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What you need to calculate is the amplitude of the sun.  Amplitude
is the true bearing of a rising or setting body measured north or south
of due east or due west.

The formula is

    Sin(Amplitude) = Sin(Declination)/Cos(Latitude)

Amplitude is north for north declination and south for south declination.

For example: if the sun's amplitude is 10.2 degrees north and your
latitude is 40 degrees north then the amplitude is 13.4 degrees north.
This means the sun will rise with true bearing 90-13.4 or 76.6 degrees.
Likewise, the sun will set with true bearing 270+13.4 or 283.4 degrees.

If the moon's declination is 7.75 degrees south and your latitude is
20 degrees south, the amplitude is -8.2 degrees or 8.2 degrees south.
This gets tricky.  Since the declination is south, the moon rises
at 90 - Amplitude degrees.  The amplitude is -8.2 so the bearing
is 90 - -8.2 = 90+8.2 = 98.2 degrees.  The moon will set at
270 + -8.2 or at 261.8 degrees.  This happens on September 7 of this
year.

South declination always results in the phenomenon occurring south of
due east or west.  When the declination of the body is north, it rises
and sets north of due east or due west.

Good luck adjusting your compass.

   

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