Ch 04-02 The Ptolemaic and Copernican Systems

• The Ptolemaic system ( ~ 140 AD )
  
  
   
• The Copernican system (Copernicus, 1473 ~ 1543)
  
  
   
  This system is still with a uniform circular motion and about 2^◦ errors in prediction like the Ptolemaic system,
  but is "simpler" and able to determine periods and distances of planets.
  
   
  • Sidereal and synodic periods
    
    
     
    for inferior planets
    for superior planets
    
    P: sidereal period of the planet
    E: sidereal period of the Earth (measurable)
    S: synodic period of the planet (measurable)
     
    (This can be understood by considering f_syn = f_inner - f_outer .)
     
  • Distance estimate for planets
    
    
     
    α is the greatest elongation of the inferior planet.
    β can be known by measuring the time interval represented by the blue and red arcs with arrows, given the period of the superior planet.