HISTORY OF ASTRONOMY
Historia de la Astronomía
Curso optativo de profundización
AST1521 – ASP5021
Semestre 2014 A
Lunes-Miércoles h 14-15;20
Sala N2 – Campus San Joaquín
Instituto de Astrofísica
Pontificia Universidad Católica de Chile
Rodolfo Angeloni
NEXT ACTIVITIES
Seminarios – 2nd round
Miércoles 28 de Mayo – (15+5) min X 4 grupos
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The Antikythera Mechanism – Guerrero & Zuñiga
The Archimedes’ Palimpsest – Henriquez & Vargas
About Aristarchus’ “On sizes and distances” – Collao & Walker
“Ptolemy’s Longitudes…” - Herrera & Vergara
26/05/2014
History of Astronomy
NEXT ACTIVITIES
Lunes 2 de Junio
Auditorium Bralic, 14hs
Clase en videoconferencia
desde el Observatorio ESO de la Silla
26/05/2014
History of Astronomy
NEXT ACTIVITIES
Seminarios – 3nd round
Miércoles 18 de Junio – (15+5) min X 4 grupos
26/05/2014
History of Astronomy
NEXT ACTIVITIES
Prueba Final
Lunes 23 de Junio, 14hs
Sala N2
26/05/2014
History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
The Julian calendar was instituted in Rome by Julius Caesar in the 45 B.C.
It reached its final form by A.D. 8 and continued in use without further change
until A.D. 1582, when it was modified by the Gregorian reform
The Julian calendar adopts a mean length of 365 1/4 days for the year
26/05/2014
History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
¿How many years have elapsed between 1st January 23 BC and 1st January 47?
The Julian calendar adopts a mean length of 365 1/4 days for the year
26/05/2014
History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
Kalendae, Nonae, Idus
The Roman manner of designating the days of the month was not the same as our own
The first day of the month was called Kalendae.
The 5th of most months was called Nonae.
The 13th day of most months was called Idus.
However, four months had the Nonae on the 7th
and the Idus on the 15th (March, May, July,
October).
Other days of the month were specified in terms
of the days remaining until the next of these
three guideposts.
The Roman way of counting the days continued in use to the end of Middle Ages
26/05/2014
History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
The week
The week was not originally a feature of the Julian calendar
As the week penetrated to the western Mediterranean,
the practice grew up of naming the days of the week after the planets
Tiu
Woden
Thor
Frigga
The seven-day planetary week was made official
by the emperor Constantine in AD 321
26/05/2014
History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
Julian year: 365,25 days
Tropical year: 365,2422 days
1 𝐽𝑢𝑙𝑖𝑎𝑛 𝑦𝑒𝑎𝑟 = 1 𝑡𝑟𝑜𝑝𝑖𝑐𝑎𝑙 𝑦𝑒𝑎𝑟 + 0,0078 𝑑𝑎𝑦
By the XVI century, the equinox had moved by…
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History of Astronomy
INTERMEZZO
The Julian and Gregorian Calendars
The Gregorian Reform
Gregorius XIII - 1582
Bishop Gregory, servant of the servants of God
For the perpetual remembrance of this matter:
Amongst the most serious tasks of our pastoral office, not the
least of them is to see to it that the affairs which the holy
Council of Trent reserved to the Apostolic See are conducted,
with God's help, to a desirable conclusion.
[…]
There are two principal parts in the breviary. One comprises
the prayers and divine praises to be offered on feast days
and ordinary days; and the other relates to the annual
recurrence of Easter and the feasts that depend on it, to be
measured by the movement of the sun and moon.
Gregorius XIII, Inter gravissimas, 24 Feb 1582
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History of Astronomy
Medieval and Early Renaissance Astronomy
Georg von Peuerbach (1423-1461)
Theoricae novae planetarum
26/05/2014
History of Astronomy
Medieval and Early Renaissance Astronomy
Georg von Peuerbach (1423-1461)
Theoricae novae planetarum
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History of Astronomy
Medieval and Early Renaissance Astronomy
Johann Müller (Regiomontanus, 1436-1476)
Epytome in Almagesti Ptolemei
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History of Astronomy
Medieval and Early Renaissance Astronomy
Johann Müller (Regiomontanus, 1436-1476)
Ephemerides (printed in 1474)
1475-1506
26/05/2014
History of Astronomy
Medieval and Early Renaissance Astronomy
26/05/2014
History of Astronomy
Medieval and Early Renaissance Astronomy
Suggested Readings
Evans’ On Julian and Gregorian Calendars
Russo’s The Early Renaissances
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History of Astronomy
COPERNICUS
and the culmination of Greek program
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Alessandro Piccolomini (1508-1579) De le stelle fisse - 1540
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Giovanni Paolo Gallucci (1538-1621) Theatrum Mundi - 1588
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Osiander’s Foreword
For it is the duty of an astronomer to compose the history of the
celestial motions through careful and expert study. Then he must
conceive and devise the causes of these motions or hypotheses
about them. Since he cannot in any way attain to the true causes,
he will adopt whatever suppositions enable the motions to be
computed correctly from the principles of geometry.
