Assignment 6 (Developed Greek Astronomy) Flashcards
According to later tradition, ____ took up ______ challenge to explain the movements of the heavenly bodies on the basis of ________ and _______ movements.
Eudoxus, Plato, uniform, and ordered
What is plato’s challenge?
‘saving the appearances’: explaining the
movements of the planets (here including the sun and the moon along with the five planets) on the basis of movements that are uniform and ordered.
Why these conditions of saving the appearances?
Uniform and ordered movements because aesthetic
judgements that place a high value on simplicity, consistency, and uniformity.
Eudoxus’ Model
uniform motion of concentric spheres with complex spheres
How do we know Eudoxus’ Model?
Aristotle and Simplicituswrote about it
How does Eudoxus’ Model meet Plato’s challenge of saving the appearances?
explains multiple and varied movements of the celestial bodies by means of a model that involves only regular, uniform, circular movement
What does Eudoxus’ Model fail at?
- Does not explain specific forms of planetary retrogradation.
- Does not explain why seasons are of different legnths
- does not account for variations in diameter of moon or brightness of planets (brightest in retrograde)
retrograde, prograde, station
retrograde: moving backward
prograde: moving forward
station: not moving!
Describe aristotle’s life timeline. (birth, who he studied with)
Born in 384 BCE, studied under Plato until Plato died.
What did Aristotle do?
- Wrote about lots of things
- Regarded math as useful but not standard for all knowledge
- profound interest in physical material world not underlying nature (importance of induction not deduction)
- adopted callippus’ modified version of eudoxus’ geometrical model of concentric spheres
- incorporated the model of concentric spheres into a physical model of the cosmos
What were the basic assumptions of Aristotle’s model of the physical cosmos?
Observations:
1. there are 4 elements: fire, air, water, earth. Each has inherent motion (up: fire, air, down: water, earth) Elements subject to change
2. Motion of celestial bodies is circular
Assumptions:
1. Ffith element with inherent circular motion called aether
2. Because circular motion is unceasing and does not have an opposite (up and down), element must be divine, eternal, unchanging
What were the basic principles of Aristotle’s model incorporated Eudoxus’ model of concentric spheres? (8)
- heavens form a sphere (observation from Eudoxus)
- earth at center of spehere (Aristotle premise that earth and water inherent downward)
- earth at rest and spheres rotate around it (eudoxus)
- earth is a sphere (Aristotle first to explicitly state and support via proofs)
- size of earth in relation to heavens is minute (observation of no parallax)
- outermost sphere of fixed stars consists of aether (aristotle observation)
- within sphere are speheres of seven planets with moon loweset and closest to earth. the closer to earth the less pure eather is. all superlunary world is divine (aristotle inference)
- sublunary sphere, earth as we know it only has 4 elements subject to change (observation)
What were Eudoxus’ major contributions to the development of Greek astronomy?
- model of concentric spheres
- treatise Phaenomena: first comprehensive catalogue in Greek of constellations and stars with calendar for risings and settings
What does it mean to ‘save the appearances/phenomena’? Greek
Greek sozein ‘to save, preserve, maintain’
What is the origin of the phrase ‘save the appearances/phenomena’? and what evidence by who?
Found most frequently in simplicius’ commentary on Aristotle and works contemporary with Simplicius (6th CE), aready in use by Plutarch and Sosigenes by 2nd century. ALMOST ALWAYS IN REFERENCE TO EUDOXUS
What were Eudoxus’ two major astronomical works?
Two treatises:
1. Peri tachon (On Speeds): presented model of concentric spheres
2. Phaenomena: first comprehensive Greek catalog of stars and constellations with calendar for annual risings and settings
Greek etymology of phenomena?
Greek verb phainesthai ‘to appear’ (used as a technical term to descsribe movements of celestial body)
What are the two main sourcs of information for Eudoxus’ Phaenomena?
- Poem of Aratus (first half of 3rd century BCE) based on Eudoxus’ prose
- Commentary by Hipparchus (mid 2nd c BCE) on Eudoxus’ original and Aratus’ poem
Why is Phaenomena important?
Eudoxus collected all traditions about stars and constellations and organized them systematically, perhaps adding his own.
What were the major borrowings from Babylonian Traditions?
- Zodiac: set of constellations that lie along ecliptic
- Names of planets
What is the ecliptic?
circle in the celestial sphere defined by the apparent path the sun takes around the stars (lunar eclipses occur only when the moon intersects with this circle)
What Greek prhase is zodiac derived from?
