## Solar Declination Angle

The declination of the sun is the angle between the equator and a line drawn from the center of the Earth to the center of the sun. The declination angle, denoted by δ, varies seasonally due to the tilt of the Earth on its axis of rotation and the rotation of the Earth around the sun. If the Earth were not tilted on its axis of rotation, the declination would always be 0°. However, the Earth is tilted by 23.45° and the declination angle varies plus or minus this amount. Only at the spring and fall equinoxes is the declination angle equal to 0°.

Fig.1. Solar declination angle.

Despite the fact that the Earth revolves around the sun, it is simpler to think of the sun revolving around a stationary Earth. This requires a coordinate transformation. Under this alternative coordinate system, the sun moves around the Earth.

The declination angle δ can be calculated by the following equation:

δ = 23.45° sin[

^{360}⁄

_{365}(d-81)]

where d is the day of the year, with Jan 1 as d=1. A more accurate expression for the declination angle δ is:

δ = sin

^{-1}{sin(23.45°) sin[

^{360}⁄

_{365}(d-81)]}

The declination is zero at the equinoxes (March 21 and September 21), positive during the northern hemisphere summer and negative during the northern hemisphere winter. The declination reaches a maximum of 23.45° on June 21 (summer solstice in the northern hemisphere) and a minimum of -23.45° on December 21 (winter solstice in the northern hemisphere).