VOL. 77, No 4 • APRIL 2013 • $250
Page 2 GRIFFITH OBSERVER April 2013
Copernicus, Capella, and Circumsolar Orbits
Dr. Lydia Philpott
Los Angeles, California
FOURTH PRIZE
BOEING GRIFFITH OBSERVER SCIENCE WRITING CONTEST
N
icolaus Copernicus gets the credit for putting all of the planets known to him into circumsolar orbits.
Although 1800 years earlier Aristarchus of Samos argued on behalf of a sun-centered system of planets, the
geocentric cosmic geography of Aristotle prevailed for two millennia, until the heliocentric plan Copernicus
described was developed by Johannes Kepler and popularized. Its validity was solidified by Isaac Newton, who
explained the physical principles that govern the motion of the planets.
We are familiar with the establishment’s resistance to the heliocentric orbits in the Copernican cosmology, but
in fact, not all circumsolar orbits were orbita non grata. This month, Dr. Lydia Philpott describes her encounter with
sun-centered planets in an anonymous Latin manuscript from ninth-century France. In astronomy, there’s always
something new under the sun.
Dr. Philpott last appeared in the June, 2012, issue of the Griffith Observer, with another Boeing Science Writing
Contest winner, “Gravity’s Optics and Other Worlds.” She researched quantum gravity at Imperial College, where she
earned her Ph.D. in theoretical physics. Earlier, as an undergraduate at the University of Aukland, she was part of
the Microlensing Observations in Astrophysics project and then continued her studies at the Australian National
University and the University of Cambridge, in England. She now works as a programmer at U.C.L.A., where she is
a member of the THEMIS mission and investigates the earth’s magnetic fields. She figures summer holidays spent
camping under clear New Zealand skies guaranteed her future career in astronomy.
Married to a medieval historian, Dr. Philpott now pays more attention to the history of science and has, as she
says, “someone to point me to all the interesting books.” Apparently some of them prompted her to get acquainted
with predecessors of Copernicus.
—E.C.K.
I
magine…in the year 850, or thereabouts, Despite the labors of monks like this
an Irishman living in northeast France con- Irishman, the thirteen centuries between
templated the intricacies of astronomy. He Ptolemy and Copernicus are glossed over in the
spent hours in the library, read the authori- abbreviated history of astronomy that most of
ties on the subject, painstakingly copied out us encounter. One sentence usually suffices: The
the important texts and passages, and asked Ptolemaic geocentric universe was burdened
a skilled friend to draw him a diagram of the with an increasing number of epicycles until
orbits of the planets. Copernicus began an astronomical revolution
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middle of the ninth-century. The handwriting
and presence of Irish in addition to Latin in
the manuscript suggest the scribe was Irish. The
manuscript now resides in Karlsruhe, Germany,
but unlike the scribe, we need not undertake
a long journey. With the help of digital librar-
ies, we are free to examine it without leaving
the chair. Karlsruhe Aug. 167 is available in
digital form at the St. Gall Project http://www.
stgallplan.org and also through the Badische
Landesbibliothek http://www.blb-karlsruhe.de/.
As a compilation of various items, the man-
uscript is perhaps analogous to what a student
today might produce when taking notes for a
course or studying for a test. The items related
to astronomy include complicated tables for the
The ninth-century Irish monk who prepared this dia-
gram of the orbits of the planets lodged them with mili-
tary discipline in the upper half of this page in a column
that extends up from center of their concentric paths
around the earth, which is labeled “terra.” In order of as-
cent, they are the moon, the sun, Mercury, Venus, Mars,
Jupiter, and Saturn, and the plan shows that Mercury
and Venus occupy smaller circles centered on the sun. A
magnified version of the circumsolar situation appears
on the lower half of the page. The earth (“terra”) is still
identified at the center, and the sun is on the large circle.
Venus is directly above the sun, and Mercury is below it.