Greek phrase: zōdiakos kyklos, ‘the little-animal circle’ (first
attested in the late 4 th c. BCE)
What is the greek/english meaning for eclipse?
Greek ekleipsis ‘failure to appear’
from verb ekleipein ‘to forsake, abandon’
How did Babylonian astronmer-priests divide the ecliptic?
Into 12 equal segments of 30 degrees each with each segment associated with a nearby constellation (first in Babylonian tablet dating to 464 BCE)
What evidence is there that there are extensive borrowings from Babylonian zodiac?
- figures of the greek zodiac are almost same as those of babylonian zodiac: bull (latin Taurus), Twins (gemini), crab (cancer), lion (leo), etc.
- distinctive representation of some signs. ex: archer (sagittarius) depicted as centaur with bow, ‘Goat-Horn’ (capricorn) depicted as hybrid goat-fish
What is strange about Eudoxus’ naming of planets?
Planets didn’t have much importance at first. Individual planets with specific deities (ex: hermes, aphrodite, ares, zeus, kronos) is first attested in late 4th c BCE.
- old Greek tradition was to identify celestial bodies as gods (helios sun, selene moon)
- odd group of deities (almost certain greek ‘translation’ of ancient babylonian associations of planets from own deities) ex: marduk, ruling god = zeus, nergal, the god of war = ares. later ‘translated’ to latin’
How many parts did Eudoxus divide sky into?
46
Modern researchers think Eudoxus was using a ___________ on which figures representing constellations were drawn.
star-globe, farnese ATLAS
Why is Phaenomena important?
- systematic arrangement of stars into constellations make it easier to identify individual stars
What is ‘bayer designation’?
system of naming constellations that goes back to Ptolemy and eudoxus. Developed by Johann Bayer (1603) Most stars visible to the
naked eye: a Greek or Latin letter followed by the Latin name of the constellation in the possessive case Ex: alpha of the Centaur
What is the importance of Aratus’ Phaenomena?
One of most popular poems in Graeco-Roman antiquity.
What the average educated person would have known about astronomy: the idea of the celestial sphere, with its main circles; the constellations, and the general dates of the annual risings and settings; no doubt also something about the planets and their movements.
arktikos
‘connected with the bear’ source of english ‘arctic’
Greek milk
gala
Milky circle
galaxias kyklos
tropic etymology
turning point
The equator (latin)
aequator ‘the one that makes equal’
isēmerinos kyklos, ‘equal-day circle’
latin equal
aequus
what is the only cluster of constellations based on greek myth?
andromeda and perseus group (invented by greek in 5th century bce)
What is the connection between consetllations and Greek myth?
Bears guarding infant Zeus, etc.
BUT: Myth is relatively unimportant in Aratus’ account of constellations
eccentric etymology
off-center
phaenomena etymology
appearances
anomaly etymology
inequality
The Farnese Atlas
a surviving example of an ancient star-globe, with figures representing the constellations
When is the helenistic period?
Period between the death of Alexander the Great and the reign of the first Roman emperor, Augustus, roughly 300 to 1 BCE
What were the three main points to the Eudoxan/Aristotelian Model?
- heavens consist of a series of spheres
- earth is at center of spheres
- earth at rest and spheres rotate around it
Who is Heraclides Ponticus?
Postulated: Heaven and stars at rest while earth moves about the poles of the equator from west to east with one revolution a day.
late 4th c BCE, studied with Plato in Athens
What were Aristarchus’s key points? Also, when was he active?
~279 BCE
1. Earth orbits sun (heliocentric theory)
2. sphere of fized stars are so distant that earth’s orbit has same ratio to it as center of sphere has to surface (addresses potential objection that lack of parallax between winter and summer proves earth doesn’t move)
What was Aristarchus’s second key point and why was it necessary?
Sphere of stars is so far away that the earth’s orbit has the same ration to it as center of sphere to surface of sphere of fixed stars.
Addresses the potential objection that the lack of observable parallax in the positions of the stars between the winter and summer solstices proves that the earth cannot move any significant distance.
hypothesis greek
to place under/ to suppose
Aristarchus main points!
- He accepted the hypothesis of Heraclides Ponticus that the earth turns on its axis.
- The philosopher Cleanthes thought that the Greeks should prosecute him for impiety.
- He proposed that the earth orbits around the sun.
- apparently no impact on dev of Greek astronomy
Eratosthenes contribution:
- Katasterismoi: catalogue of constellations, similar to that of Eudoxus and Aratus, which included a myth for every constellation to provide its back-story
- circumference of earth
Who was Eratosthenes?
