Download Greek and Hellenistic Astronomy

Greek and Hellenistic Astronomy
Robert H. van Gent
Mathematical Institute
Utrecht University
“The School of Athens” (Scuola di Atene), fresco made in 1509/11 by Raphael of Urbino in
the Apostolic Palace (Vatican City). In the centre Plato (left) and Aristotle (right) are seen
debating in the company of numerous illustrious classical scholars and philosophers.
Thales of Milete (c. 624-c. 546 BCE)
According to the Greek historian Herodotus, the Greek
philosopher Thales predicted an eclipse of the Sun
(probably the one on 28 May 585 BCE) which occurred
during a battle between the Lydians and the Persians.
Later sources claim that he visited Egypt where visited
the pyramids and computed their heights from their
shadows.
An often repeated anecdote relates how he, during a
nightly stroll, fell into a well and so became the stereotype
of the “absent-minded astronomer”.
Plato (424/23-348/47 BCE)
Established the famous Academy of Athens and
is regarded as the founder of Western science
and philosophy.
Wrote dozens of treatises (“Socratic Dialogues”)
on numerous topics.
His views on the cosmos and its origin were
described in detail in the Timaeus (this book also
contains the first part of his famous story of the
lost city of Atlantis which was continued in the
Critias).
Plato also discussed astronomical topics in
other works, such as Phaedo, Phaedrus, The
Republic (Politeia) and The Laws (Legibus).
Plato was a pupil of Socrates (c. 469-399 BCE),
his most famous pupil was Aristotle.
Oil on popular wood ascribed to Joos van Wassenhove
(c. 1475) for the studiolo of Federico II da Montefeltro in
Urbino (Louvre, Paris)
Aristotle of Stagira (384-322 BCE)
Pupil of Plato and founder of the Lyceum of
Athens. His works greatly influenced
Hellenistic, Islamic and medieval-European
philosophy and science.
Aristotle’s views on the cosmos are described,
together with those of earlier Greek
philosophers, in the following works:
• De Caelo (“The Heavens”)
• Meteorologia (“Meteorological Phenomena”)
According to Aristotle all motion below the
lunar orb was rectilinear and directed to the
centre of the Earth, while all celestial motions
were circular, uniform and eternal.
According to historical tradition the Macedonian
conqueror Alexander the Great (356-323 BCE)
was tutored by Aristotle.
Oil on popular wood ascribed to Joos van Wassenhove
(c. 1475) for the studiolo of Federico II da Montefeltro in
Urbino (Louvre, Paris)
The Five Regular or
Platonic Polyhedrons
Described by the Greek mathematician
Euclid in the 13th book of the Elements.
Plato linked them in the Timaeus (c. 360
BCE) with the four elements of the
‘sublunary’ world.
Later philosophers added the dodecahedron to represent the fifth element
(quintessence or aether) from which the
‘supralunary’ world is made up.
polyhedron
F
V
E
element
tetrahedron
4
6
4
fire
cube
6
12
8
earth
octahedron
8
12
6
air
dodecahedron
12
30
20
aether
icosahedron
20
30
12
water
The City of Alexandria
The city of Alexandria, founded in 332/31 BCE by Alexander the Great, was laid out
according to a rectangular street plan of which the major axis was directed to the
direction where the Sun rose on 20 July (the traditional Egyptian New Year’s Day,
coinciding with the heliacal rising of the bright star Sirius, the Dog Star)
Measurement of the
Earth’s Circumference by
Eratosthenes of Cyrene
(276-194 BCE)
Eratosthenes measured the
angle α as 7.2°. From this he
deduced a circumference of
(360/7.2) × 5000 = 250 000
stadia.
Assuming 1 stadion ≈ 185.4
m, this then results in a
circumference of c. 46 400 km
– about 15% too large.
Eratosthenes assumed that Alexandria and Syene (in
southern Egypt) were 5000 stadia distant from each
other and were located on the same meridian. On the
day of the summer solstice (c. 21 June) a vertical
gnomon in Syene was observed to cast no shadow at
noon while a similar vertical gnomon in Alexandria
was observed to produce a measurable noon shadow.
Eratosthenes’s method was
later also applied by Poseidonius of Apameia, Islamic
mathematicians and the
Dutch astronomer and
mathematician Willebrord
Snellius.