Each is on its own orbit. (Karlsruhe, Badische Landesbib-
liothek Cod. Aug. 167, f1 6r, reproduced with permission,
Karlsruhe Badische Landesbibliothek)
with his controversial heliocentric construc-
tion. When someone showed me an astronomi-
cal diagram in the ninth-century manuscript
known as Karlsruhe, Badische Landesbibliothek The Alexandrian astronomer Ptolemy ruled the king-
Cod. Aug. 167, I realized I knew next to noth- dom of astronomy for 15 centuries, and in this illus-
ing about astronomy in the middle ages. tration from Margarita Philosophica (1508) by Gregor
Karlsruhe, Badische Landesbibliothek Cod. Reisch, Ptolemy is portrayed as a European king. He ob-
serves the sky with a quadrant while Urania, the Muse
Aug. 167 (Aug 167) is believed by the manu- of Astronomy, points the way. (reprinted in Watchers of
script scholar Bernhard Bischoff to have been the Stars by Patrick Moore, New York: G.P. Putnam’s Sons,
written in northeast France, sometime in the 1974)
Page 4 GRIFFITH OBSERVER April 2013
calculation of important dates, such as Easter,
based on the positions of the moon, sun, et
cetera; Bede’s On the Nature of Things, On Times,
and The Reckoning of Times; a scrap of parch-
ment bound into the manuscript with selected
excerpts on astronomy from the work of Pliny
the Elder, Martianus Capella, and others; and a
meticulously executed diagram of the planetary
orbits.
The diagram of planetary orbits caught my
attention for one particular reason: The moon,
sun, Mars, Jupiter, and Saturn orbit the earth
on concentric circular orbits, but Mercury and
Venus orbit the sun. Was this a common view
of the universe at the time? Where does this fit
in the journey between the universe of Ptolemy
Ptolemy’s earth-centered cosmos is based on Aristotle’s
and that of Copernicus?
universe, which is portrayed here in a 1500 edition of the
Ptolemy and Copernicus mark crucial best-selling astronomy textbook, De Sphaera, written by
milestones in the history of astronomy, but Johannes de Sacrobosco in the thirteenth century. The
Copernicus did not simply pick up a 1300-year- earth is surrounded by rings of water, air, and fire, and
old manuscript of Ptolemy, dash it to the beyond the fire, seven more rings are dedicated to the
sun, moon, and planets. The stars, represented by the 12
ground in disgust, and write his masterpiece in
figures of the zodiac, enclose the system. (from the Paris
its place. Though we often forget it, science sel- edition published by Jacques LeFèvre d’Etaples, from
dom progresses in such abrupt leaps and starts. S.K. Heninger, Jr., The Cosmographical Glass: Renaissance
At the very minimum, for Copernicus even to Diagrams of the Universe. San Marino: California: The
know of the work of Ptolemy there must have Huntington Library, 1977)
FRONT COVER
Circumsolar Circumstances
The cosmos is centered on the earth in this ninth-century diagram in the Leiden Aratea. The document is a copy of the
treatise prepared in the first century A.D. by Claudius Caesar Germanicus, who based his composition on the earliest
known (third century B.C.) ancient Greek sky guide, the Phaenomena by Aratus of Soli. This is the last illustration in
the manuscript, and it depicts the configuration of the planets on 28 March 579 A.D. The moon is just to the right
of the earth, and Mars is above and beyond the moon to the right. Jupiter is near the outer ring of zodiac signs and
month disks, at the “7 o’clock” position. Saturn is above the earth, at about “11 o’clock,” and also touches the zodiac
circle. Mercury and Venus are just to the left of the earth, and both are on circumsolar circles, with the sun just a little
farther to the left. Even though Mercury and Venus travel around the sun, they are carried around the earth by the
sun. The personified figures Mercury and Venus, like those in all of the other planet medallions, have their feet toward
the earth. All of the circles are labeled in Latin and include quotations from Pliny the Elder on each planet’s apogee
and perigee. The diagram really doesn’t have anything to do with text of the manuscript and probably was added in
the process of copying. It is the oldest known illustration of the positions of the planets on a specific day. Elsewhere
in this issue, Dr. Lydia Philpott follows the thread of the circumsolar orbits of Mercury and Venus from the ninth cen-
tury to the heliocentric system of Copernicus seven centuries later. Please see “Copernicus, Capella, and Circumsolar
Orbits.” (Bibliotheek der Rijksuniversiteit te Leiden (Leiden University Library), ms VLQ 79, fol. 93v, reproduced with
permission, cover design by Robert Smith)
April 2013 GRIFFITH OBSERVER Page 5
been people throughout the intervening cen-
turies interested in astronomy and copying the
manuscripts on the subject.
