THE USE OF QUATERNIONS IN THE CALCULATION OF THE SUN’S APPARENT MOVEMENT ACCORDING TO MERCURY AND ITS COMPARISON WITH THE SUN’S APPARENT MOVEMENT ACCORDING TO EARTH

Deniz GÜÇLER

Abstract

In this paper, the apparent movement of the Sun according to Mercury has been studied and a comparison of this movement has been made with the apparent movement of the Sun according to Earth. The curve of the apparent movement of Mercury is obtained by using quaternions. To achieve this, the celestial sphere is accepted to have a radius of r = 1. The equatorial plane of Mercury is intercepted by its elliptical plane on axis X of the coordinate system. This system coincides with the equatorial coordinate system of Mercury. The apparent movement of the Sun according to Mercury is accepted to begin at point (1, 0, 0). The curve drawn by this point is calculated by using quaternions as rotation operators. For both the daily and yearly apparent movements of the Sun according to Mercury, a quaternion each is defined. These quaternions are used to produce rotation operators for each movement. Afterward, a comparison is made between this curve and the curve produced by the apparent movement of the Sun according to Earth. This paper, in which the discipline of mathematics joins that of astronomy, helps present the usefulness of quaternions as rotation operators and simultaneously helps new astronomers perceive the apparent movement of the Sun on other planets.

Pages: 347 - 355