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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 motio 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