To begin with Ptolemy is, of course, not to
begin at the beginning. The very influential geo-
centric model of the universe that appeared in
Ptolemy’s Almagest in the second century A.D.,
like any scientific theory, drew strongly on ideas
that preceded it. Without Eudoxus, Aristotle,
Hipparchus (to name only a few), there would
be no “Ptolemaic” system.
At the simplest level, the Ptolemaic universe
placed the spherical earth at the very center of
the cosmos, and surrounded it with the plan-
etary spheres in the following order: moon,
Mercury, Venus, sun, Mars, Jupiter, and Saturn.
This set of nested spheres was enclosed by the
sphere of the fixed stars. The Ptolemaic system The equant is the center of the epicycle’s orbital motion,
persisted a millennium and a half. Its longevity and because it coincides with neither the center of the
was not due to the general geocentric concept, orbital circle (the deferent) nor the earth, it allows the
but to its detailed geometric modeling of the planet to appear to move with varying speed. It was de-
vised by Ptolemy in the second century A.D. to model
motion of each planet (a term that at the time the motion of a planet with an orbit beyond the sun,
included also the moon and sun) that allowed like Mars. (illustration Lydia Philpott and Robert Smith)
the positions of the planets to be predicted with
great accuracy.
In On the Heavens, Aristotle argued that Epicycles were not a new concept at the
circular motion alone is the most perfect and time of Ptolemy, but the equant was almost cer-
eternal motion. Like those before him, and like tainly his invention. It is hard to create mod-
many for centuries after, Ptolemy was guided by els of planetary motion from uniform circular
the principle that heavenly bodies move with motion because the planets do not actually
uniform circular motion. Attempting to work move at a uniform speed as viewed from the
with this strong constraint, Ptolemy made use earth. The sun, for example, exhibits no retro-
of three main ideas in his planetary models: the grade motion and so needs no major epicycle,
epicycle, the equant, and the eccentric. The epi- but it moves slightly more rapidly during the
cycle is undoubtedly the most familiar of these. northern-hemisphere winter than it does during
Instead of orbiting the earth on a simple circle, the northern-hemisphere summer. To account
the planet rotates on a small circle, which itself for this non-uniform speed and yet still main-
rotates around the primary circle (the defer- tain a description in terms of uniform circular
ent). Adjusting the speed at which the epicycle motion, Ptolemy gave the planets a uniform
rotates compared to the rotation of the deferent angular speed as measured from a point called
(primary circle) allows the planet to appear at the equant point. The equant point was neither
times to move backward, as is seen in the real the center of the deferent, nor the position of
sky. The epicycle permits replication of a plan- the earth. When the planet is nearer the equant
et’s retrograde loops. Such an epicycle is often point, it appears to travel slower. A given angle
called a major epicycle. then corresponds to a shorter arc length. This
Page 6 GRIFFITH OBSERVER April 2013
Ptolemaic system only becomes apparent when
you realize that each planet (including the
moon and sun) require different parameters–
different eccentrics, epicycles of different size,
differently placed equant points...possibly even
minor epicycles on major epicycles, eccentrics
that themselves move on a deferent...the possi-
bilities are practically endless.
At first glance, the planetary diagram in
the manuscript Aug 167 seems to be a simple
representation of the Ptolemaic system. A cen-
tral earth is surrounded by planets on circular
orbits. The diagram is an illustration of a cos-
mology, not an attempt to illustrate the com-
plexities, such as epicycles, that would be
needed to predict planetary motions. Now, look
a little more closely, and notice that Mercury
The equant transforms non-uniform circular motion into and Venus orbit the sun, rather than the earth.
circular motion with a uniform angular speed around a
Below this overview of the cosmos is a smaller
point that is not the center of a circular orbit. The time
the planet takes to travel along arc A is the same time diagram showing only the earth, sun, Mercury,
it takes to travel along arc B. (illustration Lydia Philpott and Venus. Again Mercury and Venus orbit the
and Robert Smith) sun, but while Mercury is shown with a circular
orbit, Venus describes an elongated orbit that
is not only a very clever mathematical trick, it both takes it farther from, and brings it closer
is also reminiscent of what we now know as to the earth than Mercury. It also approaches
Kepler’s second law of planetary motion. A line closer to the sun. Is this a clarification of the
joining a planet to the sun sweeps out equal larger diagram, or an alternative? The diagram
areas in equal times. has no caption to help us, the only text that
The final component in Ptolemy’s plan- accompanies it is a list of the signs of the zodiac.
