he would have known that what he observed could not have been Mercury.
Figure 8.2:
A sunspot3
The scientic study of sunspots in the West began after the telescope had been brought into astronomy
in 1609.
Although there is still some controversy about when and by whom sunspots were rst observed
through the telescope (Chapter 3), we can say that Galileo and Thomas Harriot
4 were the rst, around the
5
6
end of 1610; that Johannes and David Fabricius and Christoph Scheiner rst observed them in March
1611, and that Johannes Fabricius was the rst to publish on them. His book,
De Maculis in Sole Observatis
("On the Spots Observed in the Sun") appeared in the autumn of 1611, but it remained unknown to the
other observers for some time.
Figure 8.3:
Harriot's sunspot drawings.7
3 http://cnx.org/content/m11970/latest/ss_detailed.gif
4 "Thomas Harriot" <http://cnx.org/content/m11979/latest/>
5 "Johannes Fabricius" <http://cnx.org/content/m11961/latest/>
6 "Christoph Scheiner" <http://cnx.org/content/m12126/latest/>
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
41
In the meantime, Galileo had shown sunspots to a number of people in Rome during his triumphant visit
there in the spring of 1611. But although some of his corespondents began making regular observations a
few months later, Galileo himself did not undertake a study of sunspots until April 1612. Scheiner began his
serious study of spots in October 1611 and his rst tract on the subject, Tres Epistolae de Maculis Solaribus
Scriptae ad Marcum Welserum ("Three Letters on Solar Spots written to Marc Welser8 ") appeared in January
1612 under the pseudonym "Apelles latens post tabulam," or "Apelles waiting behind the painting."
9 Welser
was a scholar and banker in Augsburg, who was a patron of local scholars.
Figure 8.4:
Sunspot plate from Scheiner's Tres Epistolae.10
Scheiner, a Jesuit mathematician at the university of Ingolstadt (near Augsburg), wished to preserve the
perfection of the Sun and the heavens and therefore argued that sunspots were satellites of the Sun. They
appeared as black spots when they passed in front of the Sun but were invisible at other points in their
orbits. Their orbits had to be very close to the Sun for their shapes were foreshortened as they approached
its edge. Scheiner observed sunspots through a telescope equipped with colored glasses.
In the winter of 1611-12, when Galileo received a copy of Scheiner's tract from Welser along with a
request for his comments, he was ill, and what little energy he had he was devoting to the publication of his
Discourse on Bodies in Water. When, however, that book was at the printer's, in April 1612, he turned his
11 , who was in Florence12 at the time.
attention to sunspots with the help of his protege Benedetto Castelli
It was Castelli who developed the method of projecting the Sun's image through the telescope, a technique
that made it possible to study the Sun in detail even when it was high in the sky. Galileo wrote his rst
letter to Welser on sunspots, in which he argued that spots were, in fact, on the surface of the Sun or in
its atmosphere, and although he could not say for certain what they were, they appeared to him most like
clouds.
While Scheiner wrote in Latin, Galileo wrote his letter in Italian, and Welser had to have it translated
7 http://cnx.org/content/m11970/latest/harriot_ss1.gif
8 "Marc Welser" <http://cnx.org/content/m11964/latest/>
9 Legend has it that the famous Greek painter Apelles once
hid behind one of his painting to hear what people said about
it. When a shoemaker praised the way Apelles had rendered shoes in the painting, Apelles revealed himself and thanked the
shoemaker for the compliment, but this man now proceeded to give his not so complimentary opinions about other aspects of
the painting. Apelles answered "Let the shoemaker stick to his last."
10 http://cnx.org/content/m11970/latest/tres_epistolae.gif
11 "Benedetto Castelli" <http://cnx.org/content/m11957/latest/>
12 "Florence and Tuscany" <http://cnx.org/content/m11936/latest/>
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CHAPTER 8. SUNSPOTS
42
before Scheiner could read it. Scheiner had continued his solar observations, and by the time he had mastered
Galileo's letter he had already nished two more letters of his own to Welser.
He now added a third, in
which he commented that his observations agreed precisely with those of Galileo and defended his judgment
that sunspots were solar satellites. This second series of letters was published by Welser in October 1612
under the title
De Maculis Solaribus . . . Accuratior Disquisitio
("A More Accurate Disquisition . . . on
Sunspots"). Scheiner maintained his pseudonym of Apelles "or, if you prefer, Odysseus under the shield of
Ajax." In the meantime, Galileo had written a second letter to Welser in August 1612.
In this letter he
showed a large number of sunspot observations, made at roughly the same time of the day, so that the Sun's
orientation was the same and the motion of the spots across its disk could be easily followed. Upon receiving
Scheiner's second tract he wrote yet a third, dated December 1612, attacking Apelles's opinions once again.
At the end of his last letter Galileo mentioned the Copernican System (Chapter 2) favorably in a way that
some scholars have interpreted as his rst endorsement of that theory.
