Daylight Hours & Solar Geometry

Latitude, day of the year and the sunrise and sunset you read off a clock, turned into day length, solar noon, noon sun elevation and solar declination, each checked against the NOAA solar-position series.

ScienceSolarDeclinationDaylightNoaa
Daylight Hours & Solar Geometry screenshot

Enter a latitude, a day of the year and the sunrise and sunset times you read off a clock, and the page works out the day length, the solar noon, how high the sun actually gets at noon, and the solar declination behind all of it. Each number is checked against the NOAA solar-position series rather than a lookup table.

Sun geometry
Day length from the times you entered
NOAA geometric check
Declination uses the NOAA solar-position series (0.006918 - 0.399912 cos g + 0.070257 sin g - 0.006758 cos 2g + 0.000907 sin 2g - 0.002697 cos 3g + 0.00148 sin 3g, g = 2pi(d-1)/365). Noon elevation is 90 - |latitude - declination|. The geometric day length uses hour angle 2 acos(-tan lat tan decl) / 15. Real refraction and the solar disc radius move the observed sunrise a few minutes either side of that.
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