# Math Tutorials and Moreby George

## Math Tutorials and Moreby George

### Copernicus (1473–1543)

Nicolas Copernicus was a Polish mathematician and astronomer who served as Canon (an administrative position) for the church in Frauenberg. In the early 1500s he developed a sun-centered model that was the first real challenge to the long accepted model of Aristotle and Ptolemy. His major work was called Revolutions of the Celestial Spheres which was published just before his death in 1543. A Lutheran Minister Andrew Osiander handled the publication and inserted a preface without Copernicus' knowledge. In this preface he wrote that Copernicus was merely offering a hypothesis, not a true account of the workings of the heavens. Although this clearly did not represent Copernicus' viewpoint, it probably protected this work from close scrutiny by the church. Copernicus' model offered the advantages that it didn't need epicycles in order to produce retrograde movement and it didn't need an equant point in order to produce non-uniform motion. However, epicycles were added in order to obtain accurate predictions. The accuracy of his model was good, but it was no better than Ptolemy's model. As far as complexity, Copernicus' model was at least as complex as Ptolemy's model. Figure 5 shows Copernicus' model for Mars. The models for Jupiter and Saturn were similar to that of Mars, but the models for Venus and Mercury were even more complex.

In this model Mars follows a circular path around the point A. The point A follows a circular path around the point B. The point B also moves, but always stays in the same position relative to the point C. The point C is the center of the circular path followed by the Earth (not shown). C follows a circular path around the point D which in turn follows a circular path around the Sun. As with Ptolemy's model, Copernicus assumed that the points moved around their circular paths at a constant speed. In the years that followed, a number of astronomers used Copernicus' model to make predictions. However, most viewed his model as a computational tool and not a representation of reality.