Figure 8.5:
"Helioscopium" used by Scheiner for his later sunspot observations.13
Galileo's three letters were published in Rome by the Lyncean Academy
14 in the summer of 1613. About
a third of the copies had reprints of the two tracts by Apelles (whose identity had in the meantime become
known) in their original Latin. There was little doubt about the winner of this contest. Scheiner's language
was convoluted, and not only did Galileo demolish his argument, he also criticized Scheiner's a priori method
of argument: the Sun is perfect, therefore it cannot have spots on its surface.
Up to this point, relations between Galileo and Scheiner were not strained. Scheiner had treated Galileo
with great respect, and Galileo had been courteous in his language. Ten years later, in his Assayer, Galileo
complained about those who would steal his priority of discovery, mentioning the case of sunspots but
not mentioning Scheiner. It is almost certain that Galileo was complaining about several others who had
published on sunspots but who had not recognized his priority. Scheiner, who at this time was settling in
Rome, took Galileo's complaint to be directed at him and became Galileo's sworn enemy.
13 http://cnx.org/content/m11970/latest/helioscopium.gif
14 "Accademia dei Lincei" <http://cnx.org/content/m11955/latest/>
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43
(a)
(b)
(c)
Sunspot drawings from Scheiner's Rosa Ursina. (a) large version15 (b) large version16 (c)
large version17
Figure 8.6:
15 http://cnx.org/content/m11970/latest/scheiner_rosa_ursina1-l.gif
16 http://cnx.org/content/m11970/latest/scheiner_rosa_ursina2-l.gif
17 http://cnx.org/content/m11970/latest/scheiner_rosa_ursina3-l.gif
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CHAPTER 8. SUNSPOTS
44
Scheiner had in the meantime published several important books on optics, and he had continued his
18 which
study of the Sun. He published his results in a massive tome, Rosa Ursina, ("The Rose of Orsini"),
became the standard treatise on sunspots for over a century. Scheiner had abandoned his opinion that spots
were solar satellites, and he indeed came out in favor of the system of Tycho Brahe
19 and abandoned the
perfection of the heavens. His method of illustrating the motion of individual spots across the face of the
Sun became the standard way of rendering this motion and the changing shapes of the spots.
Figure 8.7:
Sunspot drawing by Gassendi20
After this time, however, sunspot activity was drastically reduced. When, in 1671, a prominent sunspot
was observed, it was treated as a rare event. Sunspot activity increased again after about 1710. The period
of low activity is now referred to as the Maunder Minimum, after Edward Walter Maunder (1851-1928),
one of the rst modern astronomers to study the long-term cycles of sunspots. Modern studies of sunspots
originated with the rise of astrophysics, around the turn of the century. The chief early investigator of these
phenomena in the United States was George Ellery Hale (1868-1938), who built the rst spectro-heliograph
and built the Yerkes and Mount Wilson observatories, including the 200-inch telescope on Palomar Mountain.
18 The rose refers to the Sun, Cardinal Orsini was his patron who
19 "Tycho Brahe" <http://cnx.org/content/m11946/latest/>
20 http://cnx.org/content/m11970/latest/gassendi_ss.gif
paid for the printing.
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45
(a)
Figure 8.8:
(b)
Sunspots drawings by Hevelius (a) large version21 (b) large version22
21 http://cnx.org/content/m11970/latest/hevelius_ss1.bmp
22 http://cnx.org/content/m11970/latest/hevelius_ss2.bmp
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46
CHAPTER 8. SUNSPOTS
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Chapter 9
1
The Biography of Galileo Galilei
9.1 Galileo's Early Life
Galileo was born in Pisa, Italy
2 on February 15, 1564.
Galileo's mother was Giulia degli Ammannati.
3
His father, Vincenzo Galilei , was a musician.
Galileo was the rst of six (though some people believe
seven) children. His family belonged to the nobility but was not rich. In the early 1570's, he and his family
4
moved to Florence .
9.2 The Pendelum
n 1581, Galileo began studying at the University of Pisa, where his father hoped he would study medicine.
While at the University of Pisa, Galileo began his study of the pendulum
5 while, according to legend, he
watched a suspended lamp swing back and forth in the cathedral of Pisa. However, it was not until 1602 that
Galileo made his most notable discovery about the pendulum - the period (the time in which a pendulum
swings back and forth) does not depend on the arc of the swing (the isochronism). Eventually, this discovery
would lead to Galileo's further study of time intervals and the development of his idea for a pendulum clock.
9.3 On Motion
In 1581, Galileo began studying at the University of Pisa, where his father hoped he would study medicine.
While at the University of Pisa, Galileo began his study of the pendulum while, according to legend, he
watched a suspended lamp swing back and forth in the cathedral of Pisa. However, it was not until 1602
that Galileo made his most notable discovery about the pendulum - the period (the time in which a pendulum
swings back and forth) does not depend on the arc of the swing (the isochronism). Eventually, this discovery
would lead to Galileo's further study of time intervals and the development of his idea for a pendulum clock.
