Copernican revolution in the complex plane

Starting from a simplified model of the Ptolemaic system in the complex plane, we show that Copernicus?? innovation did not merely consist of choosing a reference frame in which the planetary motions were simpler, but in finding the size of the planetary orbits expressed in what we now call astronomical units. In modern times a misleading appeal to relativity and a comparison only on the grounds of precision has led some to consider the Ptolemaic and the Copernican systems as basically equivalent. This erroneous point of view has resulted in the neglect of the main scientific content of the Copernican theory and has left Copernicus only to historians and philosophers of science. It is time to restore Copernicus to the teachers of physics as an incomparable opportunity to show the formidable power of theoretical investigation.