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