9.4 Mechanical Devices
In 1592, Galileo was appointed professor of mathematics at the University of Padua. While teaching there,
he frequently visited a place called the Arsenal, where Venetian ships were docked and loaded.
Galileo
had always been interested in mechanical devices. Naturally, during his visits to the Arsenal, he became
1 This content is available online at <http://cnx.org/content/m11933/1.4/>.
2 "Italy" <http://cnx.org/content/m11960/latest/>
3 "Vincenzo Galileo" <http://cnx.org/content/m11934/latest/>
4 "Florence and Tuscany" <http://cnx.org/content/m11936/latest/>
5 "Galileo and the Pendulum" <http://cnx.org/content/m11929/latest/>
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CHAPTER 9. THE BIOGRAPHY OF GALILEO GALILEI
48
fascinated by nautical technologies, such as the sector
6 and shipbuilding. In 1593, he was presented with
the problem involving the placement of oars in galleys. He treated the oar as a lever and correctly made the
7
water the fulcrum. A year later, he patented a model for a pump . His pump was a device that raised water
by using only one horse.
9.5 Family Life
Galileo was never married.
8
However, he did have a brief relationship with Marina Gamba , a woman he
met on one of his many trips to Venice. Marina lived in Galileo's house in Padua where she bore him three
children. His two daughters, Virginia and Livia, were both put in convents where they became, respectively,
9 and Sister Arcangela. In 1610, Galileo moved from Padua to Florence where he took
10
a position at the Court of the Medici family . He left his son, Vincenzio, with Marina Gamba in Padua. In
Sister Maria Celeste
1613, Marina married Giovanni Bartoluzzi, and Vincenzio joined his father in Florence.
9.6 Telescope
Galileo invented many mechanical devices other than the pump, such as the hydrostatic balance
11 . But
perhaps his most famous invention was the telescope (Chapter 3). Galileo made his rst telescope in 1609,
modeled after telescopes produced in other parts of Europe that could magnify objects three times.
created a telescope later that same year that could magnify objects twenty times.
He
With this telescope,
he was able to look at the moon (Chapter 10), discover the four satellites of Jupiter (Chapter 6), observe
a supernova, verify the phases of Venus, and discover sunspots (Chapter 8).
His discoveries proved the
Copernican system (Chapter 2) which states that the earth and other plaqnets revolve around the sun.
Prior to the Copernican system, it was held that the universe was geocentric, meaning the sun revolved
around the earth.
9.7 The Inquisition
Galileo's belief in the Copernican System (Chapter 2) eventually got him into trouble with the Catholic
12 was a permanent institution in the Catholic Church charged with the eradication of
Church. The Inquisition
heresies. A committee of consultants declared to the Inquisition that the Copernican proposition that the Sun
is the center of the universe was a heresy. Because Galileo supported the Copernican system, he was warned
13 , under order of Pope Paul V, that he should not discuss or defend Copernican
14 that he could write about Copernican theory as
theories. In 1624, Galileo was assured by Pope Urban VIII
by Cardinal Bellarmine
Dialogue
Concerning the Two Chief World Systems, Galileo was called to Rome in 1633 to face the Inquisition again.
long as he treated it as a mathematical proposition. However, with the printing of Galileo's book,
Galileo was found guilty of heresy for his Dialogue, and was sent to his home near Florence where he was
to be under house arrest for the remainder of his life. In 1638, the Inquisition allowed Galileo to move to
his home in Florence, so that he could be closer to his doctors. By that time he was totally blind. In 1642,
Galileo died at his home outside Florence.
6 "The Sector" <http://cnx.org/content/m11977/latest/>
7 "The Pump" <http://cnx.org/content/m11976/latest/>
8 "Marina Gamba" <http://cnx.org/content/m11942/latest/>
9 "Maria Celeste" <http://cnx.org/content/m11941/latest/>
10 "The Medici Family" <http://cnx.org/content/m11975/latest/>
11 "Hydrostatic Balance" <http://cnx.org/content/m12127/latest/>
12 "The Inquisition" <http://cnx.org/content/m11944/latest/>
13 "Robert Cardinal" <http://cnx.org/content/m11968/latest/>
14 "Urban VIII" <http://cnx.org/content/m11983/latest/>
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
Chapter 10
The Moon
Figure 10.1:
1
The Moon in Sidereus Nuncius
Ignoring the occasional pre-telescopic appearance of exceptionally large sunspots (Chapter 8), the Moon is
the only heavenly body which shows features to the naked eyethe Man in the Moon. These features are
permanent, and it was therefore obvious that the Moon always keeps its same face turned to us (although
there are minor perturbations that were not noticed until later).
In the philosophy of Aristotle (384-322
BCE), these features presented somewhat of a problem. The heavens, starting at the Moon, were the realm
of perfection, the sublunary region was the realm of change and corruption, and any resemblance between
these regions was strictly ruled out.
