# The declination of the sun

 — sun s rays / / I \ Equator
 — (sun) —
 Figure 1.5(a) shows the position of the earth, in the course of its orbit around the sun, seen slightly from above. If a section is taken through the earth at its two positions at mid-winter and mid-summer, the concept of declination is seen more clearly. Figure 1.5(b) is such a section, illustrating that the sun is vertically overhead at noon on a latitude of 23 j °S in mid-winter and also on 23 °N at noon in mid-summer. These two values of latitude correspond to the sun’s declination at those dates and are a consequence of the earth’s pole being tilted at an angle of about 23 to the axis of the plane in which it orbits the sun. Figure 1.5(b) also illustrates this.

 Sept 21st autumnal equinox

 March 21st vernal equinox

 Tropic of cancer ^ ooi/ o latitude V* 23./2 23i/20N

 Dec 21st Note that the sun is so far from the earth that all ^ 1 0 the rays of the sun may be considered as parallel ■ •2 to one another when they reach the earth

 Equator

 Sun’s rays

 Axis of revolution of the earth about the sun (b)

Fig. 7.5 Seasonal changes in solar declination.

The angular inclination of the pole does not vary substantially from this value owing to the gyroscopic effect of the earth’s rotating mass. As a result of this, the sun can be vertically overhead only between the latitudes 23 °N and 23 j °S. These two parallels are called the tropics of Cancer and Capricorn, respectively. They define the bounds of the Torrid Zone, often referred to as ‘the Tropics’. It follows that, at dates other than the winter

And summer solstices, the sun will be vertically overhead at noon in the tropics, at some latitude between 23 ^°N and S. In fact, the sun is vertically overhead at noon on the equator itself on two dates in the year—the autumnal equinox and the vernal (spring) equinox. On these occasions the declination is zero. Referring to Figure 7.5 it can also be inferred that the latitude of the arctic circle is 66.5° north and that of the antarctic circle 66.5° south.

The dates of the solstices and equinoxes are not always the same because the earth’s year is not exactly 365 days. An equation from which the declination can be determined is:

 (7.1)

D = 23.45 sin[360 x (284 + AO/365]

Where N is the day number, starting from 1 on 1 January. Approximate values of declination are: 21 June, 23y°N; 21 May and 21 July, 20 j°N; 21 April and 21 August, 11 j°N; 21

March and 21 September, 0°. Corresponding values for the other six months of the year

Have southerly, negative declinations.

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