They are not necessarily standard but are adopted for convenience and will be followed consistently. The final section gives some thoughts at calculating other co-ordinates systems. Bold face letters indicate vectors and normal letters indicate scalars. A subscript to the unit vectors indicate the co-ordinate system to which they belong. In both systems, azimuth angles are measured counter-clockwise from x g when looking down along the z g axis and elevation angles are measured from the xy plane.
Elevation angles are positive when the angle is measured above the xy plane.
Some of their properties are described in the next paragraphs. A dot product will be indicated by a superscripted period. This definition arises from the definition of the dot products of unit vectors. The dot product of a unit vector and a vector gives the component of the vector in the direction of the vector. The three unit vectors, x g , y g , and z g are expressed in equatorial co-ordinates and then the dot products of each unit vector and the vector are taken.