Solar constant
Encyclopedia
The solar constant, a measure of flux density
Flux density
-Formal Statement:The flux density is simply defined as the amount of flux passing through a unit-area. -Mathematical Statement:The flux density would essentially be the number of field lines passing through a defined unit-area...

, is the amount of incoming solar
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 per unit area that would be incident on a plane perpendicular to the rays, at a distance of one astronomical unit (AU)
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

 (roughly the mean distance from the Sun to the Earth). When solar irradiance
Irradiance
Irradiance is the power of electromagnetic radiation per unit area incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter , while the cgs units are ergs per square centimeter...

 is measured on the outer surface of Earth's atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

, the measurements can be adjusted using the inverse square law to infer the magnitude of solar irradiance at one AU and deduce the solar constant.

Solar output is nearly, but not quite, constant. Variations in total solar irradiance were too small to detect with technology available before the satellite era. Total solar output is now measured to vary (over the last three 11-year sunspot
Sunspot
Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. They are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature....

 cycles) by approximately 0.1%; see solar variation
Solar variation
Solar variation is the change in the amount of radiation emitted by the Sun and in its spectral distribution over years to millennia. These variations have periodic components, the main one being the approximately 11-year solar cycle . The changes also have aperiodic fluctuations...

 for details.

The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite to be roughly 1.361 kilowatt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

s per square meter (kW/m²).
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 one part per thousand from day to day. Thus, for the whole Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

 (which has a cross section
Cross section (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

 of 127,400,000 km²), the power is 1.740×1017 W
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

, plus or minus 3.5%. The solar constant does not remain constant over long periods of time (see Solar variation
Solar variation
Solar variation is the change in the amount of radiation emitted by the Sun and in its spectral distribution over years to millennia. These variations have periodic components, the main one being the approximately 11-year solar cycle . The changes also have aperiodic fluctuations...

), but over a year varies much less than the variation of direct solar irradiance at the top of the atmosphere arising from the ellipticity of the Earth's orbit. The approximate average value cited, 1.361 kW/m², is equivalent to 1.952 calories per minute per square centimeter, or 1.952 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
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...

 (4·π·RE²). 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). 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
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

.

The solar constant includes all wavelengths of solar electromagnetic radiation, not just the visible light (see Electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

). It is linked to the apparent magnitude
Apparent magnitude
The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...

 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 is based on the Sun's visual output only.

In 1838, Claude Pouillet made the first estimate of the solar constant. Using a very simple pyrheliometer
Pyrheliometer
A pyrheliometer is an instrument for direct measurement of solar irradiance. Sunlight enters the instrument through awindow and is directed onto a thermopile which converts heat to an electrical signal that can be recorded. The signal voltage is converted via a formula to measure watts per square...

 he developed, he obtained a value of 1228 W/m², very close to the current estimate. In 1884, Samuel Pierpont Langley
Samuel Pierpont Langley
Samuel Pierpont Langley was an American astronomer, physicist, inventor of the bolometer and pioneer of aviation...

 attempted to estimate the solar constant from Mount Whitney
Mount Whitney
Mount Whitney is the highest summit in the contiguous United States with an elevation of . It is on the boundary between California's Inyo and Tulare counties, west-northwest of the lowest point in North America at Badwater in Death Valley National Park...

 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 kW/m², was still too great. Between 1902 and 1957, measurements by Charles Greeley Abbot
Charles Greeley Abbot
Charles Greeley Abbot was an American astrophysicist, astronomer and Secretary of the Smithsonian Institution. He was born in Wilton, New Hampshire.-Life:...

 and others at various high-altitude sites found values between 1.322 and 1.465 kW/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  kW/m²), a variation that appeared to be due to the Sun and not the Earth's atmosphere.

The angular diameter
Angular diameter
The angular diameter or apparent size of an object as seen from a given position is the “visual diameter” of the object measured as an angle. In the vision sciences it is called the visual angle. The visual diameter is the diameter of the perspective projection of the object on a plane through its...

 of the Earth as seen from the Sun is approximately 1/11,700 radian
Radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s (about 18 arc-seconds), meaning the solid angle
Solid angle
The solid angle, Ω, is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large that object appears to an observer looking from that point...

 of the Earth as seen from the Sun is approximately 1/175,000,000 of a steradian
Steradian
The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane...

. Thus the Sun emits about 2.2 billion times the amount of radiation that is caught by Earth, in other words about 3.86×1026 watts.
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