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Using the ancient notation
d : declination of star, -south +north
L : latitude of observer, -south +north
LHA : local hour angle of star, -east +west
Hc : altitude
Zn : azimuth
Hc = asin( sin(d) sin(L) + cos(d) cos(L) cos(LHA) )
Z = acos( (sin(d) - sin(L) sin(Hc)) / (cos(L) cos(Hc)) )
If sin(LHA) < 0 then Zn = Z else Zn = 360 - Z
Other ways to write formula but his gets signs right without having to think.
Images 1-3 show azimuth for three objects at differing declinations as observed from Melbourne
Max and min Zn (i.e. direction changes) when partial derivative of Zn wrt LHA is zero.
Messy to work out closed form solution. Easier numerically.
Image 4 shows maximum azimuth vs declination for Melbourne observer. Minimum = 360 - maximum.
Generating a plot or table of values takes four lines of code using Mathematica.
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