7.1.1 Sunlight and skylight

The sun is our major light source. Its visible surface has a radius of about 6.95 10 ⁸ m. The sun's average surface temperature is 5750 K. The earth's orbit around the sun (see Fig. 7.1) is an ellipse with the sun located at one of the foci. (The numerical eccentricity ? of the orbit is very small, ? = 0.0167, and therefore, the orbit shape is almost a circle.) The distance from the earth to the sun varies with the time of the year. The average distance is R = 1.5 10 ¹¹ m (1 astronomical unit). At that distance, the solar irradiance, E ₀, outside the earth's atmosphere is (1.367 0.07) 10 ³ [W m ^?2]; this is called the solar constant. The solar irradiance falls off with the inverse of the distance squared. On any Julian day, J ( J = 1, 2,...,365), the solar irradiance, E _{0 J}, can be approximatedly calculated [189] as:

(7.1)

where R _J is the actual sun-earth distance on day J, ? = 360 /365.25 days = 0.9856 /day is the mean angular velocity of the earth around the sun, = 1.735 is an offset angle, J is the number of Julian days, counted from 1 = January 1, and ? = 0.0167 is the numerical eccentricity of the earth's orbit. The solar irradiance, thus...