Calculation
To calculate the amount of sunlight reaching the ground, both the elliptical orbit of the Earth and the attenuation by the Earth's atmosphere have to be taken into account. The extraterrestrial solar illuminance (Eext), corrected for the elliptical orbit by using the day number of the year (dn), is given by
where dn=1 on January 1; dn=2 on January 2; dn=32 on February 1, etc. In this formula dn-3 is used, because in modern times Earth's perihelion, the closest approach to the Sun and therefore the maximum Eext occurs around January 3 each year. The value of 0.033412 is determined knowing that the ratio between the perihelion (0.98328989 AU) squared and the aphelion (1.01671033 AU) squared should be approximately 0.935338.
The solar illuminance constant (Esc), is equal to 128×103 lx. The direct normal illuminance (Edn), corrected for the attenuating effects of the atmosphere is given by:
where c is the atmospheric extinction coefficient and m is the relative optical airmass.
Read more about this topic: Sunlight
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