Aristotle himself suggested that the Moon partook perhaps of some
contamination from the realm of corruption.
Although Aristotle's natural philosophy was very inuential in the Greek world, it was not without
competitors and skeptics. Thus, in his little book
On the Face in the Moon's Orb, the Greek writer Plutarch
(46-120 CE) expressed rather dierent views on the relationship between the Moon and Earth. He suggested
that the Moon had deep recesses in which the light of the Sun did not reach and that the spots are nothing
but the shadows of rivers or deep chasms. He also entertained the possibility that the Moon was inhabited.
In the following century, the Greek satirist Lucian (120-180 CE) wrote of an imaginary trip to the Moon,
which was inhabited, as were the Sun and Venus.
The medieval followers of Aristotle, rst in the Islamic world and then in Christian Europe, tried to
make sense of the lunar spots in Aristotelian terms.
1 This
Various possibilities were entertained.
content is available online at <http://cnx.org/content/m11945/1.4/>.
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
49
It had been
CHAPTER 10. THE MOON
50
suggested already in Antiquity that the Moon was a perfect mirror and that its markings were reections of
earthly features, but this explanation was easily dismissed because the face of the Moon never changes as
it moves about the Earth. Perhaps there were vapors between the Sun and the Moon, so that the images
were actually contained in the Sun's incident light and thus reected to the Earth. The explanation that
nally became standard was that there were variations of "density" in the Moon that caused this otherwise
perfectly spherical body to appear the way it does. The perfection of the Moon, and therefore the heavens,
was thus preserved.
It is a curious fact that although many symbolic images of the Moon survive in medieval and Renaissance
works of art (usually a crescent), virtually no one bothered to represent the Moon with its spots the way
it actually appeared. We only have a few rough sketches in the notebooks of Leonardo da Vinci (ca. 1500)
2 by the English physician William Gilbert3 . None of these drawings
and a drawing of the naked-eye moon
found its way into print until well after the telescope (Chapter 3) had come into astronomy.
The telescope delivered the coup de grace to attempts to explain away the Moon's spots and to the
perfection of the heavens in general. With his telescope, Galileo saw not only the "ancient" spots, but many
smaller ones never seen before. In these smaller spots, he saw that the width of the dark lines dening them
varied with the angle of solar illumination. He watched the dark lines change and he saw light spots in the
unilluminated part of the Moon that gradually merged with the illuminated part as this part grew.
The
conclusion he drew was that the changing dark lines were shadows and that the lunar surface has mountains
and valleys. The Moon was thus not spherical and hardly perfect.
Figure 10.2:
Galileo's wash drawings4
5 drew the
Galileo was not the only observer of the Moon. Indeed, he was not the rst. Thomas Harriot
rst telescopic representation of the Moon and observed our nearest neighbor for several years. His drawings,
however, remained unpublished.
Those who wished to defend the perfection of the heavens brought out the old argument about rarity
and density. In the letter of the Collegio Romano
6 mathematicians to Cardinal Bellarmine7 of April 1611,
8
Christoph Clavius (74 years old) expressed a minority opinion: "But it appears to Father Clavius more
probable that the surface is not uneven, but rather that the lunar body is not of uniform density and has
denser and rarer parts, as are the ordinary spots seen with the natural sight."[?] The other three Jesuit
2 http://cnx.org/content/m11945/latest/gilbert_moon.gif
3 "William Gilbert" <http://cnx.org/content/m11985/latest/>
4 http://cnx.org/content/m11945/latest/g_moonwash.gif
5 "Thomas Harriot" <http://cnx.org/content/m11979/latest/>
6 "Collegio Romano" <http://cnx.org/content/m11939/latest/>
7 "Robert Cardinal" <http://cnx.org/content/m11968/latest/>
8 "Christopher Clavius" <http://cnx.org/content/m11958/latest/>
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51
mathematicians on the faculty of the college, however, believed that the lunar surface was indeed uneven.
In this case the opposition faded away over the next few years.
Galileo wrote in a letter, 1610, that he would like to make a series of representations of the Moon showing
its changing phases. Presumably his purpose was to show how the shadows of individual features changed
with the illumination. It appears that he abandoned this plan when he saw that there was no need for such
an ambitious and expensive project: even the Jesuit fathers in Rome were convinced that the Moon's surface
was uneven.
Indeed, Galileo never returned to the task of representing the Moon.
(In the 1630s he did,
however, observe lunar librations, which show that the Moon does not always keep exactly the same face
turned toward the Earth.) Others did little better. Thomas Harriot
9 did make a rough map of the full Moon
10
but never published it. Representations by Christoph Scheiner , Giuseppe Biancani, and Charles Malapert
were little more than diagrams, useful only for supporting the verbal argument that the Moon's surface is
rough and uneven. These were, so to speak, generic moons, not portraits of our nearest neighbor.
