sentences:  Although he had circulated an outline of his own heliocentric theory to colleagues sometime before 1514, he did not decide to publish it until he was urged to do so late in his life by his pupil Rheticus.Copernicus's challenge was to present a practical alternative to the Ptolemaic model by more elegantly and accurately determining the length of a solar year while preserving the metaphysical implications of a mathematically ordered cosmos.Thus, his heliocentric model retained several of the Ptolemaic elements, causing inaccuracies such as the planets' circular orbits, epicycles, and uniform speeds, while at the same time introducing such innovative ideas as