etary models, the eccentric (also inherited from Although the diagram appears without com-
his predecessors), is quite simple. The circular ment on a page otherwise filled with compli-
orbit of a planet is not exactly centered on the cated tables, the texts immediately following
earth. This construction can be used to remove provide some clues to the thoughts of the scribe
minor discrepancies between the predictions of and of the understanding of astronomy at that
the model and the observations that still remain time. After several pages of calendar tables, the
after invoking epicycles and equants. An eccen- text of Bede’s De Natura Rerum begins.
tric also allows the planet to appear to move at a Bede lived in the late seventh and early
non-uniform speed when seen from the off-cen- eighth centuries, as a monk at a monastery
ter earth. Why then is the equant needed? For in northern England. He was recognized as a
the simple case of the sun, an eccentric could great scholar during his lifetime, and his works
suffice. Unfortunately, the wandering of the rest remain important. Best known, perhaps, for his
of the planets in the sky is so strange that all Ecclesiastical History of the English People, Bede
three constructions are necessary. also provided us with insight into the under-
The epicycle, eccentric, and equant are all standing of astronomy at the time through his
relatively tidy ideas. The complexity of the scientific works.
April 2013 GRIFFITH OBSERVER Page 7
De Natura Rerum, or “On the nature of cize the 6 degree “error” for Mercury, note that
things,” is a brief text, an abridged encyclope- the maximum distance of Mercury from the
dia of sorts. It ranges widely, and covers top- sun, as viewed from the earth, varies consider-
ics that include the creation of the universe to ably. From the earth, Mercury appears to keep
the irrigation of Egypt by the Nile. Bede even close company with the sun. It sometimes
tried to explain earthquakes. Bede’s work shows appears west of the sun and sometimes east. The
not only his era’s great interest in astronomical maximum angular distance it achieves from the
phenomena but also the considerable degree sun as it alternates between east and west is its
to which information was shared. In discuss- maximum elongation. In 2011, for example,
ing eclipses of the moon Bede notes that “in there were seven maximum elongations, and
the time of Alexander the Great the moon was they varied between 18.1° and 26.8°–and aver-
eclipsed in Arabia at the second hour of the aged 22.5°. (See the Mercury elongation cal-
night, just as the same eclipsed moon was ris-
ing in Sicily.” (Bede, On the Nature of Things,
translated by Calvin B Kendall and Faith Wallis,
Liverpool University Press (Liverpool), 2010, p
88.) He could tell you the length of the shadow
from a sundial in Egypt, Rome, and India, even
though he never left England, or even northern
England, in his lifetime.