Figure 10.3:
Sketches of the Moon by Scheiner11 (1614), Biancani12 (1620) and Malapert13 (1619)
If early observations and representations of the Moon were designed to address the issue of its mountainous
nature and anity with the Earth, by the 1630s the accent was shifting. The rough lunar surface was now
accepted by astronomers and they turned their attention to how telescopic observations could help them
solve the problem of longitude
14 . A lunar eclipse is an event that appears the same to all observers for whom
the Moon is above the horizon (which is, of course, not the case with solar eclipses). As the Moon enters
the Earth's shadow cone, one can mark the times at which the shadow crosses a particular feature and later
compare this time with the (local) time at which a distant colleague observed the same event. The dierence
15 But a verbal description of the lunar
in local times translates directly into their dierence in longitude.
feature under consideration was not enough. A lunar map was needed on which specic features could be
unambiguously identied.
In Aix and Provence, Nicholas Claude Fabri de Peiresc (still interested in the
problem of longitude) and his friend, the astronomer Pierre Gassendi, decided to make a moonmap. They
engaged the services of Claude Mellan, one of the foremost artists and engravers of his age. With Gassendi's
sketches and guidance, Mellan engraved three view of the Moon, rst quarter, full Moon, and last quarter.
9 "Thomas Harriot" <http://cnx.org/content/m11979/latest/>
10 "Christoph Scheiner" <http://cnx.org/content/m12126/latest/>
11 http://cnx.org/content/m11945/latest/scheinermoon.bmp
12 http://cnx.org/content/m11945/latest/biancanimoon.bmp
13 http://cnx.org/content/m11945/latest/malapertmoon.bmp
14 "Longitude at Sea" <http://cnx.org/content/m11963/latest/>
15 24 hours=360 ◦ .
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
CHAPTER 10. THE MOON
52
Figure 10.4:
Claude Mellan's moon engravings: 116 , 217 ,318 .
Mellan's three engravings are surely the nest artistic renderings of the Moon ever made, but they show
an artist's Moon, not an astronomer's Moon.
Mellan wonderfully represented what he saw through the
telescope: at rst and last quarter the details at the edge of the Moon are washed out while the features near
the terminator stand out starkly; conversely, at full Moon the features in the center are washed out while
those near the edge show prominent relief. Where the solar rays are perpendicular to the lunar surface they
cast no shadows, but where they rake the surface they throw long shadows. What astronomers needed was
a single map that showed all the features equally clearlya composite view that pictured the Moon in a way
it never appeared in reality but was accurate in its placement of individual features.
The rst such map was made by the Belgian cosmographer and astronomer Michael Florent van Langren
in 1645. Two years later a much more inuential eort was published by Johannes Hevelius. In 1647 Hevelius,
a wealthy brewer in the Polish city of Gdansk, published Selenographia, the rst treatise entirely devoted to
the Moon. Hevelius combined all the talents necessary for his task. He made his own lenses, constructed his
own telescopes, observed the Moon on every clear night for several years, drew his observations, engraved
them himself, and had the wealth to publish a sumptuous book at his own expense. In Selenographia he
presented engravings of every conceivable phase of the Moon as well as three large plates of the full Moon
19
: one of the ways the full Moon actually appeared through the telescope, one the way a maker of terrestrial
maps might represent it (using the conventions of geographers), and one a composite map of all lunar features
illuminated (impossibly) from the same side. It is this last map that was to be used by astronomers during
lunar eclipses. Hevelius also suggested a system of nomenclature based on earthly features.
Hevelius founded the science of selenography (after Selene, the goddess of the Moon) and showed astronomers how to represent heavenly bodies. Selenographia was a model for all who came after him. All
lunar maps since his time have used the convention of single illumination (although while he used morning
illumination modern maps use evening illumination after van Langren's model). He also instituted the practice of showing the entire lunar surface visible from the Earth, which, because of librations, is greater than
a hemisphere. Hevelius's nomenclature, although used in Protestant countries until the eighteenth century,
was replaced by the system published in 1651 by the Jesuit astronomer Giovanni Battista Riccioli, who gave
the large naked-eye spots the names of seas (Sea of Tranquillity, Sea of Storm, etc.) and the telescopic spots
(now called craters) the name of philosophers and astronomers (g.
18).
It should be pointed out that
although Riccioli wrote his Almagestum Novum ("New Almagest") in which this map appeared to combat
the Copernican theory (Chapter 2), he was evenhanded in assigning names: Copernicus and Kepler were
16 http://cnx.org/content/m11945/latest/mellan.bmp
17 http://cnx.org/content/m11945/latest/mella2.bmp
18 http://cnx.org/content/m11945/latest/mellan3.bmp
19 http://cnx.org/content/m11945/latest/hevelius_moon_r.gif
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53
assigned prominent craters, and even Galileo received his due.
One last note.
