Info

Duffie and Backman (1991) suggested a simple approximation for e as follows:

The use of this last expression instead of Eq. 3.23 does not make an appreciable difference. The average distance between the sun and the earth is R = 150 x 106 km. Due to the eccentricity of the earth's orbit, the distance varies by 1.7%.

3.9.2 Solar Time

Solar time is based not only on the rotation of the earth about its axis but also on the earth's revolution around the sun during which the earth does not sweep equal areas on the ecliptic plane (see Fig. 3.21).

Vernal equinox 21 March

Aphelion 2 January

Summe solstice 22 June

Vernal equinox 21 March

Aphelion 2 January

Summe solstice 22 June

Perihelion January ^Winter solstice 22 December

Autumnal equinox 21 September

Fig. 3.21 Earth's orbit around the sun 3.9.2.1 Equation of Time

Perihelion January ^Winter solstice 22 December

Autumnal equinox 21 September

Fig. 3.21 Earth's orbit around the sun 3.9.2.1 Equation of Time

These combined movements, as already mentioned in Sect. 3.5, cause small discrepancies in the sun's appearance exactly over the local meridian daily. This discrepancy is the align of time, Et, which is expressed by Spencer (1972) as

The constant multiplication factor in front of the parenthesis on the right-hand side is for conversion from radians to minutes. It varies in length throughout the year due to the following factors:

1. The tilt of the earth's axis with respect to the plane of the ecliptic containing the respective centers of the sun and the earth

2. The angle swept out by the earth-sun vector during any given period of time, which depends upon the earth's position in its orbit (see Fig. 3.21).

The standard time (as recorded by clocks running at a constant speed) differs from the solar time. The difference between the standard time and solar time is defined as the align of time, Et, which may be obtained as expressed by Woolf (1968):

Et = 229.18 (0.000075 + 0.001868 cosT - 0.032077 sinT -0.014615 cos2T - 0.04089 sin2T) .

Et = 0.1236 sinT - 0.0043 cosT + 0.1538 sin2T + 0.0609cos2T , (3.28)

Table 3.2 Harmonic coefficients

k

Ak (103) (h)

Bk (103) (h)

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