Find The Declination Of The Sun

Find the declination of the sun as it rises and bears 115° 11' at Lat 42° 27' N.

Given:

Azimuth = 115° 11'
Latitude = 42° 27' N

What is asked?

Declination of the sun

Solution:

1. Solve for the amplitude.

                  Azimuth = 115° 11'
                                 -  90°          
               Amplitude = E 25° 11' S

2. With the answer in step 1, we can now solve for the declination.

         Sin Amplitude = Sin Declination
                                   Cos Latitude   (cross-multiply to derive formula for declination)   

        Sin Declination = Sin Amplitude x Cos Latitude
                               = Sin 25° 11' x Cos 42° 27'
                               = 0.42552 x 0.73787
        Sin Declination = 0.31398
              Declination = 0.31398 inv Sin
                               = 18.3 South is the declination

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