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Early in 2015, James Morrison helped me with some formulae for calculating the
sun's altitude when given the azimuth, declination, and latitude. I'm stuck at
the last step. Here's what he wrote:
The procedure is:
1. Calculate the sun's altitude when the declination is zero: tan h0 = cos A /
tan phi
2. Calculate an auxiliary angle x from: sin x = (cos h0 sin d) / sin phi
3. Calculate sun's altitude, h, for the azimuth and declination from:
If A < 90, h = x + h0
If A > 90, h = x - h0
NOTE:
h = altitude
A = azimuth
d = solar declination
phi = latitude
The same procedures are described in his astrolabe book on pages 262-263, where
he also includes a proof.
I'm puzzled by step #3.
I assume that the azimuth at noon is 180 degrees which would make 90 degrees
due east. Why would there be mathematical symmetry around a 90 degree azimuth?
I would expect symmetry around noon when A is 180 degrees.
Can anyone explain the logic here for me?
Thank you all very much,
John
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