As the astronomical telescope (Chapter 3) with its inverted image came into use, as-
tronomers quickly adopted the habit of representing the way they saw the Moonupside down
20 . This
practice was followed until very recently. Lunar images are now constructed and stored digitally and can be
displayed in any orientation. Astronomers have therefore reverted to showing the Moon right side up.
20 http://cnx.org/content/m11945/latest/cassini_moon.gif
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
GLOSSARY
54
Glossary
A
the Church began a series of reform
atmospheric refraction
measures of their own. These reform
The change in direction of a ray of light as
measures aimed to keep Church members
it passes from space into the atmosphere.
from becoming Protestants, and were
This causes celestial objects to appear to
be in a location dierent from their
actual ones.
C
known as the Counter Reformation.
J
camera obscura
Jesuits
- The popular name for the monastic order
- A darkened boxlike device in which
called the Society of Jesus. The order
images of external objects, received
was founded by Ignatius de Loyola in
through an aperture, are exhibited in
1534, and was recognized by the pope in
their natural colors on a surface arranged
1540. The mission of the Jesuits was in
to receive them.
three areas: teaching, service to the
nobility, and missionary work in foreign
Carmelite Order
lands. Their greatest mark was made in
The Brothers of the Blessed Virgin Mary
education, and the Collegio Romano was
of Mount Carmel is one of the mendicant
their primary seminary.
orders originating on Mount Carmel in
Israel.
L
Counter Reformation
- The real or apparent oscillatory motion
of the moon.
- As dissenting groups split o from the
Catholic Church in what came to be
known as the Protestant Reformation,
the Church began a series of reform
lunar librations
P
parallax
The change in the position of an object in
measures of their own. These reform
the heavens due to the orbit of the earth.
measures aimed to keep Church members
Observable parallax in the xed stars is a
from becoming Protestants, and were
proof of the rotation of the earth around
known as the Counter Reformation.
the sun. See this explanatory diagram.
Counter Reformation
As dissenting groups split o from the
Catholic Church in what came to be
known as the Protestant Reformation,
S
sidereal period
- A period determined by or from the
stars.
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
Bibliography
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The Revised Oxford Translation.
The Complete Works of Aristotle:
Princeton University Press, Princeton, 1984. The Aristotelian cosmos
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John Kepler.
[2] Angus Armitage.
[3] Caspar.
Max. Kepler.
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Abelard Schuman, New York, 1959. Translated by C. Doris Hellman.
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[6] Michael J. Crowe.
Dover, New
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[7] Susanne Debarbat and Curtis Wilson.
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[8] Stillman Drake.
Discoveries and Opinions of Galileo.
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[10] Stillman Drake.
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Studies of Scientic Change,
[11] J. V. Field.
Scrutinizing Science: Empirical
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Kepler's Geometrical Cosmology.
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[12] Maurice A. Finocchiaro.
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Rivingtons, London, 1880. Translated by Edward Staord Carlos.
[14] Richard Fremantle.
Sidereus Nuncius, or the Sidereal Messenger.
University of Chicago Press, Chicago,
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[15] B. R. Goldstein and A. C. Bowen. A new view of early greek astronomy.
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[16] Edward Grant. Cosmology. In David C. Lindberg, editor,
Science in the Middle Ages,
pages 265302.
University of Chicago Press, Chicago, 1984. On Medieval cosmology and astronomy.
[17] Fernand Hallyn.
The Poetic Structure of the World: Copernicus and Kepler.
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[19] Vincent Ilardi. Eyeglasses and concave lenses in fteenth-century orence and milan: New documents.
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The Birth of History and Philosophy of Science: Kepler's A Defence of Tycho against
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Ursus.
The appearance of spectacles with concave lenses is discussed.
Cambridge University Press, Cambridge, 1984.
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[21] Johannes Kepler.
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Frankfurt and Erlange.
Johannes Kepler Gesammelte Werke.
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Epitome of Copernican Astronomy [books IV and V]; The Harmonies of the World
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Translated by Charles Glenn Wallis. In Great
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Kepler's Conversation with Galileo's Sidereal Messenger.
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1965. Translated by Edward Rosen.
The Six-Cornered Snowake.
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Somnium: the Dream, or Posthumous Work on Lunar Astronomy.
[26] Johannes Kepler.
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Wisconsin Press, Madison, 1967. Translated by Edward Rosen.
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Abaris Books, New York,
1981. Translated by A. M. Duncan.
New Astronomy.
[28] Johannes Kepler.
Cambridge University Press, Cambridge, 1992.
Translated by
William H. Donahue.
[29] Henry King.
The History of the Telescope.
Grin, London, 1955.
The most convenient source for
information on the general development of the telescope.
Johannes Kepler and Planetary Motion.
[30] David C. Knight.
[31] Arthur Koestler.
Chatto and Windus, London, 1965.
The Watershed: a Biography of Johannes Kepler.
The Copernican Revolution.
[32] Thomas S. Kuhn.
Doubleday, Garden City, 1960.