Of the planets, we learn from Bede both
their order (moon, Mercury, Venus, sun,
Mars, Jupiter, Saturn) and the time they take
to complete a circuit of the zodiac. During
their travels Venus, we are told, is never farther
than 46 degrees away from the sun in the sky,
Mercury never more than 22 degrees from the
sun. Bede was not an astronomer himself. He
likely took his numbers directly from Pliny the
Elder, who died, memorably, during the erup-
tion of Vesuvius in 79 A.D., some six hundred
years before De Natura Rerum appeared. In his
Natural History, Pliny further attributed these
numbers to Timaeus (ca. 345 B.C.-250 B.C.),
Cidenas (fourth century B.C.) and Sosigenes
(first century B.C.). (C. Plini Secundi Naturalis
historiae libri XXXVI, ed. Karl Mayhoff,
Teubner (Leipzig), 1906.) With such a long
tradition of copying, and apparently little in
the way of observation, it seems remarkable Martianus Capella wrote The Marriage of Philology and
that these numbers conform so well to modern Mercury in the fifth century A.D. His allegorical treatise
values of 47 degrees for Venus and 28 degrees deals with the relationship between learning (Philol-
ogy) and profitable enterprise (Mercury), and the Seven
for Mercury. (See, for example, The Data Book Liberal Arts served as bridesmaids at the wedding. This
of Astronomy, Patrick Moore, IOP Publishing edition of the book was published in 1539. (Whipple Li-
Ltd (London), 2000.) Before rushing to criti- brary, University of Cambridge)
Page 8 GRIFFITH OBSERVER April 2013
culator available at http://www.fourmilab.ch/ quote from the intriguingly titled The Marriage
images/3planets/elongation.html.) The value of of Philology and Mercury, by Martianus Capella:
28° is the absolute maximum possible. Now Venus and Mercury, although
The De Natura Rerum confirms that the they have daily risings and settings,
behavior of Mercury and Venus is slightly dif- do not travel about the earth at all;
ferent from that of the other planets, but there rather they encircle the sun in wider
is no statement that would inspire the diagram revolutions. The center of their orbits
in Aug 167. is set in the sun. As a result they are
On a small scrap of parchment bound sometimes above the sun; more often
between the pages of De Natura Rerum, we find they are beneath it, in a closer approx-
some clues. Some notes in old Irish, excerpts imation to the earth. Mercury’s and
from Pliny on the subject of the planets, and a Venus’ greatest elongation from the
sun is one and one half signs. When
both planets have a position above the
sun, Mercury is closer to the earth;
when they are below the sun, Venus
is closer, inasmuch as it has a broader
and more sweeping orbit.
This translation of the Latin is taken from
The Marriage of Philology and Mercury, Volume
2, translated by William Stahl and Richard
Johnson, Columbia University Press (New
York), 1977, p 333. The Latin text in Aug. 167
differs only slightly from the base text used for
this translation.
Here then, in unambiguous terms, is the
motivation for the diagram. Was Martianus
Capella a scientific revolutionary? Unfortunately
not.
Martianus Capella lived in north Africa in
the fifth century. The considerable popularity of
his work in the centuries that followed is a good
indication of its importance. Rather like Bede’s
De Natura Rerum, The Marriage of Philology
and Mercury would be most aptly described as
a textbook or encyclopaedia, although at first
glance, you could be forgiven for mistaking The
During 1302-1310, Giovanni Pisano designed and con-
structed the pulpit that still may be seen in the Duomo
Marriage of Philology and Mercury for a fable. It
in Pisa, Italy, Seven panels on the pedestal of central does indeed tell an elaborate allegorical tale of
plinth that supports the pulpit illustrate the Seven Lib- the betrothal and wedding of the god Mercury
eral Arts, who were bridesmaids at Capella’s wedding to the maiden Philology. After an introduction
of Philology and Mercury, and Astronomy was one of to a considerable cast of deities and a whirl-
the Seven Liberal Arts. Filosofia, the personification of
philosophy, accompanies another of the Seven Liberal
wind tour of the heavens, the handmaidens
Arts, Gramatica (grammar), in this view. (photograph to Philology are given the floor: Grammar,
E.C. Krupp, 17 November 2004) Dialectic, Rhetoric, Geometry, Arithmetic,
April 2013 GRIFFITH OBSERVER Page 9
Astronomy, and Harmony–the seven liberal
arts. In the discussion of astronomy, Martianus
Capella covers a great range of topics in consid-
erable detail. Need to know what constellation
is setting when Scorpio (the astrological sign)
is rising? No problem. The length of the lon-
gest day in Rhodes? The time for any planet to
complete its orbit? The number of days the sun
lingers in Sagittarius? At what times Ursa Major
can be seen in Arabia or India? Answers to all
these can be found in The Marriage of Philology
and Mercury. Martianus Capella never set foot
in India, and he didn’t, I’m sure, spend his time
making observations of the planets. His work
is a compendium of knowledge, a collection
of facts and figures gathered from an array of
sources that today gives us a glimpse of what
an interested person in the Middle Ages would
have learned about astronomy.
Although it is tempting to think that
Capella’s views on the orbits of Mercury and
Venus were unusual or revolutionary at the
time of their writing, there is nothing in the An eleventh-century copy of Martianus Capella’s The
text to suggest that heliocentric orbits were even Marriage of Philology and Mercury illustrates the struc-
remotely controversial. The heliocentric orbits ture of the geocentric cosmos Capella described. The
are mentioned multiple times, without fanfare. crescent moon identifies the smallest orbit in the plan.
