Astronomy of Greece
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I) The Astronomy of Ancient Greece
A) Based on the astronomy of Babylon and Egypt
1) Heavily influenced by astrology
B) Astrology is not the same as astronomy
1) Not a science
2) Belief that heavenly bodies influence and control human lives
and feelings
C) Astronomy is a science
1) Study of celestial bodies
(a) Magnitude
(b) Motions
(c) Constitution
II) Important figures
A) Thales (624-546 BCE)
1) Founder of Greek astronomy
2) Founder of the Milesian (pre-Ionian) School
3) Predicted an eclipse (about 585 BCE)
(a) Halted a war between the Medes and the Lydian’s
(b) Thales’ action revealed the great strengths of astronomers at
this time
(1) These events had a disturbing effect on public behavior
(2) Astronomers became important to rulers
4) Little else is known of Thales
(a) Unknown whether he believed if the Earth was flat or
spherical
(b) Genius lay in his emphasis on gaining knowledge through
observation of natural phenomena
(c) Rejected mythology as a means of scientific explanation
(d) Began the search for the natural causes of celestial
phenomena
B) Anaximander (610-546 BCE)
1) Believed the Universe was contained within the rim of a huge
wheel filled with fire
(a) The holes in the rim, through which the fire could be seen,
were the planets and the stars
2) First philosopher who speculated that the sky contained
separate spheres through which the planets traveled
(a) Concept dominated astronomical thought up to the 17th century
3) Explained the existence of the ‘Unlimited’
(a) A boundless reservoir from which all things come and to which
all things return
(1) This is the first mention of the ‘Law of Return of all
Things’ which is still central to the cyclical concepts of astrology
4) Made the first known map of the Earth
5) Second leader of the Milesian School
(a) pupils included
Anaximenes and Pythagoras
C) Anaximenes (585-528 BCE)
1) Regarded as an important figure in the development of
astronomy, although little is known of his work
2) Developed the notion of ‘macrocosm and microcosm’
(a) ‘As above, so below.’
3) Observed obliquity of the ecliptic
4) Believed stars were like nails attached to transparent spheres
of crystalline material which turned around the Earth like a hat on a head
(a) The belief in crystalline spheres persisted, like many other
ancient notions up to the work of Johannes Kepler in the 17th century
D) Heraclitus (535-475 BCE)
1)
"Weeping Philosopher" & "The Obscure"
2)
Believed that change is central to the Universe
(a) "Everything flows, nothing stands still."
(b) "No man can cross the same river twice, because neither the man
nor the river are the same."
E) Pythagoras (586-490 BCE)
1) Regarded as one of the most brilliant and influential
philosophers of all time
2) Educated in the mathematics of the Ionian school
3) Knew both Thales and Anaximander
4) Studied in Egypt
5) Studied in Babylon
6) Discovered musical notes can be applied to mathematics as he
passed a blacksmith shop
(a) The anvils used
where all sized in proportion to each other and hence the sound emanating from
the striking of
the anvil was based on this proportional size
7) Main theory
(a) Planets in motion moved based on mathematical equations,
hence they would create a noise which could be described as a
musical note
(b) Used by Kepler
F) Plato (428-347 BCE)
1) The reality we see is only a distorted shadow of the perfect
ideal form
(a) Allegory of the
Cave
(b) Car accident
2) The most perfect form is the circle
G) Aristotle (384-322 BCE)
1) Two reasons for Earth being round
(a) Ship on the horizon
(b) Earth’s shadow on moon was curved
(1) Flat Earth could not produce a curved shadow
2) Geo-centric model of Solar System
3) Teacher of Alexander the Great
H) Aristarchus (310-230 BCE)
1) Proposed the Earth orbited the sun
2) First to propose the theory that the Earth rotated on an axis
I) Eratosthenes (276-195 BCE)
1) Devised a method for determining the Earth’s circumference to
within 5% of the currently accepted value
(a) Eratosthenes
knew that on the summer solstice at noon in the city of Swenet (Syene, now
Aswan) on the
Tropic of Cancer, the sun
would appear at the zenith (directly overhead.) He also knew, from
measurement,
that in his hometown of
Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle
(7°12')
south of the zenith at the
same time. Assuming that Alexandria was due north of Syene he concluded
that the
distance from Alexandria to
Syene must be 1/50 of the total circumference of the Earth. His estimated
distance
between the cities was 5000 stadia
(about 500 miles or 950 km.) He rounded the result to a final value of 700
stadia per degree, which
gives a circumference of 252,000 stadia. While it is not known the exact
size of the
stadion he used, if we assume that
Eratosthenes used the "Egyptian Stadium" of about 157.5 m, his
measurement turns out to be
39,690 km (the actual value is 40,075.16 km or 24,901.55 miles). His error
is
less than 5%!
