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CHAPTER  2
                              Orbital Principles






                        Around 350 B.C.,  the renowned Greek philosopher Aristotle made the
                      deduction that was to influence man’s perception and understanding of the
                      motions of the planets for over two thousand years! Aristotle was of  the
                      opinion that  all  the  heavenly bodies,  including the  sun, the  wanderers
                      (planets), and the stars, were in circular motion about a fixed and unmov-
                      ing Earth. So authoritative was Aristotle that the Catholic church later
                      accepted this view as its official doctrine on the matter and used its reli-
                      gious influence to enforce this position. As a direct result, Galileo was
                      arrested for espousing views to the contrary in  1600 A.D.!  However, a
                      century before Galileo, the first serious questioning of Aristotle’s views
                      had already begun.
                        Astronomy (or rather astrology) was very popular at the time of Coper-
                      nicus,  around  1500 A.D.,  and  the  inability to  accurately describe the
                      motions of the heavenly bodies increased efforts to find a better explana-
                      tion than Aristotle’s. Copernicus was both an astronomer and mathemati-
                      cian,  and  he  used  the  observed  angular  positions  of  the  planets  and
                      trigonometry to correctly place the solar system in its proper order, with
                      the  sun at the center and the earth as just  another wanderer in motion
                      about the sun like the other planets. However, the idea of a moving earth
                      and similarity with the other planets was quite radical at the  time and
                      made his heliocentric (sun-centered) hypothesis hard to accept.
                        For instance, Tycho Brahe, the late sixteenth-century astronomer, com-
                      pletely rejected the notion. Tycho, in the years prior to his death in 1601,
                      conducted the most exhaustive and accurate recording of the movements
                      of the planets to date. He was sure that his data held the secret to the mys-
                      tery of planetary movements, but his mathematical ability was too poor to
                      check out his theories. Therefore, Tycho solicited the assistance of math-
                      ematicians like Johannes Kepler.
                        After Tycho’s death, Kepler came into possession of most of  the obser-
                      vational records kept over the many years. Kepler believed in the Coperni-



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