385L37.

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Presentation transcript:

385L37

Ptolemaic Contributions • consolidation of earlier models/theories • extension and refinement of Hipparchan trigonometrics • refinement of armillary sphere • data-driven expansion of model • epi-epicycles • mobile eccentricity • equant orbit

Armillary Sphere • Eratosthenes credited with invention; developments by Hipparchus and Ptolemy • geocentric model • rings represent equator, ecliptic, celestial latitudes and longitudes • plots solar and stellar positions and angles • observational instrumentation

Retrogression • exact speed of retrogression varies over time • length of retrograde loops varies : shorter (fast) vs. longer (slow)

Epicycle & Eccentric • epicycle predicts only uniform retrograde loops • eccentric predicts regular changes in angular velocity • eccentric + epicycle predicts irregular seasonal lengths • neither predicts both position and speed of retrogression

Ptolemaic Modifications • re-arrangement of existing models: epi-epicycles • new combinations of models : mobile eccentrics • equant orbits

epi-epicycle (Ptolemy)

Mobile Eccentric (Ptolemy) planet (P) on epicycle orbiting point (C) on deferent point (C) orbiting point (G) on epicycle point (G) orbiting eccentric point (F), where E = Earth

equant (Ptolemy)

Uniform, Eccentric, Equant Orbits

Eccentric, Equant, Retrogression

BODY EUDOXOS KALLIPPOS ARISTOTLE PTOLEMY Moon 3 5 Sun 6 Planets 20 23 44 68+ Stars 1 TOTAL 27 34 56 80+

Astronomical Premises 1 sphericity of universe and all celestial objects 2 circularity of all celestial motion 3 perpetual nature of all celestial motion 4 uniformity of all celestial motion 5 uniformity of celestial position/place 6 geocentricity 7 stationary Earth 8 rotation of celestial sphere

• Eudoxan spheres consistent with all premises • epicyclic model violates uniform place (5) premise • eccentric and equant models violate circular (2) and geocentric (6) premises

Ptolemaic Universe http://www.youtube.com/watch?v=EpSy0Lkm3zM

Ptolemaic Contributions • consolidation of previous models • rigorous mathematization, esp. measurement of angular velocities • enhanced predictability of celestial events (star tables, ephemerides, navigational charts) • reduction (NOT elimination) of some contrary observational data, creation of new contradictories • triumph as mathematical model of universe, failure as astronomical model • skewing of physical astronomy (Aristotle) and mathematical/technical astronomy (Ptolemy)

Mathêmatikê Syntaxis [Mathematical Compilation] (ca. 150 CE)  Megistê Syntaxis [Greatest Compilation]  Arabic Al-magest [The Greatest {Book}] (9th century)  Latin Almagest (12th century)  Copernicus (1473-1543)