J) Hipparchus (190-120 BCE)
1)
Regarded as the greatest and most influential astronomer of the
ancient world (and the only ancient astronomer
featured on the Astronomer's Monument at Griffith Observatory
in Los Angeles, CA)
2) Discovered precession
(a) The Earth's axis rotates (precesses) similar to a spinning
top
(b) Period of precession is about 26,000 years
(c) Caused by gravitational pull
3) North Celestial Pole will not always point towards the same starfield
(a) Polaris today
(b) 3000 BCE - Thuban, a star in the constellation of Draco
(c) 14,000 CE Vega, in Lyra, will be the north pole star
4) Catalogue of stellar magnitudes
K) Ptolemy (90 BCE-168 CE)
1) Ensured the continuation of Aristotle’s geocentric model by
fitting it to a mathematical model
2) Explained how planets appear to move faster, move slower, and
appear to stop and go backward over a period of time
(a) Retrograde motion
(1) Motion accounted for by placing planets on small circles
(epicycles) which moved along larger circles (deferents)
3) Work published in the Almegest
- 140 CE
Aristotle
Aristotle, more than any other
thinker, determined the orientation and the content of Western intellectual
history. He was the author of a philosophical and scientific system that
through the centuries became the foundational support for both medieval
Christian and Islamic scholastic thought. Until the end of the 17th
century, Western culture was Aristotelian. Even after the intellectual
revolutions of centuries to follow, and of our present intellectual knowledge,
Aristotelian concepts and ideas remain an important and integral part of
Western thinking.
Aristarchus
The only surviving work of
Aristarchus, On the Sizes and Distances of the Sun and Moon,
is not based on his sun-centered theory, which unfortunately has been lost.
However, his surviving work provides the details of his remarkable geometric
argument, based on observation, whereby he determined that the Sun was about
20 times as distant from the Earth as the Moon, and 20 times the Moon's size.
Both these estimates were an order of magnitude too small, but the fault was
in Aristarchus's lack of accurate instruments rather than in his correct
method of reasoning.
The diagram shows an argument used by
Aristarchus. He knew that the moon shines by reflected sunlight, so he
argued, if one measured the angle between the moon and sun when the moon is
exactly half illuminated then one could compute the ratio of their distances.
Aristarchus estimated that the angle
at the time of half illumination was 87
so the ratio of the distances is sin 3.
Of course, this is done now using modern notation. Aristarchus did not
use degrees nor had trigonometry been invented so he did not have the sine
function at his disposal. However, this is in effect the calculation he
made, correct in principle yet almost impossibly difficult to observe in
practice since determining the moment at which half illumination of the moon
occurs can only be very inaccurately determined.
Aristarchus was then faced with
calculating an approximation for what is sin 3.
He obtained the inequality
1/18 > sin 3
> 1/20
and deduced that the sun was between
18 to 20 times as far away as the moon. In fact at the moment of half
illumination the angle between the moon and the sun is actually 89
50' and the sun is actually about 400 times further away than the moon.
Eratosthenes
Despite being a leading scholar,
Eratosthenes was considered to fall short of the highest rank. While he
was recognized by his contemporaries as a man of great distinction in all
branches of knowledge, in each subject he just fell short of the highest place
of honour. This distinction gave him the nickname "Beta" or "Pentathlos"
both of which refer to as "being second." Today, we know this is a harsh
nickname to give to a man whose accomplishments in many different areas are
remembered today not only as historically important, but, remarkably still
providing a basis for modern scientific methods.
Thales
Thales believed the
principle of all things is water, which should not be considered exclusively
in a materialistic and empirical sense. It was to be considered that
which has neither beginning nor end and as an active, living, divine force.
Thales was induced to this belief by the observation that all living things
are sustained by moisture and perish without it. Anaximander
Anaximander said the
first animals were fish, which sprang from the original humidity of the
earth. Fish came to shore, lost their scales, assumed another form and
thus gave origin to the various species of animals. Man thus traces
his origin from the animals. Because of this, Anaximander has come to
be considered the first evolutionist philosopher. Anamimenes
For Anaximenes, the first principle
from which everything is generated is air. Air, through the two
opposite processes of condensation and rarefaction (which are due to heat
and cold), has generated fire, wind, clouds, water, heaven and earth.
Thus like Thales and Anaximander, he has reduced the multiplicity of nature
to a single principle, animated (hylozoism) and divine, which is the
reason for all empirical reasoning.
Heraclitus
Heraclitus disagreed with
Thales, Anaximander, and Pythagoras about the nature of the ultimate
substance and claimed instead that everything is derived from the Greek
classical element fire, rather than from air, water, or earth. This led to
the belief that change is real, and stability illusory.
Pythagoras
Pythagoras is most
remembered for his famous geometry theorem. However, it was not
Pythagoras that developed the theorem. The theorem was known to the
Babylonians 1000 years before Pythagoras was born. Pythagoras was the
first to prove the theorem correct.