Measuring the Distances of the
Moon and the Sun by Aristarchus
of Samos (c. 310-c. 230 BCE)
Aristarchus measured the elongation
(angle between the Moon and the Sun)
when the Moon is exactly half lit as 87°.
From this he inferred that the distance
to the Sun was between 18 and 20
times the lunar distance [in reality, the
distance ratio is about 390].
From observations of lunar eclipses
Aristarchus determined the ratio of the
diameters of the Earth and the Moon as
c. 2.85.
From the angular diameter of the Moon
(½°) the distance to the Moon can then
be inferred. By using a wrong value (2°)
Aristarchus computed a distance of 20
terrestrial radii, whereas the true
distance is about 60 terrestrial radii.
Claudius Ptolemy of Alexandria
(c. 100-175 CE)
Author of several works which defined the
mathematical sciences in the Late
Classical, Islamic and European world until
well into the Renaissance:
•
Mathematike Syntaxis (Almagest)
•
Hypotheseis ton planomenon (Hypotheses
regarding the movements of the planets)
•
Apotelesmatika (Tetrabiblos, Quadripartitium)
•
Geographike Hypogesis (Geographia,
Cosmographia)
•
Harmonikon (Harmonics)
•
Optics
Oil on popular wood ascribed to Joos van Wassenhove
(c. 1475) for the studiolo of Federico II da Montefeltro in
Urbino (Louvre, Paris)
The “known world” according to the 1482 printed edition of the Cosmographia of Claudius Ptolemy
The geocentric or Ptolemaic world system
Andreas Cellarius, Harmonia Macrocosmica, Amsterdam, 1660
As Babylonian astronomers had already noted, the outer planets (Mars, Jupiter and Saturn) do
not move in uniform speed and direction with respect to the fixed stars, but, at times, are also
observed to become stationary or move in opposite (westward or retrograde) direction.
The inner planets (Mercury and Venus) were observed to exhibit similar movements with respect
to the Sun.
The apparent motion of a planet according to the epicycle model of Ptolemy
The apparent motion of a planet according to the heliocentric model of Copernicus
The geocentric world system of Claudius Ptolemy
(Note that in this simplified diagram the outer planets are not correctly placed in their epicycles – the lines
connecting the planets with their deferent circles should be parallel with the Earth-Sun line)
The Motion of the Outer Planets (Mars, Jupiter, Saturn) According to Claudius Ptolemy
The planet (P) is assumed to move with a constant speed (equal to that of the mean Sun) on a small circle
(epicycle), which in turn moves on a larger circle (deferent) with the Earth (O) placed at a small distance from the
centre (M). As seen from the equant point (E), the centre (C) of the epicycle moves with a uniform speed.
The Motions of the Sun, the Moon and the Planets According
the Geometric-Kinematical Models of Claudius Ptolemy
Summary of the Contents of the Almagest
I & II
III
IV to VI
VII & VIII
IX to XIII
– introductory chapters on spherical trigonometry
– theory of the Sun‘s apparent motion
– theory of the Moon’s motion and luni-solar eclipses
– the fixed stars, the constellations and the Milky Way
– theory of planetary motion
The Sun, the Moon and the Planets
The Geocentric World System
@ Dennis Duke http://www.csit.fsu.edu/~dduke/
The Dimensions of the Cosmos According to Claudius Ptolemy
distance (Earth radii)
Planet
min
mean
max
diameter
(Earth = 1)
Moon
33
48
64
1/4 + 1/24
Mercury
64
115
166
1/27
166
622½
1079
1/4 + 1/20
Sun
1160
1210
1260
5 + 1/2
Mars
1260
5040
8820
1 + 1/7
Jupiter
8820 11503
14189
4 + 1/3 + 1/40
Saturn
14189 17026
Venus
19865 4 + 1/ 4 + 1/20
The relative dimensions of the celestial bodies in the world system of Claudius Ptolemy
Andreas Cellarius, Harmonia Macrocosmica (Amsterdam, 1660)
Some Astronomical Instruments Described
by Claudius Ptolemy
Cunningham, The Cosmographical Glasse (1559)
19th-century engraving of an astronomer
at the observatory of Alexandria
The Antikythera
Mechanism
Discovered in 1900/01 in a
Roman shipwreck (c. 80 BCE)
off the coast of the Greek
island of Antikythera.
Recent investigations indicate
that it was a complex and
highly sophisticated
mechanical device capable of
displaying various calendars
and the movements of the
Sun, the Moon and the five
then known planets.