The next orbit belongs to the sun, which is symbolized
In the passage quoted above from the beginning
with a rayed disk. The two orbits centered on the sun are
of the chapter on astronomy, and during the occupied by Mercury and Venus. Mars, Jupiter, Saturn,
detailed discussions of the motions of Mercury and the zodiac ring complete the plan. Other configura-
and Venus, Capella wrote, tions of the circumsolar planets are sketched below the
“the circles of [Mercury] and Venus...do not main plan. (Florence: Biblioteca Medicea Laurenziana,
San Marco 190, f. 102r)
encompass the globe of the earth within their
orbits...” (ibid, Volume 2, p 341.)
He added, “Located on its own epicycle, middle orbit are different, so the points about
[Venus] goes about the sun...” (ibid, Volume 2, which they revolve are different. Consequently,
p 342.) the earth is not the center of the sun’s orbit, but
Lest we think Martianus too humble to take is eccentric to it.” (ibid, Volume 2, p 330.)
credit for a novel idea, look no further than Capella seems conveniently to forget how
his earlier discussion of the eccentric, in which prominently this idea features in Ptolemy’s
he explained, “...a notion which all men have Almagest. Far from being revolutionary, a helio-
believed until now, that, inasmuch as the earth centric model of Mercury and Venus was appar-
is the center of the universe and the outermost ently a “commonplace feature in the popular
sphere, it is also the center of the sun’s orbit; but handbooks.” (Ibid, Volume 2, footnote on
this is manifestly not true. For just as the spaces pg 377. See also the discussion in Volume 1,
encompassed by the celestial circle and the pp 189-90.) Had the idea been even remotely
Page 10 GRIFFITH OBSERVER April 2013
novel, I’m sure Martianus would not have hesi-
tated to assure us of his brilliance in devising it.
History, however, decided Martianus was due
some credit, and his name has firmly become
attached to the heliocentric model for Mercury
and Venus.
The work of Martianus was copied over
and over in its entirety by many scribes. It was
excerpted and diagrammed by people like our
ninth-century Irishman in northeast France.
Finally, once it was printed, it made it all the
way to the sixteenth century and into the hands
of Nicolaus Copernicus. How do we know
that Copernicus had even heard of Martianus
Capella? Copernicus said so. In the first book
Copernicus illustrated the arrangement of the planets
of his De revolutionibus orbium coelestium with a simple heliocentric plan in the first (1543) edition
Copernicus singled out Martianus for praise: of De Revolutionibus Orbium Coelestium. In this scheme
Consequently I think we should every orbit is circumsolar. (De Revolutionibus Orbium
certainly not despise the argument Coelestium, Libri VI, Nuremberg, from S.K. Heninger, Jr.,
which was well known to Martianus The Cosmographical Glass: Renaissance Diagrams of the
Universe. San Marino: California: The Huntington Library,
Capella, who wrote the Encyclopedia, 1977)
and certain other Latin writers. For
they believe that Venus and Mercury
revolve round the sun which in the surrounded by circular planetary orbits (moon,
middle of them... because they do Mercury, Venus, sun, Mars, Jupiter, Saturn) to
not go round the earth, like the a central sun surrounded by circular planetary
rest... the center of their orbits is in orbits (Mercury, Venus, earth, Mars, Jupiter,
the region of the sun... (Copernicus, Saturn) with the moon orbiting the earth. Just
On the Revolutions of the Heavenly as in the Ptolemaic system, the details are far
Spheres, Book 1, Chapter X, trans- more complicated. The Ptolemaic system is not
lated by A.M. Duncan, David & truly geocentric. The earth is not the exact cen-
Charles (Newton Abbot), 1976, p ter of any orbit. Likewise, the Copernican sys-
48.) tem is not really heliocentric. Copernicus made
Copernicus is often credited with beginning use of the same eccentric technique and placed
a scientific revolution. He cast aside the overly the sun near, but not at the center of any of
complicated and antiquated Ptolemaic system the planets’ orbits. By realizing that the planets
