Astronomy - Basic Concepts - Retrograde Motion - Geocentric - Ptolemy - -  Scientific Revolution - Professor Robert A. Hatch
RETROGRADE  MOTION  -  GEOCENTRIC
Dr Robert A. Hatch  -  University of Florida


The animated illustration above represents retrograde motion from a geocentric (earth - centered) perspective.  Here the earth is depicted in the center of a planetary orbit, for example Mars.  Because the earth is assumed to be fixed and stable in the center of the cosmos (geocentric and geostatic), and further, all heavenly bodies are assumed to move around the central earth, some device was needed to describe the apparent retrograde loop that planets make when in opposition to the sun.  To account for the apparent backward looping of the planet, Claudius Ptolemy (fl. 140 AD) devised a very elegant geometrical construction to describe this motion.  His model involved a large circle (deferent) and a second smaller circle (epicycle) on which the planet moved.  The result was that the planet moved with a double motion.  Specifically, the planet moved with uniform angular speed around the center of the epicycle, and in turn, the center of the epicycle moved with uniform angular speed around the equant point.  The equant point, by definition, was an imaginary point situated near the earth.  Its exact position varied from planet to planet.  In each case its location was determined by observation and calculation.  The result was a simple and accurate description of planetary motion.  But theory aside, what would you see?  Viewed from earth, the planet would appear to undergo a 'looping' retrograde motion against the backdrop of the 'fixed stars.'  To all appearances, the planet would move in its direct order, gradually slow down and finally appear to stop (stationary point one).  The planet would then appear to reverse its direction (undergo retrograde).  After reversing direction the planet would again slow down and appear to stop a second time (stationary point two).  Finally, the planet it would reverse direction a second time and continue to move its original direction.  In sum, from a geocentric perspective, retrograde motion was one of the major astronomical problems requiring attention in order to 'save the appearances.'  To this end, Ptolemy's model was unsurpassed for simplicity, accuracy, and elegance until Copernicus some 1400 years later.

 
But a footnote is perhaps in order.  Copernicus' cosmological contribution was not without a certain irony.  Celebrated for having put the earth in motion about the sun, Copernicus roundly rejected Ptolemy's equant point as inelegant and contrary to Plato's Dictum.  Driven by empirical evidence, Ptolemy was indeed forced to introduce the now infamous equant point and thereby abandon Plato's Dictum.  By tradition at least, Plato's Dictum held that planetary appearances were to be accounted for by means of uniform circular motion (or compounded uniform circular motion) around a central point.  Copernicus boldly followed tradition in rejecting Ptolemy on this point.  But the Copernican Achievement, at least in retrospect,  had a planetary down side.  To be sure, Copernicus' model explained away the 'sun-linked' motions of Mercury and Venus, just as it accounted for the periodic uniformities in each element of Ptolemy's model (one earth year).  And most importantly, for present purposes, the Copernican system explained away retrograde motion, it was not a real motion, Copernicus argued, but an illusion resulting from the very structure of the planetary system.  But less celebrated consequences were pointed out by later 'Copernicans' (notably Kepler and Boulliau).  While the specific model proposed by Nicolas Copernicus was ingenious from a cosmological perspective, it was quite useless in describing the more subtle motions of the 'elliptical way.'  Arguably (to end animated pedagogy with a scholarly suggestion) Copernicus represents a retrograde step for geometrical astronomy.

 
Here I wish to acknowledge my debt to J-B Delambre.  I have imitated his rhetorical flourishes, just for fun, but I have inverted most of his conclusions.  No offense is intended. Afterall, Jean-Baptiste needs no defense.  He was a brilliant historian and astronomer.  His Greek, however, was not so good as he sometimes hoped, his foot and meter not always so certain.  To compare his interpretations of Copernicus, Kepler, and Boulliau, See:  Histoire de l'astronomie moderne, T. 1-2 Paris 1821, reprint 1969 New York & London.

  
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