Plato's Academy
The best overview of Plato's views
can be gained from examining what he thought a proper course of education
should consist:
"...the exact sciences - arithmetic,
plane and solid geometry, astronomy and harmonics would be studied for 10
years. Then dialectic, which is the art of conversation and answer; the
ability to pose and answer questions about the essences of things..."
Plato's Academy flourished until 529
CE when it was closed down by the Christian Emperor Justinian who claimed it
was a pagan establishment. Having survived for 900 years it is the longest
surviving university known. The sign over his school stated:
"Let no one
unversed in geometry enter here."
Hipparchus
The main contributions of Hipparchus
includes the production of a table of chords, an early example of a
trigonometric table. Some historians have put forth the idea that
trigonometry was invented by him. The purpose of this table of chords
was to give a method for solving triangles which avoided solving each triangle
from first principles. Hipparchus also introduced the division of a
circle into 360 degrees.
Hipparchus calculated the length of
the year to within 6.5 minutes and discovered the precession of the equinoxes.
Hipparchus's value of 46" for the annual precession is good compared with the
modern value of 50.26" and much better than the figure of 36" that Ptolemy was
to obtain nearly 300 years later. It is believed that Hipparchus's star
catalogue contained about 850 stars, not listed in a systematic coordinate
system but using different ways to designate the position of a star. His
star catalogue, completed around 129 BCE, has been claimed to have been used
by Ptolemy as the basis of his own star catalogue.
Ptolemy
One of the most
influential Greek astronomers and geographers of his time, Ptolemy propounded
the geocentric theory into a form that prevailed for 1400 years.
The Almagest is
the earliest of Ptolemy's works and gives in detail the mathematical theory of
the motions of the Sun, Moon, and planets. Ptolemy made his most
original contribution by presenting details for the motions of each of the
planets. The Almagest was not superseded until
Copernicus presented his heliocentric theory in the book De
Revolutionibus of 1543.
The final five books of the
Almagest discuss planetary theory. This is Ptolemy's
greatest achievement since there does not appear to have been any satisfactory
theoretical model to explain the complicated motions of the five planets
before the Almagest. Ptolemy combined the epicycle
and eccentric methods to give his model for the motions of the planets. The
path of a planet "P" consisted of circular motion on an epicycle, the center
"C" of the epicycle moving round a circle whose center was offset from the
earth. The planetary theory which Ptolemy developed here is a
sophisticated mathematical model to fit observational data. The model he
produced, although complicated, represents the motions of the planets fairly
well.
Troubling observations
of varying planetary brightness and retrograde motion could not be
accommodated by the firmly held belief that planetary spheres moved with
constant angular velocity, and the objects attached to them were always the
same distance from the earth because they moved on spheres with the earth at
the center.
The "solution" to these
problems came in the form concentric spheres: planets were attached, not to
the concentric spheres themselves, but to circles attached to the concentric
spheres. These circles were called "epicycles", and the concentric
spheres to which they were attached were termed the "deferents".
The centers of the
epicycles executed uniform circular motion as they went around the deferent at
uniform angular velocity and at the same time the epicycles (to which the
planets were attached) executed their own uniform circular motion.
However, in practice,
even this was not enough to account for the detailed motion of the planets on
the celestial sphere. In more sophisticated epicycle models further
"refinements" were introduced that put epicycles on epicycles.
The fact that ancient astronomers
could convince themselves that the elaborate scheme of epicycles could still
correspond to "uniform circular motion" is testament to the power of three
ideas that we now know to be completely wrong. These ideas were so
ingrained in the astronomers of an earlier age that they were essentially
never questioned. The ideas were:
1. All motion in the heavens is
uniform circular motion.
2. The objects in the heavens are
made from perfect material and hence cannot change their intrinsic properties.
3. The Earth is at the center of the
universe.
These ideas concerning uniform
circular motion and epicycles were catalogued by Ptolemy in 150 CE. This
picture of the structure of the Solar System has come to be called the
"Ptolemaic Universe."
By the Middle Ages, these ideas took
on a new power as the philosophy of Aristotle (newly rediscovered in Europe)
was adopted to Medieval theology in the great synthesis of Christianity and
Reason undertaken by philosopher-theologians such as Thomas Aquinas. The
"Prime Mover" of Aristotle's universe became the God of Christian theology,
the outermost sphere of the Prime Mover became identified with the Christian
Heaven, and the position of the Earth at the center of it all was understood
in terms of the concern that the Christian God had for the affairs of mankind.
Thus, the ideas largely originating
with pagan Greek philosophers were recognized by the Catholic church and
eventually assumed the power of religious dogma. As we will see in our
discussion of modern astronomers, to challenge this view of the Universe was
not merely a scientific issue. It became a theological one as well and
subjected dissenters to the considerable and not always benevolent power of
the Church.
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