JCMT Pointing Model - Parameter 1

The amount by which the main azimuth drive is north of the vertical.

In the following diagram :

N and W show north and west,
Z is the zenith
P is the pole of the azimuth drive, tilted north by theta from Z
S is a star at true (azimuth,elevation) = (A,E), while w.r.t. P, S is at (A',E'), i.e.
SA = E, SA' = E', SZ = 90-E, SP = 90-E'.
( Azimuth at the JCMT is measured from North through East, South and West).

Then in the triangle SAA', where angle ASA' = e,
sin(AA')/sin(e) = sin(E')/sin(90) , i.e.
sin(AA') = sin(E')sin(e) .

In triangle SZP,
sin(e)/sin(theta) = sin(SZP)/sin(SP) = sin(360-A)/cos(E') , so
sin(AA') = - sin(A)tan(E')sin(theta), which, for small theta, and on the sky, is
daz = - theta*sin(A)*sin(E')

Also in triangle SZP, if the arc SP is dropped onto SZ at B, then ZB is the change in elevation = theta*cos(SZP) = theta*cos(360-A) = theta*cos(A).

Thanks to Kiran Gothe of the Indian Astronomical Observatory for pointing out an error in a previous version of these derivations.