ABSTRACT
This chapter considers several rules from transforming coordinates from one system to another. Two techniques will be used, that of matrix rotation and that of 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, for example, in passing from the geocentric to the heliocentric coordinates of a comet. The inverse transformation is obtained by interchanging the role of (x, y, z) with (X, Y, Z), paying attention to maintain the positive sense on the angles. Spherical trigonometry is the second method of transformation. It gives the elements necessary to carry out the transformation between equatorial and ecliptic coordinates. The legislation of several countries refer to the start and end of the civil night for obligations such as switching on and off the road lamps, the car lights, etc.
