Obtaining the Parametric Equation of the Curve of the Sun’s Apparent Movement by Using Quaternions

The purpose of this article is to express the daily and yearly apparent movement of the Sun in the same curve by using quaternions as a rotation operator. To achieve this, the daily and yearly apparent movement of the Sun, the algebraical structure of quaternions and how quaternions work as rotation operators has been examined. For each of the apparent movements of the Sun, a quaternion that will work as a rotation operator has been determined. Afterwards, these two rotation operators have been applied to the vector that is found between point (0,0,0) and the accepted starting point of the apparent movement of the Sun. As a result, a curve on a sphere is obtained. The importance of this study is to emphasize the use of quaternions in other areas of study and to provide the science of astronomy a new outlook with regards to expressing the apparent movement of the Sun.