## (Az,El) Coordinate System

This 2D coordinate system corresponds to the telescope azimuth and elevation axes. As noted in the previous section

• in the focal plane, the (Az,El) axes point towards those parts of the field which are at higher azimuth and elevation respectively

These axes should not be confused with the (Az,El) axes of rotation , which are the axes about which the telescope rotates. The Az axis of rotation is vertical and the El axis of rotation is horizontal and rotates as the telescope Az changes. If this document ever needs to refer to the axes of rotation, it will say so!

As can be seen from See Telescope coordinate systems looking towards sky (excludes Nasmyth foci) , the (Az,El) coordinate system is right-handed when looking towards the sky.

The (Az,El) coordinate system is really a spherical system. This document refers loosely to (Az,El) as tangent plane Cartesian coordinates. In the tangent plane coordinates, a given change in a star's El corresponds to the same change in the telescope's El. However, a given change in a star's Az corresponds to a change in the telescope's Az which is greater by a factor of 1/cos(El) (the details aren't important, but to see what is happening, consider a star near the zenith: a large change in telescope Az hardly moves the star).

For the purposes of this document, no distinction is drawn between the telescope (Az,El) coordinate system and the astrometric (Az,El) coordinate system. If the telescope were perfect, these two coordinate systems would be identical. However, the telescope axes are not precisely orthogonal to each other and the telescope is not perfectly horizontal. These errors are accounted for by the telescope pointing model. One practical result of the errors is that, while the parallactic angle (PARANG keyword) is the correct angle to rotate between North and the astrometric positive Elevation axis (astrometric vertical), it is not quite the correct angle to rotate between North and the telescope positive Elevation axis.