consolidation of earlier modelstheories extension and refinement of Hipparchan trigonometrics refinement of armillary sphere datadriven expansion of model epi epicycles ID: 695044
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Slide1
385L37Slide2
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 Slide3
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 positionsand angles• observational instrumentationSlide4
Retrogression
• exact speed of retrogression varies over time
• length of retrograde loops varies : shorter (fast) vs. longer (slow)Slide5
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 retrogressionSlide6
Ptolemaic Modifications
• re-arrangement of existing models: epi-epicycles
• new combinations of models : mobile eccentrics
• equant orbitsSlide7
epi-epicycle
(Ptolemy)Slide8
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 = EarthSlide9
equant
(Ptolemy)Slide10
Uniform, Eccentric,
Equant
OrbitsSlide11
Eccentric, Equant, RetrogressionSlide12
BODY
EUDOXOS
KALLIPPOS
ARISTOTLEPTOLEMYMoon3555Sun
3
5
6
6
Planets
20
23
44
68+
Stars
1
1
1
1
TOTAL
27
34
56
80+Slide13
Astronomical Premises
1
sphericity
of universe and all celestial objects2 circularity of all celestial motion3 perpetual nature of all celestial motion4 uniformity of all celestial motion5 uniformity of celestial position/place6 geocentricity7 stationary Earth8 rotation of celestial sphereSlide14
•
Eudoxan
spheres consistent with all premises
• epicyclic model violates uniform place (5) premise• eccentric and equant models violate circular (2) and geocentric (6) premisesSlide15
Ptolemaic Universe
http://
www.youtube.com
/watch?v=EpSy0Lkm3zMSlide16
Ptolemaic Contributions
• consolidation of previous models
• rigorous
mathematization, esp.measurement of angular velocities• enhanced predictability of celestialevents (star tables, ephemerides,navigational charts)• reduction (NOT elimination) ofsome contrary observational data,creation of new contradictories• triumph as mathematical modelof universe, failure as astronomicalmodel• skewing of physical astronomy
(Aristotle) and mathematical/technical
astronomy (Ptolemy)Slide17
Mathêmatikê
Syntaxis
[Mathematical Compilation] (ca. 150 CE) Megistê Syntaxis [Greatest Compilation] Arabic Al-magest
[
The Greatest
{
Book
}]
(9
th
century) Latin
Almagest
(12
th
century) Copernicus
(1473-1543)