A Planetary Pretzel


     “If one were to put all this together, and were at the same time to believe that the sun really moves through the zodiac in the space of a year, as Ptolemy and Tycho Brahe believed, he would then have to grant that the circuits of the three superior planets through the ethereal space, composed as they are of several motions, are real spirals, not (as before) in the manner of balled up yarn, with spirals set side by side, but more like the shape of pretzels, as in the following diagram.” (pp. 118-119)

     “This is the accurate depiction of the motions of the star Mars, which it traversed from the year 1580 until 1596, on the assumption that the earth stands still, as Ptolemy and Brahe would have it.  These motions, continued farther, would become unintelligibly intricate, for the continuation is boundless, never returning to its previous path.  Take note, too, that since the circle of Mars requires such a vast space, the spheres of the sun, Venus, Mercury, the moon, fire, air, water and earth, have to be included in the tiny little circle around the earth...
     “Copernicus, by attributing a single annual motion to the earth, entirely rids the planets of these extremely intricate spirals, leading the individual planets into their respective orbits, quite bare and very nearly circular.”
(pp. 119-120)