N. Copernicus, De Revolutionibus, Foreword
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Osiander’s Foreword
For these hypotheses need not be true nor even probable.
On the contrary, if they provide a calculus consistent with
the observations, that alone is enough.
N. Copernicus, De Revolutionibus, Foreword
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Heliocentric model of the solar
system in Copernicus' manuscript
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Nicolaus Copernicus
1473-1543
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Nicolaus Copernicus
1473-1543
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Nicolaus Copernicus
1473-1543
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
I was impelled to consider a different system of deducing the
motions of the universe's spheres for no other reason than the
realization that astronomers do not agree among themselves
in their investigations of this subject.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
…in determining the motions not only of these bodies [the Sun
and the Moon] but also of the other five planets, they do not
use the same principles, assumptions, and explanations of the
apparent revolutions and motions. For while some employ only
homocentrics, others utilize eccentrics and epicycles, and yet
they do not quite reach their goal.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
For although those who put their faith in homocentrics showed
that some non-uniform motions could be compounded in this way,
nevertheless by this means they were unable to obtain any
incontrovertible result in absolute agreement with the phenomena.
On the other hand, those who devised the eccentrics seem thereby
in large measure to have solved the problem of the apparent
motions with appropriate calculations...
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
…But meanwhile they introduced a good many ideas which
apparently contradict the first principles of uniform motion. Nor
could they elicit or deduce from the eccentrics the principal
consideration, that is, the structure of the universe and the true
symmetry of its parts.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
On the contrary, their experience was just like some one taking
from various places hands, feet, a head, and other pieces, very well
depicted, it may be, but not for the representation of a single
person; since these fragments would not belong to one another at
all, a monster rather than a man would be put together from them.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
For a long time, then, I reflected on this confusion in the astronomical traditions
concerning the derivation of the motions of the universe's spheres. I began to be
annoyed that the movements of the world machine, created for our sake by the
best and most systematic Artisan of all, were not understood with greater
certainty by the philosophers, who otherwise examined so precisely the most
insignificant trifles of this world.
For this reason I undertook the task of rereading the works of all the
philosophers which I could obtain to learn whether anyone had ever proposed
other motions of the universe's spheres than those expounded by the teachers of
astronomy in the schools.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
And in fact first I found in Cicero that Hicetas supposed the earth to move.
Later I also discovered in Plutarch that certain others were of this opinion.
[…]
Therefore, having obtained the opportunity from these sources, I too began
to consider the mobility of the earth. And even though the idea seemed
absurd, nevertheless I knew that others before me had been granted the
freedom to imagine any circles whatever for the purpose of explaining the
heavenly phenomena.
N. Copernicus, De Revolutionibus, Preface
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
The Relation of Heliocentric and Geocentric Models
For accurate astronomical prediction, it makes no difference
whether the Earth goes around the Sun or the Sun goes around the Earth
The accuracy of a theory depends on the technical details
Superior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
The Relation of Heliocentric and Geocentric Models
𝑂𝑃 = −𝑆𝑂 + 𝑆𝑃
𝑂𝑃 = 𝑆𝑃 + −𝑆𝑂
Superior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
The Relation of Heliocentric and Geocentric Models
The planet’s orbit in the Sun-centered model becomes the deferent circle in
the Earth-centered model. And the orbit of the Earth becomes the epicycle.
Superior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
The Relation of Heliocentric and Geocentric Models
The planet’s orbit in the Sun-centered model corresponds to the epicycle in the
Earth-centered model. And the orbit of the Earth corresponds to the deferent circle
𝑂𝑃 = −𝑆𝑂 + 𝑆𝑃
Inferior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Advantages of the Sun-Centered System
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Advantages of the Sun-Centered System
It is clear that each of the six planets in its motion shares
something with the Sun, and the Sun’s motion is, so to
speak, the common mirror and measure for their motion.
