ptolemy and the puzzle of the planets - dartmouth collegeastro4/lectures/lecture5.pdf · 850...
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Ptolemy and the Puzzle of thePlanets
Puzzle of “wandering stars” Irregular speeds through sky Move W to E, roughly along ecliptic Retrograde from E to W, varying loops
(not the major luminaries) Changing brightness Maximal elongations for Mercury (28°)
and Venus (47°)
Babylonians on the planets Earliest known planetary observations Venus tablet (-1760)
Dates of appearances/disappearances
Predictive planet astrology (-300)Lists of dates for oppositions, entry into
zodiacal signsBased on linear zig-zag functionsNO geometrical model or explanatory
(structural) theory
Plato’s legacy ‘Save the phenomena’ quantitatively Only uniform, circular motion Crystalline spheres, concentric to the
Earth at the center of the cosmos Spheres may have tilted axes
Eudoxus’s hippopede (all retrograde loopshave fixed shape and size)
Aristotle’s legacy Celestial/terrestrial realms Aether and circular motion in heavens Heavy earth at center of cosmos Plenum cosmos of 56 spheres Physical rather than quantitative or
predictive model
Task of lecture Greek measurements of the cosmos Apollonius’s invention of non-Platonic
mathematical models for planetarymotion (-200)
Ptolemy’s mathematical models,influential for 1400 years (+150)
Measuring the cosmos Eratosthenes (c. -270, Alexandria)
Circumference of the Earth
Aristarchus (c. -290)Relative Sun - Moon distancesAbsolute Sun- Moon sizes
Hipparchus (c. -130)850 stellar positions (long. and lat.)Precession of equinoxesConstructed lunar & solar models
Eratosthenes on thecircumference of the Earth
Sunlight atnoon
Syrene
Alexandria
α
α
Alexandria to Syrene =5000 stades (measured)α= 1/50 circle (measured)
Thus, circumference =250,000 stades!
Earth
Assumes:--Spherical earth--Incoming solar raysare parallel--Euclidean geometry
Aristarchus on bisected Moon(relative distances)
Moon
Earth
Sun
Measure α when Moon isexactly at quarterIf α = 87°, ES/EM = 19
α
Aristarchus on lunar eclipses(relative sizes)
Moon
Earth
Sun
Measure length of time Moon remains in shadowFinds Dias = 6 3/4 Diae, Diam = 1/3 Diae
Hipparchus’s armillary sphere
Longitude (λ)Latitude (β)
Apollonius’ models (c. -200)
Earth
Planet
Eccentric (off-centerEarth) model
α
slower
fasterEpicycle model(both equivalent, butanti-Aristotlian!)
Earth
Center
Ptolemy (ca. +100 - 170) Alexandria in Egypt Works on Geography, Optics, Harmonica,
and in astronomy/astrology: TetrabiblosHandy TablesPlanetary HypothesesMathematical syntaxis (compilation) = “The
Greatest” = Almagest
Models of the Almagest Seven predictive, quantitative, independent
models for 5 planets, Sun & Moon Eccentric (saves unequal speeds) from Apollonius Epicycle (saves retrograde motion, brightness) Equant (saves varying retro loops) - NEW Central cranks for Mercury and Moon - NEW Methods for determining parameters from
selected observations (Ptolemy’s most originalcontribution)
Result: Add ca. 20 numbers and get λ, β
Superior planetary model
Earth
Equant
Deferent (roughly in plane of ecliptic)
Epicycle
Planet
Observed planetary position
α
Center of Uniformmotion
Evaluation of Ptolemy models Violates uniform motion (equant) Violates concentric spheres (epicycle) Saves all known phenomena
but creates problem for lunar sizes! Predicts positions to ± 1° accuracy No absolute distances, physical status of the
circles remains ambiguous Unexplained dependency of models on solar
position
Unexplained links to Sun!
Venus
Mercury Sun
Earth
JupiterMars
Conclusions re Ptolemy Defines mathematical astronomy until 1600
Contrasts with physical cosmology of Aristotle &Eudoxus (concentric spheres)
Successfully “saves the phenomena” withcircles
Cheating on Plato (uniform circular motion)creates major research problem for medievalIslamic astronomers