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Ptolemy and the Puzzle of the Planets 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 signs Based on linear zig-zag functions NO 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 loops have 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 planetary motion (-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 distances Absolute Sun- Moon sizes Hipparchus (c. -130) 850 stellar positions (long. and lat.) Precession of equinoxes Constructed lunar & solar models Eratosthenes on the circumference of the Earth Assumes: --Spherical earth --Incoming solar rays are parallel --Euclidean geometry Sunlight at noon Alexandria α α Earth Syrene Alexandria to Syrene = 5000 stades (measured) α= 1/50 circle (measured) Thus, circumference = 250,000 stades! Aristarchus on bisected Moon (relative distances) Moon Measure α when Moon is exactly at quarter If α = 87°, ES/EM = 19 Sun α Earth Aristarchus on lunar eclipses (relative sizes) Moon Earth Sun Measure length of time Moon remains in shadow Finds Dias = 6 3/4 Diae, Diam = 1/3 Diae Hipparchus’s armillary sphere Latitude (β) Longitude (λ) Apollonius’ models (c. -200) Planet slower α Center Earth Earth faster Eccentric (off-center Earth) model Epicycle model (both equivalent, but anti-Aristotlian!) Ptolemy (ca. +100 - 170) Alexandria in Egypt Works on Geography, Optics, Harmonica, and in astronomy/astrology: Tetrabiblos Handy Tables Planetary Hypotheses Mathematical 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 original contribution) Result: Add ca. 20 numbers and get λ, β Superior planetary model Observed planetary position Epicycle Center of Uniform motion Planet α Equant Earth Deferent (roughly in plane of ecliptic) 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! Mercury Earth Sun Venus Mars Jupiter Conclusions re Ptolemy Defines mathematical astronomy until 1600 Contrasts with physical cosmology of Aristotle & Eudoxus (concentric spheres) Successfully “saves the phenomena” with circles Cheating on Plato (uniform circular motion) creates major research problem for medieval Islamic astronomers