ABSTRACT
In this chapter, the authors consider several rules for transforming coordinates from one system to another. Two techniques will be used: matrix rotation and spherical trigonometry. In the majority of cases, the transformations will be rigid rotations around the origin. In other cases, a translation of origin must be added, e.g., in passing from the geocentric to the heliocentric coordinates of a comet. Later on, they encounter phenomena that give rise to slight distortions of the celestial sphere, such as the aberration and the gravitational deflection of light. In modern telescopes, sophisticated pointing algorithms take into account refraction and several other factors here neglected, including flexures of the structure and misalignments of the optics.
