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Steradian
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a ''length'' on the circumference, a solid angle in steradians, projected onto a sphere, gives an ''area'' on the surface. The name is derived from the Greek 'solid' + radian. The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. , dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steradian Cone And Cap
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radians, projected onto a circle, gives a ''length'' on the circumference, a solid angle in steradians, projected onto a sphere, gives an ''area'' on the surface. The name is derived from the Greek 'solid' + radian. The steradian, like the radian, is a dimensionless unit, the quotient of the area subtended and the square of its distance from the centre. Both the numerator and denominator of this ratio have dimension length squared (i.e. , dimensionless). It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian (W⋅sr−1). The steradian was formerly an SI supplementary unit, but thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solid Angle
In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the ''apex'' of the solid angle, and the object is said to ''subtend'' its solid angle at that point. In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a '' steradian'' (symbol: sr). One steradian corresponds to one unit of area on the unit sphere surrounding the apex, so an object that blocks all rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, 4\pi. Solid angles can also be measured in squares of angular measures such as degrees, minutes, and seconds. A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much small ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International System Of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. Established and maintained by the General Conference on Weights and Measures (CGPM), it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radiant Intensity
In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are ''directional'' quantities. The SI unit of radiant intensity is the watt per steradian (), while that of spectral intensity in frequency is the watt per steradian per hertz () and that of spectral intensity in wavelength is the watt per steradian per metre ()—commonly the watt per steradian per nanometre (). Radiant intensity is distinct from irradiance and radiant exitance, which are often called '' intensity'' in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity. Mathematical definitions Radiant intensity Radiant intensity, denoted ''I''e,Ω ("e" for "energetic", to avoid confusion with photomet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Derived Unit
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m". Special names The International Sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Supplementary Unit
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m". Special names The International Sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SI Derived Units
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density. The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m". Special names The International Sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IAU Designated Constellations By Area
The International Astronomical Union (IAU) designates 88 constellations of stars. In the table below, they are ranked by the solid angle that they subtend in the sky, measured in square degrees and millisteradians. These solid angles depend on arbitrary boundaries between the constellations: the list below is based on constellation boundaries drawn up by Eugène Delporte in 1930 on behalf of the IAU and published in ''Délimitation scientifique des constellations'' (Cambridge University Press). Before Delporte's work, there was no standard list of the boundaries of each constellation. Delporte drew the boundaries along vertical and horizontal lines of right ascension and declination; however, he did so for the epoch B1875.0, which means that due to precession of the equinoxes, the borders on a modern star map (e.g., for epoch J2000) are already somewhat skewed and no longer perfectly vertical or horizontal. This skew will increase over the centuries to come. However, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Quantity
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spat (angular Unit)
The spat (symbol sp), from the Latin ''spatium'' ("space"), is a unit of solid angle. 1 spat is equal to 4 steradians or approximately square degrees of solid angle . Thus it is the solid angle subtended by a complete sphere at its center. See also * Turn (angle) — the plane angle counterpart of the spat, equivalent to 2 radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...s References {{Reflist Units of solid angle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Degree
__NOTOC__ A square degree (deg2) is a non- SI unit measure of solid angle. Other denotations include ''sq. deg.'' and (°)2. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere. Analogous to one degree being equal to radians, a square degree is equal to ()2 steradians (sr), or about sr or about . The whole sphere has a solid angle of which is approximately : : 4 \pi \left(\frac\right)^2 \, ^2 = \frac\,\, ^2 = \frac \,\, ^2 \approx 41\,252.96 \,\, ^2 Examples * The full moon covers only about of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly ), so the moon's disk covers a circular area of: ()2, or 0.2 square degrees. The moon varies from 0.188 to depending on its distance to the Earth. * Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only as well. * It would take times the fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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