Harvard University Press, Cambridge, 1957. The best
account of the Copernican revolution.
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The Copernican Revolution.
Harvard University Press, Cambridge, 1957. On the
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Ptolemaic astronomy in the period leading up to Galileo's discoveries.
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[35] Martha List.
57
Bibliographia Kepleriana. Second edition.
Beck, Munich, 1968.
Novelties in the Heavens: Rhetoric and Science in the Copernican Controversy.
[36] Jean Dietz Moss.
University of Chicago Press, Chicago, 1993.
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Harriot: Renaissance Scientist. Clarendon Press, Edited by John W. Shirley, pp. 129-165. Oxford,
[37] John D. North.
1974.
A Survey of the Almagest.
[38] Olaf Pedersen.
Odense University Press, Odense, 1974. Good expositions of
the technical details of the Ptolemaic System.
[39] Olaf Pedersen. Astronomy. In David C. Lindberg, editor,
Science in the Middle Ages,
pages 30337.
University of Chicago Press, Chicago, 1984. On Medieval cosmology and astronomy.
[40] Olaf Pedersen and Mogens Pihl.
Early physics and astronomy : a historical introduction.
MacDonald
and Janes; American Elsevier, (London; New York, 1974. (2nd ed. Cambridge: Cambridge University
Press, 1993) Good expositions of the technical details of the Ptolemaic System.
[41] Edward Rosen. The invention of eyeglasses.
Journal for the History of Medicine and Allied Sciences,
11:1346, 183218, 1956. For the invention of spectacles.
[42] Edward Rosen.
Copernicus and the Scientic Revolution.
Krieger, Malabar, FL, 1984.
a useful, if
eccentric biography of Copernicus with a collection of documents concerning his life.
[43] Edward Rosen.
Three Imperial Mathematicians: Kepler Trapped Between Tycho Brahe and Ursus.
Abaris Books, New York, 1986.
[44] Kunitomo Sakurai. "the solar activity in the time of galileo".
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[46] Justin D. Schove.
Sunspots Cycles.
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Hutchinson Ross Stroudsburg, PA, 1983.
[47] William R. Shea. "galileo, scheiner, and the interpretation of sunspots".
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Galileo's Intellectual Revolution: Middle Period (1610-1632).
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[50] Bruce Stephenson.
Kepler's Physical Astronomy.
[51] tr. G. J. Toomer, editor.
Ptolemy's Almagest.
Springer Verlag, New York, 1987.
Duckworth; Springer Verlag, 1984, London; New York.
The best translation of the Almagest.
[52] Albert Van Helden. "annulo cingitur: the solution of the problem of saturn".
of Astronomy,
Journal for the History
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[53] Albert Van Helden. "saturn and his anses".
Journal for the History of Astronomy,
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Scienza di Firenze,
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5:105121, 1974.
Annali dell'Istituto e Museo di Storia della
see also for discussion of the problem of the invention of the
telescope.
[55] Albert van Helden.
Astronomy,
The development of compound eyepieces, 1640-1670.
Journal for the History of
8:2637, 1977. see also for discussion of the problem of the invention of the telescope.
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BIBLIOGRAPHY
58
[56] Albert van Helden. The invention of the telescope.
Transactions of the American Philosophical Society,
67(4), 1977. The entire problem of the invention of the telescope is discussed.
[57] Adriaan W. Vliegenthart. "galileo's sunspots: Their role in 17th-century allegorical thinking".
Physis,
7:273280, 1965.
[58] Robert S. Westman.
and michael maestlin.
Three responses to the copernican theory:
In Robert S. Westman, editor,
Johannes praetorius, tycho brahe,
The Copernican Achievement,
University of California Press, Berkeley and Los Angeles, 1975.
pages 285345.
For the dierent receptions of De
Revolutionibus.
Available for free at Connexions <http://cnx.org/content/col10432/1.1>
INDEX
59
Index of Keywords and Terms
Keywords are listed by the section with that keyword (page numbers are in parentheses). Keywords
do not necessarily appear in the text of the page. They are merely associated with that section.
apples, Ÿ 1.1 (1) Terms are referenced by the page they appear on.
A
B
C
aerial telescopes, 14
atmospheric refraction, Ÿ 4(17), 20
J
Cardinal Bellarmine, Ÿ 9(47)
Carmelite, Ÿ 2(3), 7
Christoph Clavius, Ÿ 2(3), Ÿ 10(49)
Jupiter, Ÿ 6(29)
K
L
lenses, 10
longitude, Ÿ 10(49)
lunar librations, Ÿ 10(49), 51
Copernican, Ÿ 2(3), Ÿ 4(17)
Lyncean Academy, Ÿ 8(39)
M
David Fabricius, Ÿ 8(39)
Marina Gamba, Ÿ 9(47)
Moon, Ÿ 3(9), Ÿ 6(29), Ÿ 7(33), Ÿ 9(47), Ÿ 10(49)
Cosimo II, Ÿ 6(29)
Counter Reformation, Ÿ 2(3), 7, Ÿ 4(17), 18, 20
Marc Welser, Ÿ 8(39)
Medici, Ÿ 7(33), Ÿ 9(47)
Copernicus, Ÿ 3(9)
P
De Motu, Ÿ 9(47)
myopia, 10
Paolo Antonio Foscarini, Ÿ 2(3)
parallax, 6
pendulum, Ÿ 9(47)
Europa, Ÿ 6(29)
Pope Urban VIII, Ÿ 9(47)
presbyopia, 10
Florence, Ÿ 8(39), Ÿ 9(47)
Ptolemaic System, Ÿ 5(23)
Ptolemy, Ÿ 2(3)
Galiileo, Ÿ 5(23)
Galilei, Ÿ 9(47)
Galileo, Ÿ 3(9), Ÿ 4(17), Ÿ 7(33), Ÿ 8(39),
Ÿ 9(47), Ÿ 10(49)
Ganymede, Ÿ 6(29)
geocentric, Ÿ 9(47)
geocentric astronomy, Ÿ 3(9)
I
Kepler, Ÿ 4(17)
longitude at sea, Ÿ 6(29)
Copernican theory, Ÿ 10(49)
H
Jupiter's satellites, Ÿ 4(17)
Collegio Romano, Ÿ 10(49)
Ÿ 9(47)
E
F
G
Johannes, Ÿ 4(17)
Christoph Scheiner, Ÿ 8(39)
Copernican System, Ÿ 5(23), Ÿ 6(29), Ÿ 8(39),
D
Jesuit, Ÿ 10(49), 50
Ÿ 8(39)
Biography, Ÿ 9(47)
camera obscura, Ÿ 8(39), 39
Giordano Bruno, Ÿ 2(3)
Hans Lipperhey, Ÿ 3(9)
hydrostatic balance, Ÿ 9(47)
Ex.
apples, 1
Johannes Kepler, Ÿ 2(3), Ÿ 3(9), Ÿ 6(29),
Benedetto Castelli, Ÿ 8(39)
Callisto, Ÿ 6(29)
Ex.
S
pump, Ÿ 9(47)
Satellites, Ÿ 6(29)
satellites of Jupiter, Ÿ 3(9), Ÿ 9(47)
Saturn, Ÿ 7(33)
Science, Ÿ 3(9), Ÿ 5(23)
sector, Ÿ 9(47)
sidereal, 33
sidereal period, Ÿ 7(33)
Simon Marius, Ÿ 6(29)
Sister Maria Celeste, Ÿ 9(47)
Index of Forbidden Books, Ÿ 2(3)
sunspot, Ÿ 7(33)
Inquisition, Ÿ 9(47)
Sunspots, Ÿ 8(39), Ÿ 10(49)
Io, Ÿ 6(29)
System, Ÿ 2(3)
Italy, Ÿ 9(47)
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INDEX
60
T
Telescope, Ÿ 3(9), Ÿ 6(29), Ÿ 8(39), Ÿ 10(49)
Thomas Harriot, Ÿ 8(39), Ÿ 10(49)
Tycho Brahe, Ÿ 2(3), Ÿ 4(17), Ÿ 8(39)
V
W
Vincenzo Galilei, Ÿ 9(47)
William Gilbert, Ÿ 10(49)
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ATTRIBUTIONS
61
Attributions
Collection:
solar system
Edited by: Joel Thierstein
URL: http://cnx.org/content/col10432/1.1/
License: http://creativecommons.org/licenses/by/2.0/
Module: "Copernican System"
By: Albert Van Helden
URL: http://cnx.org/content/m11938/1.3/
Pages: 3-8
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "Galileo's Telescope"
By: Albert Van Helden
URL: http://cnx.org/content/m11932/1.4/
Pages: 9-16
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "Johannes Kepler"
By: Albert Van Helden
URL: http://cnx.org/content/m11962/1.2/
Pages: 17-21
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "Ptolemaic System"
By: Albert Van Helden
URL: http://cnx.org/content/m11943/1.3/
Pages: 23-27
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "Satellites of Jupiter"
By: Albert Van Helden
URL: http://cnx.org/content/m11971/1.2/
Pages: 29-32
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "Saturn"
By: Albert Van Helden
URL: http://cnx.org/content/m11972/1.2/
Pages: 33-38
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
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ATTRIBUTIONS
62
Module: "Sunspots"
By: Albert Van Helden
URL: http://cnx.org/content/m11970/1.4/
Pages: 39-45
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "The Biography of Galileo Galilei"
By: Albert Van Helden
URL: http://cnx.org/content/m11933/1.4/
Pages: 47-48
Copyright: Albert Van Helden
License: http://creativecommons.org/licenses/by/1.0
Module: "The Moon"
By: Albert Van Helden
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Pages: 49-53
Copyright: Albert Van Helden
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solar system
this is a guide to the solar system.
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