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Is there an accurate algorithm / method to determine the precise time of day/night when the sun is X degrees above (or below) the horizon for a given latitude Y at date Z?

Is this the same question here? Reverse Sun position algorithm? I'm having a hard time plugging in specifics.

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First, you need to know the Right Ascension and Declination of the Sun on that day. Then there are some angular relations connecting all of these. Everything is available in the RASC Observer's Handbook. Another way would be to interpolate the table produced by this program provided by the US Naval Observatory: http://aa.usno.navy.mil/data/docs/AltAz.php Hope this helps!

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