# Solar constant

The solar constant E 0 is the extraterrestrial irradiance ( intensity ) averaged over many years , which strikes the earth from the sun at an average distance from earth to sun without the influence of the atmosphere perpendicular to the direction of the radiation. The term "constant" is used conventionally, although it is not a natural constant .

## Establishment and seasonal fluctuation

The mean value for the solar constant was set in 1982 by the World Meteorological Organization in Geneva at:

${\ displaystyle E_ {0} = 1367 \ \ mathrm {\ frac {W} {m ^ {2}}} = 1367 \ \ mathrm {\ frac {J} {m ^ {2} \, s}} = 1367 \ \ mathrm {\ frac {kg} {s ^ {3}}}}$.

Due to the eccentricity of the orbit , the distance between the earth and the sun fluctuates between 147.1 and 152.1 million kilometers annually. With it, the irradiance outside the atmosphere fluctuates between 1325 and 1420 W / m². In perihelion the value is thus approx. 3.4 percent above and in aphelion approx. 3.3 percent below the annual mean.

When the weather is clear, three quarters of the sun's energy arrives at sea level, as part of it is reflected and absorbed by the atmosphere. The solar energy arriving on the ground therefore drops to around 1000 W / m² even in clear weather. Even light cirrus clouds let this value fall further, to about half of the initial value, and thus below 700 W / m².

In 2015, the solar constant was set by the IAU according to new measurement results (Resolution B3) and has been managed in this way at CODATA since then . ${\ displaystyle S_ {o} = 1361 \ mathrm {\ frac {W} {m ^ {2}}}}$

## Fluctuations and long-term increases

The radiant power of the sun itself is almost constant. The eleven-year sunspot cycle also only causes fluctuations - both in the visible spectrum and in total radiation - of less than 0.1 percent.

In the UV range below 170 nm, the radiation can vary by a factor of 2. In the X-ray range between 0.2 and 3 nm, the radiation output can be increased by up to two orders of magnitude, i.e. H. by a factor of 100. In the case of solar flares , changes by more than five orders of magnitude (ie by a factor of more than 100,000: A1 up to> X17 as on November 4, 2003) are possible in the X-ray range between 0.1 and 0.8 nm.

Medium-term disturbances of the earth's orbit, which also influence the irradiance on earth, are described by the Milanković cycles .

In the long term, as a result of natural development as a main sequence star, the sun's radiation output increases by around one percent every 100 million years. Shortly after its creation, its luminosity was only around 70 percent of its current value. When assessing the climate in the early history of the earth, this aspect must be taken into account, whereas it has not played a role since human history.

## Angle dependence

The output per square meter always relates to an area that is perpendicular to the radiation. If the sun is not perpendicular to the irradiated surface, the radiant power in relation to the irradiated area is:

${\ displaystyle E_ {0} \ cdot \ sin (\ alpha)}$, where is the angle between the direction of incidence of the radiation and the surface.${\ displaystyle \ alpha \! \;}$

## More facts

The radiant power of the sun that is constantly shining on the earth can be calculated as the product of the solar constant with the area of ​​the earth's contour . The earth's contour is approximately a circle with the (mean) earth radius R 0 = 6,371 km. The total radiant power of the sun supplied to the earth is accordingly approx. 174 petawatts (PW):

${\ displaystyle E_ {0} \ cdot \ pi R_ {0} ^ {2} = 174 {,} 3 \ cdot 10 ^ {15} \, \ mathrm {W}}$

The total surface of the earth is four times as large as the area of ​​the earth's contour. The earth constantly sends thermal radiation from the entire surface into space with a quarter of the solar constant . The surface temperature on earth has adjusted in such a way that there is an equilibrium here. ${\ displaystyle 340 {\ mathrm {\ frac {W} {m ^ {2}}}}}$

For comparison, the global energy demand of mankind was 140 PWh in 2010 . The sun therefore radiates just under more energy to the earth in one hour than the current annual world energy requirement of mankind.

The earth's atmosphere and its climate influence global radiation on the earth's surface. The geometric effect describes the air mass ( Air Mass ).

In order to exclude the influence of the atmosphere, measurements of the solar constant have been made in space since 1978. The SOHO satellite , launched in 1995 , continuously observes the sun with the Virgo radiometer . The measurements are coordinated by the Royal Meteorological Institute of Belgium .

## Radiant power of the sun

From the solar constant, the radiation performance can Φ calculate the sun, by reacting with the surface A of that envelope ball multiplied by the sun, the radius of the central Erdabstands r = 149.6 x 10 9 m has:

${\ displaystyle \ Phi = E_ {0} A = E_ {0} \ cdot 4 \ pi r ^ {2} = 3 {,} 845 \ cdot 10 ^ {26} \, \ mathrm {W}}$

The magnitude of the radiant power of the sun can also be estimated using the Stefan-Boltzmann law and, conversely, the solar constant can be estimated.

## Irradiance of the sun in Germany

Weather conditions summer winter
mostly clear sky up to 1000 W / m² up to 500 W / m²
light to medium cloudiness up to 600 W / m² up to 300 W / m²
heavy cloud cover to cloudy fog up to 300 W / m² up to 150 W / m²

## Solar constants of the planets

The following table gives the solar constant for the planets and selected other celestial bodies of the solar system:

planet Major semi-axis
in AE
Average
E e in W / m²
E e compared
to earth
Mercury 0.387 9123, 0 6.67300
Venus 0.723 2615, 0 1.91300
earth 1,000 1367, 0 1, 00000
Mars 1.524 589, 0 0.43100
(1) Ceres 2.766 179, 0 0.13100
Jupiter 5.204 50, 0 0.03700
Saturn 9,582 15th, 0 0.01100
Uranus 19,201 3.7 0.00270
Neptune 30,047 1.5 0.001110
(134340) Pluto 39,482 0.9 0.00065
(136199) Eris 67.700 0.3 0.00022

## Individual evidence

1. Hans-Günther Wagemann, Heinz Eschrich: Fundamentals of photovoltaic energy conversion (=  Teubner study books physics ). Teubner, Stuttgart 1994, ISBN 3-519-03218-X .
2. Reimann, Hans-Georg; Weiprecht, Juergen Compendium for the astronomical internship
3. The field of tension of global energy demand . kf2strategy.de
4. http://www.solar.lucycity.de/index.php/sonnenenergie/9-sonnenstrahl