SOLAR DECLINATION,d

Declination is the angular distance of the sun north or south of the earth's equator.

The earth's equator is tilted 23.45 degrees with respect to the plane of the earth's orbit around the sun, so at various times during the year, as the earth orbits the sun, declination varies from 23.45 degrees north to 23.45 degrees south.

This gives rise to the seasons. Around December 21, the northern hemisphere of the earth is tilted 23.45 degrees away from the sun, which is the winter solstice for the northern hemisphere and the summer solstice for the southern hemisphere. Around June 21, the southern hemisphere is tilted 23.45 degrees away from the sun, which is the summer solstice for the northern hemisphere and winter solstice for the southern hemisphere. On March 21 and September 21 are the fall and spring equinoxes when the sun is passing directly over the equator. Note that the tropics of cancer and capricorn mark the maximum declination of the sun in each hemisphere.

Declination is calculated with the following approximate equation from Cooper (1969):

d  = 23.45 * sin [360 / 365 * (284 + N)]

where

d  = declination

Reference: Cooper, P.I., Solar Energy, 12, 3 (1969). "The Absorption of Solar Radiation in Solar Stills."
See also: Duffie, John A., Beckman, William A., Solar Energy Thermal Processes John Wiley & Sons. 1974.

For those interested, a much more accurate (and more complex) formula for declination is given below:

Please contact me if there are errors or areas that need more elaboration. Hope this helps.