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{{short description|Intensity of sunlight or solar constant}}

[[File:Solar irradiance spectrum 1992.gif|thumb|Solar irradiance spectrum at top of atmosphere, on a linear scale and plotted against [[wavenumber]].]]

The '''solar constant''' ('''''G<sub>SC</sub>''''') measures the amount of energy received by a given area one astronomical unit away from the Sun. More specifically, it is a [[flux density]] measuring mean [[Sun|solar]] [[electromagnetic radiation]] ([[total solar irradiance]]) per unit area. It is measured on a surface perpendicular to the rays, one [[astronomical unit|astronomical unit (au)]] from the Sun (roughly the distance from the Sun to the Earth).

The solar constant includes radiation over the entire [[electromagnetic spectrum]]. It is measured by satellite as being 1.361 [[Kilo-|kilo]][[watt]]s per square meter (kW/m<sup>2</sup>) at [[solar minimum]] (the time in the 11-year [[solar cycle]] when the number of [[sunspot]]s is minimal) and approximately 0.1% greater (roughly 1.362&nbsp;kW/m<sup>2</sup>) at [[solar maximum]].<ref name=KoppLean11>{{cite journal |last1= Kopp |first1= G. |last2= Lean |first2= J. L. |author2-link=Judith Lean |doi= 10.1029/2010GL045777 |title= A new, lower value of total solar irradiance: Evidence and climate significance |journal= Geophysical Research Letters |volume= 38 |issue= 1 |pages= n/a |year= 2011 |bibcode= 2011GeoRL..38.1706K|doi-access= free }}</ref>

The solar "constant" is not a [[physical constant]] in the modern [[CODATA]] scientific sense; that is, it is not like the [[Planck constant]] or the [[speed of light]] which are absolutely constant in physics. The solar constant is an average of a varying value. In the past 400 years it has varied less than 0.2 percent.<ref name=sorce>http://lasp.colorado.edu/home/sorce/data/tsi-data/ Total Solar Irradiance Data, [[SORCE]]</ref> Billions of years ago, it was [[Faint young Sun paradox|significantly lower]].

This constant is used in the calculation of [[radiation pressure]], which aids in the calculation of a force on a [[solar sail]].

==Calculation==

[[Solar irradiance]] is measured by satellites above [[Earth's atmosphere]],<ref name=TSI20>{{cite web|url=http://acrim.com/TSI%20Monitoring.htm|title=Satellite observations of total solar irradiance|website=acrim.com|access-date=2010-10-02|archive-date=2011-07-16|archive-url=https://web.archive.org/web/20110716140550/http://www.acrim.com/TSI%20Monitoring.htm|url-status=dead}}</ref> and is then adjusted using the [[inverse square law]] to infer the magnitude of solar irradiance at one [[Astronomical Unit]] (au) to evaluate the solar constant.<ref>{{Cite web | url=http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarirradiance.html | title=NOAA Status Alert}}</ref> The approximate average value cited,<ref name=KoppLean11/> 1.3608 ± 0.0005 &nbsp;kW/m<sup>2</sup>, which is 81.65 kJ/m<sup>2</sup> per minute, is equivalent to approximately 1.951 calories per minute per square centimeter, or 1.951 [[Langley (unit)|langleys]] per minute.

Solar output is nearly, but not quite, constant. Variations in [[total solar irradiance]] (TSI) were small and difficult to detect accurately with technology available before the satellite era (±2% in 1954). Total solar output is now measured as varying (over the last three 11-year [[sunspot]] cycles) by approximately 0.1%;<ref name=Willson91>{{cite journal |last=Willson |first=Richard C.|author2=H.S. Hudson|date=1991 |title=The Sun's luminosity over a complete solar cycle |journal=Nature |volume=351 |issue=6321 |pages=42–4 |doi=10.1038/351042a0 |bibcode=1991Natur.351...42W|s2cid=4273483}}<!-- {{harvnb|Willson|1991}} --></ref> see [[solar variation]] for details.

===For extrasolar planets===
<math>L=4\pi R_{\rm star}^2\sigma T_{\rm star}^4</math> <br>
<math>L=4\pi f \  d ^2</math> <br>
Therefore:  <math>4\pi f\  d ^2 = 4\pi R_{\rm star}^2\sigma T_{\rm star}^4</math> <br>
<math display="block">   f=  \left (  \frac{R_{\rm star}^2\sigma T_{\rm star}^4}{ d ^2}  \right )  </math> <br>
Where f is the irradiance of the star at the extrasolar planet at distance d.

==Historical measurements==
In 1838, [[Claude Pouillet]] made the first estimate of the solar constant. Using a very simple [[pyrheliometer]] he developed, he obtained a value of 1.228&nbsp;kW/m<sup>2</sup>,<ref>[http://documents.irevues.inist.fr/bitstream/handle/2042/16943/meteo_2008_60_36.pdf'' The measurement of the solar constant by Claude Pouillet''], by J-L Dufresne, [http://www.smf.asso.fr/lameteo.html ''La Météorologie''] {{webarchive|url=https://web.archive.org/web/20100305140149/http://www.smf.asso.fr/lameteo.html |date=2010-03-05}}, No. 60, pp. 36–43, Feb. 2008.</ref> close to the current estimate.

In 1875, [[Jules Violle]] resumed the work of Pouillet and offered a somewhat larger estimate of 1.7&nbsp;kW/m<sup>2</sup> based, in part, on a measurement that he made from [[Mont Blanc]] in France.

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 tried to correct for effects due to atmospheric absorption. However, the final value he proposed, 2.903&nbsp;kW/m<sup>2</sup>, was much too large.

[[File:Solar radiation Langley 1903.png|thumb|A 1903 Langley bolograph with an erroneous solar constant of 2.54 calories/minute/square centimeter.]] Between 1902 and 1957, measurements by [[Charles Greeley Abbot]] and others at various high-altitude sites found values between 1.322 and 1.465&nbsp;kW/m<sup>2</sup>. Abbot showed that one of Langley's corrections was erroneously applied. Abbot's results varied between 1.89 and 2.22 calories (1.318 to 1.548&nbsp;&nbsp;kW/m<sup>2</sup>), a variation that appeared to be due to the Sun and not the Earth's atmosphere.<ref>{{EB1911|wstitle=Sun |volume=26 |page=87 |inline=1 |first=Ralph Allen |last=Sampson |author-link=Ralph Allan Sampson}}</ref>

In 1954 the solar constant was evaluated as 2.00 cal/min/cm<sup>2</sup> ± 2%.<ref>{{cite journal |title=The Solar Constant |author=Francis S. Johnson |journal= Journal of Meteorology |volume=11 |number=6 |date=December 1954 |doi=10.1175/1520-0469(1954)011<0431:TSC>2.0.CO;2 |pages=431–439|bibcode= 1954JAtS...11..432J|doi-access=free }}</ref> Current results are about 2.5 percent lower.

==Relationship to other measurements==

===Solar irradiance===
{{Main|Solar irradiance}}
{{See also|Earth's energy budget}}
The actual direct solar irradiance at the top of the atmosphere fluctuates by about 6.9% during a year (from 1.412&nbsp;kW/m<sup>2</sup> in early January to 1.321&nbsp;kW/m<sup>2</sup> in early July) due to the Earth's varying distance from the Sun, and typically by much less than 0.1% from day to day. Thus, for the whole [[Earth]] (which has a [[cross section (geometry)|cross section]] of 127,400,000&nbsp;km<sup>2</sup>), the power is 1.730×10<sup>17</sup>&nbsp;[[watt|W]] (or 173,000 [[terawatt]]s),<ref>{{cite book|isbn=978-0-470-94341-0|author=Archer, D.|date=2012|title=Global Warming: Understanding the Forecast|publisher=John Wiley & Sons }}</ref> plus or minus 3.5% (half the approximately 6.9% annual range). The solar constant does not remain constant over long periods of time (see [[Solar variation]]), but over a year the solar constant varies much less than the solar irradiance measured at the top of the atmosphere. This is because the solar constant is evaluated at a fixed distance of 1 [[Astronomical Unit]] (au) while the solar irradiance will be affected by the [[Orbital eccentricity|eccentricity]] of the Earth's orbit. Its distance to the Sun varies annually between 147.1·10<sup>6</sup> km at [[perihelion]] and 152.1·10<sup>6</sup>&nbsp;km at [[aphelion]]. In addition, several long term (tens to hundreds of millennia) cycles of subtle variation in the Earth's orbit ([[Milankovich cycles]]) affect the solar irradiance and insolation (but not the solar constant).

The Earth receives a total amount of radiation determined by its cross section (π·R<sub>E</sub><sup>2</sup>), but as it rotates this energy is distributed across the entire [[surface area]] (4·π·R<sub>E</sub><sup>2</sup>). Hence the average incoming solar radiation, 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 340&nbsp;W/m<sup>2</sup>). The amount reaching the Earth's surface (as [[insolation]]) is further reduced by atmospheric attenuation, which varies. 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, the location's [[latitude]], and the time of day.

