When Copernicus transformed Earth-based observations to heliocentric coordinates,One volume of De Revolutionibus was devoted to a description of the trigonometry used to make the transformation between geocentric and heliocentric coordinates. he was confronted with an entirely new problem. The Sun-centered positions displayed a cyclical motion with respect to time but without retrograde loops in the case of the outer planets. In principle, the heliocentric motion was simpler but with new subtleties due to the yet-to-be-discovered elliptical shape of the orbits. Another complication was caused by a problem that Copernicus never solved: correctly accounting for the motion of the Earth in the coordinate transformation. In keeping with past practice, Copernicus used the deferent/epicycle model in his theory but his epicycles were small and were called "epicyclets".
When Copernicus transformed Earth-based observations to heliocentric, coordinates,One volume of De Revolutionibus was devoted to a description of the trigonometry used to make the transformation between geocentric and heliocentric coordinates. he was confronted with an entirely new problem. The Sun-centered positions displayed a cyclical motion with respect to time but without retrograde loops in the case of the outer planets. In principle the heliocentric motion was simpler but with new subtleties due to the yet-to-be-discovered elliptical shape of the orbits. Another complication was caused by a problem that Copernicus never solved: correctly account,ing for the motion of the Earth in the coordinate transformation. In keeping with past practice Copernicus used the deferent/epicycle model in his theory but his epicycles were small and were called "epicyclets".