Peuerbach, Theoricae Novae Planetarum
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Advantages of the Sun-Centered System
𝑟𝑝 𝑅
=
𝑟0 𝑟
Superior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Advantages of the Sun-Centered System
𝑟𝑝 𝑟
=
𝑟0 𝑅
Inferior planets: transformation from the Sun-centered theory (A) to the Earth-centered theory (B)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Advantages of the Sun-Centered System
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernicus’ Commentariolus (1510’s)
1. There is not one single center for all the celestial orbs or spheres.
2. The center of the Earth is not the center of the world, but only of the heavy
bodies and of the lunar orb.
3. All the orbs encompass the Sun which is, so to speak, in the middle of them all,
for the center of the world is near the Sun.
4. The ratio of the distance between the Sun and the Earth to the height of the
firmament [i.e., the radius of the sphere of stars] is less than the ratio between
the Earth’s radius and the distance from the Sun to the Earth, in such a manner
that the distance from the Sun to the Earth is insensible in relation to the height
of the firmament.
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernicus’ Commentariolus (1510’s)
5. Every motion that seems to belong to the firmament does not arise from it, but
from the Earth. Therefore, the Earth with the elements in its vicinity accomplishes
a complete rotation around its fixed poles, while the firmament, or last heaven,
remains motionless.
6. The motions that seem to us proper to the Sun do not arise from it, but from the
Earth and our [terrestrial] orb, with which we revolve around the Sun like any
other planet. In consequence, the Earth is carried along with several motions.
7. The retrograde and direct motions which appear in the case of the planets are not
caused by them, but by the Earth. The motion of the Earth alone is sufficient to
explain a wealth of apparent irregularities in the heaven.
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Rheticus’ Narratio Prima (1540)
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernican Planetary Theory
Copernicus's theory of the superior planets
NPO is the orbit of the Earth. AGB is the
deferent circle of a superior planet, such as
Mars. Mars itself moves on a small
epicycle which is responsible for producing
an anomaly of motion more or less
equivalent to that produced by Ptolemy's
equant. From De revolutionibus, V, 4
(Nuremberg, 1543)
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernican Planetary Theory
Copernicus's minor epicycle
@ position 1
MP = CG − GP + CM = R − aR + aR = R
Hence it will be also demonstrated by this
composite movement the planet does not
describe a perfect circle in accordance with
the theory of the ancient mathematicians but
a curve differing imperceptibly from one.
N. Copernicus, De Revolutionibus, V, 4
@ position 3
MP = [CG2 + (GP + CM)2 ]1/2 = R(1 + 4a2 )1/2
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernican Planetary Theory
Comparison of the Copernican model with a
Ptolemaic eccentric-with-equant model
The Ptolemaic eccentric circle is drawn in
solid line. The oblong Copernican orbit is
drawn in dashed line. The Ptolemaic equant
point and the hidden, effective equant point of
the Copernican model coincide at E. At the
same moment (and therefore at the same
mean anomaly 𝜃 ) the position of the planet in
equant theory is P and the position in
Copernican theory is P'. As viewed from the
Sun D, there is a small difference AO in the
directions predicted by the two theories.
26/05/2014
History of Astronomy
COPERNICUS
and the culmination of Greek program
Copernican Planetary Theory
At rest, however, in the middle of everything is the sun. For in this most beautiful temple,
who would place this lamp in another or better position than that from which it can light
up the whole thing at the same time? For, the sun is not inappropriately called by some
people the lantern of the universe, its mind by others, and its ruler by still others.
[Hermes] the Thrice Greatest labels it a visible god, and Sophocles‘ Electra, the all-seeing.
Thus indeed, as though seated on a royal throne, the sun governs the family of planets
revolving around it. Moreover, the earth is not deprived of the moon's attendance. On the
contrary, as Aristotle says in a work on animal , the moon has the closest kinship with
the earth. Meanwhile the earth has intercourse with the sun, and is impregnated for its
yearly parturition.
N. Copernicus, De Revolutionibus, I, 10
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History of Astronomy
COPERNICUS
and the culmination of Greek program
Suggested Readings
Biographical Notes on Copernicus
Preface to the “De revolutionibus…”
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History of Astronomy