Ptolemaic Model •  100AD Alexandria, Egypt – the Almagest •  Geocentric, uniform circular motion •  Planets carried around Earth on Crystalline Spheres •  Predicted Moon & Sun positions okay •  A few problems

Problem: Hipparchus 150BC •  21 March to 21 Sept not equal to 21 Sept to 21 March •  10+30Apr+31May+30Jun+31July+31Aug+21Sep=184 days •  9+31Oct+30Nov+31Dec+31Jan+28Feb+21Mar=181 days •  Sun/Earth moves too fast for half its orbit. Not uniform circular motion •  Earth placed off center of circle – Not Geocentric •  Planet/Sun has uniform circular motion as seen from Equant point

Inferior and Superior Planets •  Inferior –closer to Earth than Sun & tied to Earth-Sun line •  Superior –farther from Earth than the Sun

Problem: Planets Wander thru Stars •  Prograde=Direct Eastward motion of planets with respect to stars •  Retrograde=Backward Westward motion of Planets relative to stars •  Retrograde motion happens when planet is brightest & opposite sun

Ptolemy’s Explanation of Retrograde Motion

•  Deferent is the big circle •  Epicycle is small circle •  Preserves uniform circular

motion •  Planet closest to Earth and

thus brightest during retrograde

Retrograde Animation •  Planet travels on epicycle •  Epicycle travels on deferent

Ptolemy’s Planet Spacing •  Solar System had to be

big enough to keep planets from colliding

•  Venus and Mercury were tied to sunline

•  Needed 80 circles

Copernicus 1473-1543 •  Time of first printing press (~1450) •  Columbus discovers America showing

Ptolemy’s map incomplete •  Martin Luther&Reformation 1483-1546 •  Church administrator in Poland •  Wrote pamphlet on heliocentric system •  On death bed published the book

“nobody read” 1542

Copernican Revolution

•  Sun centered = Heliocentric •  Earth is –NOT- special •  Paradigm shift (Kuhn 1962) •  Much simpler scientific theory •  But he retained uniform

circular motion & epicycles •  Planetary tables were not a

great improvement

Retrograde According to Copernicus

Retrograde Motion in the Copernican System

Planetary Configurations

•  Inferior and superior planets •  Oppositions, conjunctions,

elongations, and quadratures •  Relative planet spacing from

the geometry •  Sine (Greatest Elongation) =

Orbital radius / Earth’s orbital radius

Retrograde motion is: a.  The apparent backward=westward motion of a

planet relative to stars as seen from Earth b.  Occurring at opposition to sun when the planet

is at its brightest c.  Explained by the Greeks by a system of

Deferents and Epicycles d.  Explained by Copernicus by the Earth lapping

the superior planets e.  All of these