===Apparent magnitude===

The solar constant includes all wavelengths of solar electromagnetic radiation, not just the [[visible light]] (see [[Electromagnetic spectrum]]). It is positively correlated with the [[apparent magnitude]] of the Sun which is −26.8. The solar constant and the magnitude of the Sun are two methods of describing the apparent brightness of the Sun, though the magnitude is based on the Sun's visual output only.

===The Sun's total radiation===
The [[angular diameter]] of the Earth as seen from the Sun is approximately 1/11,700 [[radian]]s (about 18 [[minute and second of arc|arcseconds]]), meaning the [[solid angle]] of the Earth as seen from the Sun is approximately 1/175,000,000 of a [[steradian]]. Thus the Sun emits about 2.2 billion times the amount of radiation that is caught by Earth, in other words about 3.846×10<sup>26</sup> watts.

==Past variations in solar irradiance==
Space-based observations of solar irradiance started in 1978. These measurements show that the solar constant is not constant. It varies with the 11-year sunspot [[solar cycle]].
When going further back in time, one has to rely on irradiance reconstructions, using sunspots for the past 400 years or cosmogenic radionuclides for going back 10,000 years.
Such reconstructions show that solar irradiance varies with distinct periodicities. These cycles are: 11 years (Schwabe), 88 years (Gleisberg cycle), 208 years (DeVries cycle) and 1,000 years (Eddy cycle).<ref>{{cite journal |last1= Wang |display-authors= etal |year= 2005 |title= Modeling the Sun's Magnetic Field and Irradiance since 1713|journal= The Astrophysical Journal |volume= 625 |issue= 1| pages= 522–538 |doi= 10.1086/429689 |bibcode=2005ApJ...625..522W|doi-access= free }}</ref><ref>Steinhilber et al. (2009), Geophysical Research Letters, Volume 36, L19704, {{doi|10.1051/0004-6361/200811446}}</ref><ref>{{cite journal |last1= Vieira |display-authors= etal |year= 2011 |title= Evolution of the solar irradiance during the Holocene|journal= Astronomy & Astrophysics |volume= 531 |page= A6 |doi= 10.1051/0004-6361/201015843 |bibcode=2011A&A...531A...6V|arxiv= 1103.4958|s2cid= 119190565 }}</ref><ref>{{cite journal |last1= Steinhilber |display-authors= etal |year= 2012 |title= 9,400 years of cosmic radiation and solar activity from ice cores and tree rings| journal= Proceedings of the National Academy of Sciences |volume= 109| issue= 16|pages= 5967–5971| doi= 10.1073/pnas.1118965109 |pmid=22474348 |pmc=3341045|bibcode= 2012PNAS..109.5967S|doi-access= free }}</ref><ref>{{cite journal |last1= Vieira |first1= L. E. A. |last2= Norton |first2= A. |last3= Kretzschmar |first3= M. |last4= Schmidt |first4= G. A. |last5= Cheung |first5= M. C. M. |year= 2012 |title= How the inclination of Earth's orbit affects incoming solar irradiance |url= https://hal-insu.archives-ouvertes.fr/insu-01179873/file/grl29502.pdf|journal= Geophys. Res. Lett. |volume= 39 |issue= 16|page= L16104 |doi= 10.1029/2012GL052950 |bibcode=2012GeoRL..3916104V|doi-access= free }}</ref>

Over billions of years, the Sun is gradually expanding, and emitting more energy from the resultant larger surface area. The unsolved question of how to account for the clear geological evidence of liquid water on the Earth billions of years ago, at a time when the sun's luminosity was only 70% of its current value, is known as the [[faint young Sun paradox]].

==Variations due to atmospheric conditions==
At most about 75% of the solar energy actually reaches the earth's surface,<ref>{{Cite web|url=https://www.astro.uni-jena.de/Teaching/Praktikum/pra2002/node68.html|title=Hinweise|website=www.astro.uni-jena.de}}</ref> as even with a cloudless sky it is partially reflected and absorbed by the atmosphere. Even light cirrus clouds reduce this to 50%, stronger cirrus clouds to 40%. Thus the solar energy arriving at the surface with the sun directly overhead can vary from 550&nbsp;W/m<sup>2</sup> with cirrus clouds to 1025&nbsp;W/m<sup>2</sup> with a clear sky.

==See also==
{{cmn|
*[[Formation and evolution of the Solar System]]
*[[Irradiance]]
*[[List of articles related to the Sun]]
*[[List of solar cycles]]
*[[Radiation pressure]]
*[[Solar wind]]
*[[Stellar evolution]]
*{{Section link|Sun|Life phases}}
*[[Sunlight]]
}}

==References==
{{Reflist}}
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[[Category:Atmospheric radiation]]
[[Category:Photovoltaics]]
[[Category:Radiometry]]
[[Category:Sun]]