KEPLER'S  ELLIPSE  &  AREA  'LAWS'
Professor Robert A. Hatch  -  University of Florida

 



 
 

Kepler devised his first two 'calculational rules' for planetary motion during the years 1601 - 1605 and published them in his New Astronomy (Astronomia nova) in 1609.  What has come to be known as Kepler's first law of planetary motion states that planets move on an elliptical orbit with the sun at one focus of the ellipse.  The so-called second law states that a radius vector drawn from that focus (the geometrical and physical center of the sun) to any point in the orbit will sweep out equal areas in equal times.  Kepler's area law (equal areas in equal times) should not be confused with Claudius Ptolemy's equant principle, that is, the center of a planetary epicycle sweeps out equal angles in equal times.  Ptolemy's long-standing dominance in the history of astronomy was due in large measure to his belief that the distance between the eccentric earth and the equant point was bisected.  In retrospect, we now know that Ptolemy's use of the bisection of the eccentricity was a good practical approximation to the two foci of a Keplerian ellipse. 

  
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