Solar constantEdit

Solar radiation Langley 1903

A 1903 Langley bolograph with an erroneous solar constant of 2.54 calories/minute/square centimeter.

Solar irradiance spectrum 1992

Solar irradiance spectrum at top of atmosphere, on a linear scale and plotted against wavenumber.

The solar constant is the amount of incoming solar electromagnetic radiation per unit area, measured on the outer surface of Earth's atmosphere in a plane perpendicular to the rays.[1] The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite to be roughly 1,366 watts per square meter (W/m²),[2] though this fluctuates by about 6.9% during a year (from 1,412 W/m² in early January to 1,321 W/m² in early July) due to the earth's varying distance from the Sun, and typically by much less than one part per thousand from day to day. Thus, for the whole Earth (which has a cross section of 127,400,000 km²), the power is 1.740×1017 W, plus or minus 3.5%. The solar constant does not remain constant over long periods of time (see Solar variation). The approximate average value cited,[2] 1,366 W/m², is equivalent to 1.96 calories per minute per square centimeter, or 1.96 langleys (Ly) per minute.

The Earth receives a total amount of radiation determined by its cross section (π·RE²), but as it rotates this energy is distributed across the entire surface area (4·π·RE²). Hence the average incoming solar radiation (sometimes called the solar irradiance), taking into account the angle at which the rays strike and that at any one moment half the planet does not receive any solar radiation, is one-fourth the solar constant (approximately 342 W/m²). At any given moment, the amount of Solar radiation received at a location on the Earth's surface depends on the state of the atmosphere and the location's latitude.

The solar constant includes all wavelengths of solar electromagnetic radiation, not just the visible light (see Electromagnetic spectrum). It is linked to the apparent magnitude of the Sun, −26.8, in that the solar constant and the magnitude of the Sun are two methods of describing the apparent brightness of the Sun, though the magnitude only measures the visual output of the Sun.

In 1884, Samuel Pierpont Langley attempted to estimate the Solar constant from Mount Whitney in California. By taking readings at different times of day, he attempted to remove effects due to atmospheric absorption. However, the value he obtained, 2,903 W/m², was still too great. Between 1902 and 1957, measurements by Charles Greeley Abbot and others at various high-altitude sites found values between 1,322 and 1,465 W/m². Abbott proved that one of Langley's corrections was erroneously applied. His results varied between 1.89 and 2.22 calories (1,318 to 1,548  W/m²), a variation that appeared to be due to the Sun and not the Earth's atmosphere.[3]

The angular diameter of the Earth as seen from the Sun is approximately 1/11,000 radians, meaning the solid angle of the Earth as seen from the sun is approximately 1/140,000,000 steradians. Thus the Sun emits about two billion times the amount of radiation that is caught by Earth, in other words about 3.86×1026 watts.[4]


  1. Satellite observations of total solar irradiance
  2. 2.0 2.1 "Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". Retrieved on 2005-10-05.
  3. This article incorporates text from the article "Sun" in the Encyclopædia Britannica, Eleventh Edition, a publication now in the public domain.
  4. The Sun at nine

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