The Interpretation of the Apparent Motion of the Sun Through the Spherical Spiral

Authors : Deniz Güçler, Nejat Ekmekçi

Pages : 248-254

Doi:10.7212/karaelmasfen.1282168

View : 34 | Download : 47

Publication Date : 2023-12-29

Article Type : Research Paper

Abstract :This paper shows that the apparent motion of the Sun traces a spherical spiral in a limited section of the sphere. The rotation operator that produces the curve is in turn produced by a quaternion. The way the components of the quaternion correspond to the daily apparent motion of the Sun is shown. To achieve this, first, the spherical spiral formula is obtained using quaternions. It is known that the spherical spiral is a locus of a point P moving at constant angular speed ω along the meridian of a sphere while also rotating at constant angular speed cω around the polar axis where c > 2. Therefore, two rotations occur at the same time, and for each rotation, a quaternion can be defined. The directions of these quaternions form a 90° angle with each other. In this paper, it is shown that if this angle was 23° 27\' then the curve that would form would coincide with the apparent motion of the Sun. The product of these quaternions gives the quaternion which produces the rotation operator that forms this curve. Afterward, it is shown that the quaternion rotation angle converted in time units displays the time the Sun needs to move from one point to another. On the other hand, the rotational axis for small angles is the same as the axis of the equatorial plane. The importance of this work is twofold: it gives the science of astronomy a new perspective regarding the interpretation of the apparent motion of the Sun, and at the same time it is an important example of a work that shows the convenience that the use of quaternions brings to other fields of science.
Keywords : Küresel spiral, Kuaterniyonlar, Güneşin görünürdeki hareketi, Dönme hareketi