Ptolemy and the Puzzle of the Planets

18 Pages·2005·1.19 MB·English

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 Alexandria Sunlight at
noon
α
Syrene
α
Alexandria to Syrene =
5000 stades (measured)
α= 1/50 circle (measured)
Earth
Thus, circumference =
250,000 stades!
Aristarchus on bisected Moon
(relative distances)
Measure α when Moon is
Moon
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 Dia = 6 3/4 Dia , Dia = 1/3 Dia
s e m e