and introduced the modern heliocentric model orbit the sun, and not the earth, Copernicus rid
of the universe. His ideas faced stiff opposition himself of the need for major epicycles for the
from most quarters. There is no doubt that planets. The retrograde motion is clearly just a
Copernicus’s work was of great importance, but consequence of the changing angles between
was it really that revolutionary? Was the oppo- the earth, sun, and planet in question. This
sition to Copernican theory really as blind or is a major improvement, but unfortunately
irrational as we are often led to believe? Copernicus could not banish epicycles alto-
The simple image of the Copernican uni- gether. He still had to deal with the non-uni-
verse moves us from Ptolemy’s central earth form speed of the planets, and apparently find-
April 2013 GRIFFITH OBSERVER Page 11
With the benefit of hindsight, people fre-
quently belittle Copernicus’s contemporaries
for their obstinance in holding to the Ptolemaic
system in the face of Copernicus’s “far simpler”
model. We are often told that the number of
epicycles needed in the Ptolemaic system multi-
plied in the centuries following its initial devel-
opment. In reality, only the myth of epicycles
multiplied. The Encyclopaedia Britannica from
the mid-1960s would have us believe that by
the time Alfonso X of Castile commissioned
the Alfonsine Tables of planetary positions in
the thirteenth century, “each planet had been
provided with from 40 to 60 epicycles to rep-
resent after a fashion its complex movement
among the stars.” (Encyclopaedia Britannica,
An epicyclet and an eccentric mimic the motion of Mars Volume 2, 1963, p 645.) This is more than a
in the heliocentric Copernican scheme. The solid line is minor exaggeration. After recomputing the
the deferent, centered on O, but the broken line is path Alfonsine Tables, historian of science Owen
the actually planet follows. (illustration Lydia Philpott
Gingerich concluded that the classic Ptolemaic
and Robert Smith)
system was used for their construction, with
no extra epicycles-on-epicycles introduced at
all. (Owen Gingerich, “Crisis versus Aesthetic
ing Ptolemy’s equant distasteful, Copernicus in the Copernican Revolution,” Vistas in
solved this by making use of minor epicycles, Astronomy, Vol 17, 1975, pp 85-95.)
or epicyclets. Consider a planet that is moving Had I lived at the time of Copernicus, I fear
along its primary circle at a uniform speed but, that I too would have been reluctant to put
in the time that it takes to complete one cir- aside a theory that had worked very well for
cuit of its primary circle, is also traveling once so long in favor of a new theory that was not
around its epicyclet. (A detailed explanation really any less complicated, didn’t offer better
of the Copernican model for superior planets predictive power, and required me to believe
can be found in History and Practice of Ancient that the firm planet beneath my feet was both
Astronomy, James Evans, Oxford University spinning on its axis and hurtling around the
Press, 1998.) The resulting motion is the sum sun. Although the desire to create a beauti-
of two uniform circular motions and appears ful theory is often the motivation for progress
non-uniform and actually describes a slightly in science, adopting a new theory solely for its
flattened circle. (Copernicus, On the Revolutions aesthetic value won’t get us far. Science works
of the Heavenly Spheres, Book 5, Chapter IIII, by demanding good evidence for new theories
translated by A.M. Duncan, David & Charles before adopting them. Is it really that surprising
(Newton Abbot), 1976, p 48.) As in the that De revolutionibus orbium coelestium was not
Ptolemnaic system, the exact epicycles and immediately embraced?
eccentrics needed for each planet are different. Galileo’s observations of the moons of
Copernicus’s system, although fundamentally Jupiter, nearly 70 years after the publication
different from Ptolemy’s, was therefore nearly as of De revolutionibus, are often cited as a turn-
complicated. ing point in public opinion on the theory.
