Solar constant

Last updated February 05, 2025

The solar constant (G_SC) 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 solar electromagnetic radiation (total solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one 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 watts per square meter (kW/m²) at solar minimum (the time in the 11-year solar cycle when the number of sunspots is minimal) and approximately 0.1% greater (roughly 1.362 kW/m²) at solar maximum.^[1]

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.^[2] Billions of years ago, it was 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,^[3] 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.^[4] The approximate average value cited,^[1] 1.3608 ± 0.0005 kW/m², which is 81.65 kJ/m² per minute, is equivalent to approximately 1.951 calories per minute per square centimeter, or 1.951 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%;^[5] see solar variation for details.

For extrasolar planets

$L=4\pi R_{\rm {star}}^{2}\sigma T_{\rm {star}}^{4}$
$L=4\pi f\ d^{2}$
Therefore: $4\pi f\ d^{2}=4\pi R_{\rm {star}}^{2}\sigma T_{\rm {star}}^{4}$
$f=\left({\frac {R_{\rm {star}}^{2}\sigma T_{\rm {star}}^{4}}{d^{2}}}\right)$
Where $\sigma$ is the Stefan-Boltzmann constant ( $\approx 5.67e^{-8}Wm^{-2}K^{-4}$ ) and 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 kW/m²,^[6] close to the current estimate.

In 1875, Jules Violle resumed the work of Pouillet and offered a somewhat larger estimate of 1.7 kW/m² 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 kW/m², was much too large.

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 kW/m². 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 kW/m²), a variation that appeared to be due to the Sun and not the Earth's atmosphere.^[7]

In 1954 the solar constant was evaluated as 2.00 cal/min/cm² ± 2%.^[8] Current results are about 2.5 percent lower.

Relationship to other measurements

Solar irradiance

The actual direct solar irradiance at the top of the atmosphere fluctuates by about 6.9% during a year (from 1.412 kW/m² in early January to 1.321 kW/m² 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 of 127,400,000 km²), the power is 1.730×10¹⁷ W (or 173,000 terawatts),^[9] 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 eccentricity of the Earth's orbit. Its distance to the Sun varies annually between 147.1·10⁶ km at perihelion and 152.1·10⁶ 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_E²), but as it rotates this energy is distributed across the entire surface area (4·π·R_E²). 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 W/m²). 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 radians (about 18 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 3.846×10²⁶ 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).^[10]^[11]^[12]^[13]^[14]

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,^[15] 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 W/m² with cirrus clouds to 1025 W/m² with a clear sky.

Related Research Articles

The greenhouse effect occurs when greenhouse gases in a planet's atmosphere insulate the planet from losing heat to space, raising its surface temperature. Surface heating can happen from an internal heat source or come from an external source, such as its host star. In the case of Earth, the Sun emits shortwave radiation (sunlight) that passes through greenhouse gases to heat the Earth's surface. In response, the Earth's surface emits longwave radiation that is mostly absorbed by greenhouse gases. The absorption of longwave radiation prevents it from reaching space, reducing the rate at which the Earth can cool off.

Sunspots are temporary spots on the Sun's surface that are darker than the surrounding area. They are one of the most recognizable Solar phenomena and despite the fact that they are mostly visible in the solar photosphere they usually affect the entire solar atmosphere. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sunspots appear within active regions, usually in pairs of opposite magnetic polarity. Their number varies according to the approximately 11-year solar cycle.

Sunlight is a portion of the electromagnetic radiation given off by the Sun, in particular infrared, visible, and ultraviolet light. On Earth, sunlight is scattered and filtered through Earth's atmosphere as daylight when the Sun is above the horizon. When direct solar radiation is not blocked by clouds, it is experienced as sunshine, a combination of bright light and radiant heat (atmospheric). When blocked by clouds or reflected off other objects, sunlight is diffused. Sources estimate a global average of between 164 watts to 340 watts per square meter over a 24-hour day; this figure is estimated by NASA to be about a quarter of Earth's average total solar irradiance.

<span class="mw-page-title-main">Radiation pressure</span> Pressure exerted upon any surface exposed to electromagnetic radiation

Radiation pressure is mechanical pressure exerted upon a surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength that is absorbed, reflected, or otherwise emitted by matter on any scale. The associated force is called the radiation pressure force, or sometimes just the force of light.

The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.

The Solar cycle, also known as the solar magnetic activity cycle, sunspot cycle, or Schwabe cycle, is a periodic 11-year change in the Sun's activity measured in terms of variations in the number of observed sunspots on the Sun's surface. Over the period of a solar cycle, levels of solar radiation and ejection of solar material, the number and size of sunspots, solar flares, and coronal loops all exhibit a synchronized fluctuation from a period of minimum activity to a period of a maximum activity back to a period of minimum activity.

The solar luminosity (L_☉) is a unit of radiant flux conventionally used by astronomers to measure the luminosity of stars, galaxies and other celestial objects in terms of the output of the Sun.

Direct insolation is the insolation measured at a given location on Earth with a surface element perpendicular to the Sun's rays, excluding diffuse insolation. Direct insolation is equal to the solar irradiance above the atmosphere minus the atmospheric losses due to absorption and scattering. While the solar irradiance above the atmosphere varies with the Earth–Sun distance and solar cycles, the losses depend on the time of day, cloud cover, humidity, and other impurities.

Radiative forcing is a concept used to quantify a change to the balance of energy flowing through a planetary atmosphere. Various factors contribute to this change in energy balance, such as concentrations of greenhouse gases and aerosols, and changes in surface albedo and solar irradiance. In more technical terms, it is defined as "the change in the net, downward minus upward, radiative flux due to a change in an external driver of climate change." These external drivers are distinguished from feedbacks and variability that are internal to the climate system, and that further influence the direction and magnitude of imbalance. Radiative forcing on Earth is meaningfully evaluated at the tropopause and at the top of the stratosphere. It is quantified in units of watts per square meter, and often summarized as an average over the total surface area of the globe.

In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre. The CGS unit erg per square centimetre per second (erg⋅cm⁻²⋅s⁻¹) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.

Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body. It has a specific, continuous spectrum of wavelengths, inversely related to intensity, that depend only on the body's temperature, which is assumed, for the sake of calculations and theory, to be uniform and constant.

Earth's energy budget is the balance between the energy that Earth receives from the Sun and the energy the Earth loses back into outer space. Smaller energy sources, such as Earth's internal heat, are taken into consideration, but make a tiny contribution compared to solar energy. The energy budget also takes into account how energy moves through the climate system. The Sun heats the equatorial tropics more than the polar regions. Therefore, the amount of solar irradiance received by a certain region is unevenly distributed. As the energy seeks equilibrium across the planet, it drives interactions in Earth's climate system, i.e., Earth's water, ice, atmosphere, rocky crust, and all living things. The result is Earth's climate.

The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature when the body's emissivity curve is not known.

Solar irradiance is the power per unit area received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/m²) in SI units.

A solar balloon is a balloon that gains buoyancy when the air inside is heated by solar radiation, usually with the help of black or dark balloon material. The heated air inside the solar balloon expands and has lower density than the surrounding air. As such, a solar balloon is similar to a hot air balloon. Usage of solar balloons is predominantly in the toy market, although it has been proposed that they be used in the investigation of planet Mars, and some solar balloons are large enough for human flight. A vent at the top can be opened to release hot air for descent and deflation.

For most numbered asteroids, almost nothing is known apart from a few physical parameters and orbital elements. Some physical characteristics can only be estimated. The physical data is determined by making certain standard assumptions.

The air mass coefficient defines the direct optical path length through the Earth's atmosphere, expressed as a ratio relative to the path length vertically upwards, i.e. at the zenith. The air mass coefficient can be used to help characterize the solar spectrum after solar radiation has traveled through the atmosphere.

The planetary equilibrium temperature is a theoretical temperature that a planet would be if it were in radiative equilibrium, typically under the assumption that it radiates as a black body being heated only by its parent star. In this model, the presence or absence of an atmosphere is irrelevant, as the equilibrium temperature is calculated purely from a balance with incident stellar energy.

Solar observation is the scientific endeavor of studying the Sun and its behavior and relation to the Earth and the remainder of the Solar System. Deliberate solar observation began thousands of years ago. That initial era of direct observation gave way to telescopes in the 1600s followed by satellites in the twentieth century.

Solar phenomena are natural phenomena which occur within the atmosphere of the Sun. They take many forms, including solar wind, radio wave flux, solar flares, coronal mass ejections, coronal heating and sunspots.

References

1 2 Kopp, G.; Lean, J. L. (2011). "A new, lower value of total solar irradiance: Evidence and climate significance". Geophysical Research Letters. 38 (1): n/a. Bibcode:2011GeoRL..38.1706K. doi: 10.1029/2010GL045777 .
↑ http://lasp.colorado.edu/home/sorce/data/tsi-data/ Total Solar Irradiance Data, SORCE
↑ "Satellite observations of total solar irradiance". acrim.com. Archived from the original on 2011-07-16. Retrieved 2010-10-02.
↑ "NOAA Status Alert".
↑ Willson, Richard C.; H.S. Hudson (1991). "The Sun's luminosity over a complete solar cycle". Nature. 351 (6321): 42–4. Bibcode:1991Natur.351...42W. doi:10.1038/351042a0. S2CID 4273483.
↑ The measurement of the solar constant by Claude Pouillet, by J-L Dufresne, La Météorologie Archived 2010-03-05 at the Wayback Machine , No. 60, pp. 36–43, Feb. 2008.
↑ One or more of the preceding sentences incorporates text from a publication now in the public domain : Sampson, Ralph Allen (1911). "Sun". In Chisholm, Hugh (ed.). Encyclopædia Britannica . Vol. 26 (11th ed.). Cambridge University Press. p. 87.
↑ Francis S. Johnson (December 1954). "The Solar Constant". Journal of Meteorology. 11 (6): 431–439. Bibcode:1954JAtS...11..432J. doi: 10.1175/1520-0469(1954)011<0431:TSC>2.0.CO;2 .
↑ Archer, D. (2012). Global Warming: Understanding the Forecast. John Wiley & Sons. ISBN 978-0-470-94341-0.
↑ Wang; et al. (2005). "Modeling the Sun's Magnetic Field and Irradiance since 1713". The Astrophysical Journal. 625 (1): 522–538. Bibcode:2005ApJ...625..522W. doi: 10.1086/429689 .
↑ Steinhilber et al. (2009), Geophysical Research Letters, Volume 36, L19704, doi : 10.1051/0004-6361/200811446
↑ Vieira; et al. (2011). "Evolution of the solar irradiance during the Holocene". Astronomy & Astrophysics. 531: A6. arXiv: 1103.4958 . Bibcode:2011A&A...531A...6V. doi:10.1051/0004-6361/201015843. S2CID 119190565.
↑ Steinhilber; et al. (2012). "9,400 years of cosmic radiation and solar activity from ice cores and tree rings". Proceedings of the National Academy of Sciences. 109 (16): 5967–5971. Bibcode:2012PNAS..109.5967S. doi: 10.1073/pnas.1118965109 . PMC 3341045 . PMID 22474348.
↑ Vieira, L. E. A.; Norton, A.; Kretzschmar, M.; Schmidt, G. A.; Cheung, M. C. M. (2012). "How the inclination of Earth's orbit affects incoming solar irradiance" (PDF). Geophys. Res. Lett. 39 (16): L16104. Bibcode:2012GeoRL..3916104V. doi: 10.1029/2012GL052950 .
↑ "Hinweise". www.astro.uni-jena.de.

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[KoppLean11-1] 1 2 Kopp, G.; Lean, J. L. (2011). "A new, lower value of total solar irradiance: Evidence and climate significance". Geophysical Research Letters. 38 (1): n/a. Bibcode:2011GeoRL..38.1706K. doi: 10.1029/2010GL045777 .

[sorce-2] ttp://lasp.colorado.edu/home/sorce/data/tsi-data/ Total Solar Irradiance Data, SORCE

[TSI20-3] "Satellite observations of total solar irradiance". acrim.com. Archived from the original on 2011-07-16. Retrieved 2010-10-02.

[4] "NOAA Status Alert".

[Willson91-5] Willson, Richard C.; H.S. Hudson (1991). "The Sun's luminosity over a complete solar cycle". Nature. 351 (6321): 42–4. Bibcode:1991Natur.351...42W. doi:10.1038/351042a0. S2CID 4273483.

[6] The measurement of the solar constant by Claude Pouillet, by J-L Dufresne, La Météorologie Archived 2010-03-05 at the Wayback Machine , No. 60, pp. 36–43, Feb. 2008.

[7] One or more of the preceding sentences incorporates text from a publication now in the public domain : Sampson, Ralph Allen (1911). "Sun". In Chisholm, Hugh (ed.). Encyclopædia Britannica . Vol. 26 (11th ed.). Cambridge University Press. p. 87.

[8] Francis S. Johnson (December 1954). "The Solar Constant". Journal of Meteorology. 11 (6): 431–439. Bibcode:1954JAtS...11..432J. doi: 10.1175/1520-0469(1954)011<0431:TSC>2.0.CO;2 .

[9] Archer, D. (2012). Global Warming: Understanding the Forecast. John Wiley & Sons. ISBN 978-0-470-94341-0.

[10] Wang; et al. (2005). "Modeling the Sun's Magnetic Field and Irradiance since 1713". The Astrophysical Journal. 625 (1): 522–538. Bibcode:2005ApJ...625..522W. doi: 10.1086/429689 .

[11] Steinhilber et al. (2009), Geophysical Research Letters, Volume 36, L19704, doi : 10.1051/0004-6361/200811446

[12] Vieira; et al. (2011). "Evolution of the solar irradiance during the Holocene". Astronomy & Astrophysics. 531: A6. arXiv: 1103.4958 . Bibcode:2011A&A...531A...6V. doi:10.1051/0004-6361/201015843. S2CID 119190565.

[13] Steinhilber; et al. (2012). "9,400 years of cosmic radiation and solar activity from ice cores and tree rings". Proceedings of the National Academy of Sciences. 109 (16): 5967–5971. Bibcode:2012PNAS..109.5967S. doi: 10.1073/pnas.1118965109 . PMC 3341045 . PMID 22474348.

[14] Vieira, L. E. A.; Norton, A.; Kretzschmar, M.; Schmidt, G. A.; Cheung, M. C. M. (2012). "How the inclination of Earth's orbit affects incoming solar irradiance" (PDF). Geophys. Res. Lett. 39 (16): L16104. Bibcode:2012GeoRL..3916104V. doi: 10.1029/2012GL052950 .

[15] "Hinweise". www.astro.uni-jena.de.

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