3rd century BCE
- director of library of Alexandria (famous mathematician)
- major treatise on geography (orthogonal coordinates)
- poet
why is it important that Eratosthenes offers various interpretation sof individual constellations?
the figure came first and was only later identified with a myth. myth developed (becoming more important with increased dev of astronomy in hellenistic period)
What is the circumference of the earth?
angle difference / 360º = distance / circumference
Object covering the Sun exactly is ____ times its diameter away:
108
During a lunar eclipise, moon fits ____ times in Earth’s shadow
5/2
During a solar eclipse, moon-Earth distance is ___ moon diameters
108
When and why did astronomers give up on Eudoxus’ model?
Eudoxus’ model failed to ‘save the appearnaces’ (failed to explain observable celestial phenomena)
3rd and 2nd cent BCE
Anomaly
‘anomalous’ inequality
If sun moves at uniform speed in perfectly circular motion, seasons must be exactly equal. Who proved they are not?
Callippus.
Spring 94 days
Summer 92 days
Autumn 89 days
Winter 90 days
Descripe the eccentric hypothesis
The movement of the sun is perfectly regular, uniform, and circular, but the center of its orbit is slightly displaced from the earth, the assumed center of the cosmos. (the sun does not orbit exaclty the point of earth)
Apogee and perigee
apogee: point at which sun is at greatest distance from earth
Perigee: point where sun is closest to earth
Epicyclic hypothesis:
movement of the sun is also perfectly regular, uniform, and circular, but it does not orbit directly around the earth; instead, it orbits around a point that in turn orbits around the earth (an epicycle).
Epicyclic hypothesis, point k orbits earth in what direction?
counter clockwise
What is the deferent circle?
The orbit of point K (big circle)
What is the epicycle?
circle on a circle (the smaller circle on the deferent)
Why was the epicyclic model better at explaining planetary retrogradation?
Epicyclic model more effective and efficient. Requires only 2 uniform circular movements (planet on epicycle and deferent circle around the earth)
When was apollonius of perge alive?
240-170 BCE
When was Hipparchus of Nicaea alive?
161-128 BCE
Who was Apollonius of Perge
Treatise in 8 books on conic sections (ellipse, parabola, hyperbole)
primarily mathematician often ranked with Euclid as one of most brilliant mathematicians of ancient Greek world
What was apollonius first to demonstrate?
the mathetmatical equivalence of epicyclic and eccentric hypothesis. he helped develop the hypotheses.
What remaining Hipparchus works are there?
Commentary on Phaenomena of Eudoxus and Aratus where he corrects errors in positions of stars and dates
Why was Hipparchus a distinct figure in dev of Greek astronomy?
Shifted weight of astronomy from ‘save the apearances’ via geometric models to collection and analysis of data.
What were Hipparchus’ accomplishments?
- first effective catalogue of stars (850 stars) by place in constellation but also by comprehensive system of coordinates (mostly declinations= the star’s distance from the pole measured indegrees)
- precession of equinoxes (position of equinoctial points; where ecliptic intersects celestial sphere, do not remain constant but shift at rate of 20’’ of angle per year.
What enabled Hipparchus to make progress in the way that he did?
- Temperament (mathematical elegance was no substitute for failure to explain all the observable movements of the celestial bodies.)
- technological improvement ot instruments used for making precise observations
- historical devlpment
a. rapid dev of babylonian astronomy in 7th cen bce
b. political changes in late 4th c BCE that allowed for direct exchange of astronomical trad btwn babylonian and greeks
How do we know about Apollonius?
Although most of Apollonius of Perge’s mathematical treatise on conic sections survives, for his work on astronomy we depend mostly on comments made by Ptolemy in his Almagest
Who developed of the eccentric and epicyclic hypotheses?
Apollonius
What historical development enabled Greek astronomers of the later Hellenistic period to have more direct and immediate interactions with Babylonian astronomers?
The conquests of Alexander the Great, which brought Babylon under the rule of a Greek-speaking dynasty, meant that many Babylonian priests learned Greek
Ptolemy’s Almagest
the most comprehensive star-catalogue to date; it included more than 1,000 stars, which it located by means of a comprehensive system of orthogonal coordinates based on the ecliptic
Astronomy and astrology as two branches of the same science (who?)
Ptolemy
When was Ptolemy alive and kicking?
active 146-170 CE, wrote Almagest, the culmination of Greek mathematical astronomy