Page 12 GRIFFITH OBSERVER April 2013
Hartmann Schedel, the fifteenth-century Latin author Copernicus likely had the opportunity to study astron-
of the Nuremberg Chronicle, an illustrated, biblical his- omy rigorously at the Collegium Maius before he left
tory of the world, wrapped the Jagiellonian University, Krakow in 1495 for Bologna, Italy, to study canon law.
in Krakow, Poland, in superlatives. It boasts, he wrote, (photograph Lydia Philpott)
“many most eminent and highly-educated men, in
which all sorts of proficiencies are practiced…But the
science of astronomy stands highest there…” Nicolaus It is also said objections to heliocentric the-
Copernicus attended the university, spent much of his ory arose not because the planets did not orbit
time at the Collegium Maius, and no doubt stood in its
courtyard. (photograph Lydia Philpott)
the earth, but because the moon, attempting to
orbit a moving earth, would somehow be left
behind. Surely such an objection could equally
be applied to the models of Mercury and Venus
Directing a telescope toward Jupiter he dis- orbiting the sun? We’d do well to recall that
covered the existence of four objects that neither Ptolemy nor Copernicus offered what
were neither fixed stars nor known planets. we would now consider physical explanations
Repeated observation showed that these objects for the motions of the planets. They described
revolve about Jupiter. Here was direct evidence how the planets moved, not why the planets
to overthrow the Aristotelian view that all heav- moved. Each planet was given the circles it
enly objects must revolve around the central needed to reproduce the data that were avail-
earth. It was the beginning of the end for the able.
geocentric universe. Galileo’s discovery of Jupiter’s moons really
Galileo’s observations of Jupiter’s moons provided no evidence for or against either the
were undoubtedly steps of great importance on Ptolemaic or Copernican system. It did, how-
the path to the acceptance of a heliocentric uni- ever, force people to realize that the Copernican
verse, but the idea that everyone in the preced- system could not be easily ruled out. Here was
ing centuries was mired in Aristotelian logic is not just a theory, but a direct observation that
a gross oversimplification. Proposals for a helio- objects needn’t orbit the earth. And the Jupiter
centric universe go back as far as Aristarchus system also provided a visual analog to the idea
in the third century B.C., and the Capellan of the planets in orbit around sun.
model of Mercury and Venus in orbit around The accumulation of astronomical data
the sun, in violation of Aristotle’s dictum, does really powered the change in our understand-
not appear to have been at all contentious in the ing of planetary motions. By the time Galileo
Middle Ages. pioneered the use of the telescope, Kepler had
April 2013 GRIFFITH OBSERVER Page 13
inherited the extensive observations of Tycho
Brahe and had made the critical breakthrough.
It does neither Kepler nor Copernicus credit
to think of the Astronomia Nova as a simple
refinement of the Copernican system. Although
Kepler owed a huge debt to the heliocentricity
of Copernicus’s system, the work of Copernicus
was far more than just a statement of the
motion of the earth, and Kepler’s contribution
was far greater than simply substituting ellipses
for circles. Copernicus’s detailed models for the
motion of each planet were masterpieces, but
not one that would stand the test of time.
Kepler realized that the orbits of the planets
could be described by ellipses, and this not only
allowed far more accurate predictions of plan-
etary motion, it also provided, for the first time,
a unified model. Kepler discarded the last of the
Ptolemaic ideas. There was no more uniform
circular motion. There were no epicycles, no
equants, and no eccentrics. The orbits of all the
planets could be described by an ellipse with the
Kepler, Galileo, and Copernicus, the Three Musketeers of
sun located at one focus. The equant evolved to heliocentric orbits, conspire on behalf of the planets’ so-
the simple rule: a line joining a planet to the lar revolution on the Astronomers Monument at Griffith
sun sweeps out equal areas in equal times. Observatory. (photograph Lydia Philpott)
Kepler’s developments are, of course, not
the end of the story. Newton’s formulation of
gravity provided a physical law underlying of spacetime, gave us an even deeper physical
Kepler’s observed rules, but it also introduced understanding of, and detailed corrections to,
the complication that every planet influences the planetary motions.
the motion of every other. Einstein’s general And who are we to say we have reached the
relativity, with its concept of the curvature final answer today?
BACK COVER
Circumterrestrial Sphere
Centered in the Universe, the flagship show in Griffith Observatory’s Samuel Oschin Planetarium, brings on stage the
nested spheres Ptolemy mathematically imagined in the second century A.D. About three centuries later, Martianus
Capella, a Latin writer in north Africa, illustrated an alternative cosmology that centered Mercury and Venus on the
sun. Dr. Lydia Philpott spotlights this world system this month in “Copernicus, Capella, and Circumsolar Orbits.” (art
from Centered in the Universe, Tom Bradley, Chris Butler, Don Dixon, and Michael Kory)
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