To determine the position of the Sun in the sky at a certain moment of the year

and in a certain place, it is necessary to define a few characteristic angles. These

angles are [1]:

• the solar height or altitude a — the angle formed by the direction of the solar rays and their projection on a horizontal plane;

• the zenithal angle — the angle formed by the solar rays and the zenith direction; this angle and a are complementary;

• the solar azimuth a, which indicates the variance of the solar rays’ projection on the horizon’s plane as regards the south; by convention, eastward orientations are negative while westward orientations are positive;

• the hour angle h, which indicates the angular distance between the Sun and its midday projection along its apparent trajectory on the celestial vault; the time angle is also equal to the angle that the Earth has to rotate to bring the Sun back above the local meridian;

• the latitude L — the angle formed by the straight line that connects the place taken into consideration and the Earth’s core and its projection on the equator’s

plane; this angle is positive in the northern hemisphere but negative in the south­ern hemisphere;

• the solar declination d — the angle formed between the solar ray and the equa­tor’s plane measured on the solar midday plane, that is, the meridian plane pass­ing by the Sun; the solar declination is positive when the Sun is above the equa­torial plane and negative when it is under the equatorial plane (Fig. 4).

The solar height a and the solar azimuth a define the instant position of the Sun [1]:

sen a = sen L sen d + cos L cos d cos h (5)

sen a = cos d sen h/cos a (6)

Solar declination d is calculated using Cooper’s equation :

d = 23.45 sen[360(284 + n)/365] (7)

where n stands for the nth day of the year. Declination depends only on the date; therefore, it is the same for all places on the planet.

The hour angle for dawn ha or sunset ht can be calculated using eqn (5), avoiding sen a, as [1]: