Re: Query about solar azimuth formula

["Paul Camp" <pjcamp@coastal.edu>]

I hasten to remind that this is not my calculation. It is, as 
previously noted, taken from Peter Duffet-Smith's book Practical 
Astronomy With Your Calculator. 

Your observation is correct but recall that the calculation involves 
not the azimuth but the cosine of the azimuth. You have to exercise 
some judgement to put it in the right quadrant.

Everybody not into gory details can stop here. The following is a 
specific example. Find the altitude and azimuth of a star whose 
hour angle is 5h 51m 44s and declination is +23 degrees 13' 10". Your 
latitude is 52 degrees north.

H in decimal hours: 5.862222 hours
Convert H to degrees (x15): 87.933333
Convert D to decimal degrees: 23.219444
Find sin A: 0.331080
Find A (inverse sine): 19.334345 degrees
Find cos B: 0.229558
Find B (inverse cosine): 76.728973
Find sin H: 0.999350
  If negative, true azimuth is B
  If positive, true azimuth is 360-B
Find true azimuth: 283.271027 degrees

Finding sin H tells you whether the star has gone passt the local 
meridian or not and so which of the two possible azimuths is correct.


> Paul's hour angle explicitly enters the calculation of Sun Altitude.
> Sun Altitude enters his azimuth calculation.
>
> The Sun has the same altitude at two azimuths, except at local noon,
> so I fancy Paul's azimuth calculation is in error.
>  But I could be corrected by even a single worked counter-example.
> Say latitude N45 deg, t=14 hours, declination = 0?
>
> Humbly
> Brian
>
> At 14:26 11/7/97 EST, you wrote:
> > That would be accounted for by the hour angle of the Sun.
> >
> > > I see that Paul's Sun Altitude agrees with Margaret's.
> > > But his Sun Azimuth does not account for time of day.
> > > Perhaps a term is missing?
> > >
> > > Brian
> > >
> > > At 10:05 11/3/97 EST, Paul Camp wrote:
> > > > This is the coordinate system transformation taken from Peter 
> > > > Duffet-Smith's book Practical Astronomy with your Calculator. To go 
> > > > from equatorial to horizon coordinates:
> > > >
> > > > sinA = sinD sinL + cosD cosL cosh
> > > > cosB = (sinD - sinL sinA)/(cosL cosA
> > > >
> > > > This gives you both solar altitude and solar azimuth (I think I 
> > > > translated from Duffet-Smith's notation correctly)
> > > >
> > > > > Paul J. Camp 
> > >
> > > [Margaret]
> > >  calculate A from -
> > > > >         sinA = sinLsinD + cosLcosDcosh
> > > > >
> > > > > where   L = latitude of observer
> > > > >         D = solar declination
> > > > >         h = solar hour angle = (t-12) x pi/12  (in radians)
> > > > >         and t = mean solar time in hours.
>
> brian whatcott <inet@intellisys.net>
> Altus OK

Paul J. Camp                   "The Beauty of the Universe
Assistant Professor of Physics  consists not only of unity
Coastal Carolina University     in variety but also of 
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