Limb Darkening
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Limb Darkening
Limb darkening is an optical effect seen in stars (including the Sun), where the central part of the disk appears brighter than the edge, or ''limb''. Its understanding offered early solar astronomers an opportunity to construct models with such gradients. This encouraged the development of the theory of radiative transfer. Basic theory Optical depth, a measure of the opacity of an object or part of an object, combines with effective temperature gradients inside the star to produce limb darkening. The light seen is approximately the integral of all emission along the line of sight modulated by the optical depth to the viewer (i.e. 1/e times the emission at 1 optical depth, 1/e2 times the emission at 2 optical depths, etc.). Near the center of the star, optical depth is effectively infinite, causing approximately constant brightness. However, the effective optical depth decreases with increasing radius due to lower gas density and a shorter line of sight distance through the ...
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2012 Transit Of Venus From SF
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by  2, although by other definitions 1 is the second natural number, following  0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is ...
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Solar Atmosphere
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radiation, and is the most important source of energy for life on Earth. The Sun's radius is about , or 109 times that of Earth. Its mass is about 330,000 times that of Earth, comprising about 99.86% of the total mass of the Solar System. Roughly three-quarters of the Sun's mass consists of hydrogen (~73%); the rest is mostly helium (~25%), with much smaller quantities of heavier elements, including oxygen, carbon, neon, and iron. The Sun is a G-type main-sequence star (G2V). As such, it is informally, and not completely accurately, referred to as a yellow dwarf (its light is actually white). It formed approximately 4.6 billionAll numbers in this article are short scale. One billion is 109, or 1,000,000,000. years ago from the gravita ...
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Analytic Expression
In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions may vary with author and context. Example: roots of polynomials The solutions of any quadratic equation with complex coefficients can be expressed in closed form in terms of addition, subtraction, multiplication, division, and square root extraction, each of which is an elementary function. For example, the quadratic equation :ax^2+bx+c=0, is tractable since its solutions can be expressed as a closed-form expression, i.e. in terms of elementary functions: :x=\frac. Similarly, solutions of cubic and quartic (third and fourth degree) equations can be expr ...
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Lambert's Cosine Law
In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle ''θ'' between the direction of the incident light and the surface normal; I = I0cos(''θ'').RCA Electro-Optics Handbook, p.18 ffModern Optical Engineering, Warren J. Smith, McGraw-Hill, p. 228, 256 The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his '' Photometria'', published in 1760. A surface which obeys Lambert's law is said to be ''Lambertian'', and exhibits Lambertian reflectance. Such a surface has the same radiance when viewed from any angle. This means, for example, that to the human eye it has the same apparent brightness (or luminance). It has the same radiance because, although the emitted power from a given area element is reduced by the cosine of the emission angle, ...
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Limb Darkening Geometry
Limb may refer to: Science and technology *Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, the border or upper spreading part of a petal or sepal *Limb, in a measuring instrument, the graduated edge of a circle or arc Music * ''Limb'' (album), by Foetus, 2009 *''Limb'', an album by Justin Clayton, 1999 *"Limbs", a song by Emma Pollock from ''Watch the Fireworks'', 2007 *Limb Music, a German record label Other uses * Limb (surname), a list of people * Limb McKenry (1888–1956), American baseball pitcher *Limb Brook, a stream in Sheffield, South Yorkshire, England * Limbs Dance Company, in Auckland, New Zealand *Limbs, in archery, the upper and lower working parts of the bow; see recurve bow * Bresso Airfield, Bresso, Italy (ICAO code) *Limbu script (ISO 15924 code) See also * Limb darkening Limb darkening is an optical e ...
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Solar Corona
A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma. The Sun's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar eclipse, but it is also observable with a coronagraph. Spectroscopic measurements indicate strong ionization in the corona and a plasma temperature in excess of , much hotter than the surface of the Sun, known as the photosphere. The word ''corona'' is , in turn derived . History In 1724, French-Italian astronomer Giacomo F. Maraldi recognized that the aura visible during a solar eclipse belongs to the Sun, not to the Moon. In 1809, Spanish astronomer José Joaquín de Ferrer coined the term 'corona'. Based in his own observations of the 1806 solar eclipse at Kinderhook (New York), de Ferrer also proposed that the corona was part of the Sun and not of the Moon. English astronomer Norman Lockyer identified the first element unknown ...
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Kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point. Historically, the Kelvin scale was developed by shifting the starting point of the much-older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant to be exactly . Hence, one kelvin is equal to a change in the thermodynamic temperature that results in a change of thermal energy by . The temperature in degree Celsius is now defined as the temperature in kelvins minus 273.15, meaning ...
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Radio Wave
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (shorter than a grain of rice); at 30 Hz the corresponding wavelength is (longer than the radius of the Earth). Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and in the Earth's atmosphere at a close, but slightly lower speed. Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects, and are part of the blackbody radiation emitted by all warm objects. Radio waves are generated artificially by an electronic device called a transmitter, which is connected to an antenna which radiates the waves. They are received by another antenna connected to a radio receiver, ...
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Far-infrared
Far infrared (FIR) is a region in the infrared spectrum of electromagnetic radiation. Far infrared is often defined as any radiation with a wavelength of 15 micrometers (μm) to 1 mm (corresponding to a range of about 20  THz to 300 GHz), which places far infrared radiation within the CIE IR-B and IR-C bands. The long-wave side of the FIR spectrum overlaps with so named terahertz radiation. A.Glagoleva-Arkadiewa. (1924). "Short Electromagnetic Waves of wave-length up to 82 Microns". ''Nature'' 2844 113. do10.1038/113640a0/ref> Different sources use different boundaries for the far infrared; for example, astronomers sometimes define far infrared as wavelengths between 25 μm and 350 μm. Visible light includes radiation with wavelengths between 400 nm and 700 nm, meaning that far infrared photons have tens to hundreds of times less energy than visible light photons. Applications Astronomy Due to black-body radiation, objects with temper ...
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Spectral Line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules. These "fingerprints" can be compared to the previously collected ones of atoms and molecules, and are thus used to identify the atomic and molecular components of stars and planets, which would otherwise be impossible. Types of line spectra Spectral lines are the result of interaction between a quantum system (usually atoms, but sometimes molecules or atomic nuclei) and a single photon. When a photon has about the right amount of energy (which is connected to its frequency) to allow a change in the energy state of the system (in the case of an atom this is usually an electron changing orbitals), the photon is absorbed. Then the energy will be spontaneously re-emitted, either as one photon at the same frequ ...
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Limb
Limb may refer to: Science and technology *Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, the border or upper spreading part of a petal or sepal *Limb, in a measuring instrument, the graduated edge of a circle or arc Music * ''Limb'' (album), by Foetus, 2009 *''Limb'', an album by Justin Clayton, 1999 *"Limbs", a song by Emma Pollock from ''Watch the Fireworks'', 2007 *Limb Music, a German record label Other uses * Limb (surname), a list of people * Limb McKenry (1888–1956), American baseball pitcher *Limb Brook, a stream in Sheffield, South Yorkshire, England * Limbs Dance Company, in Auckland, New Zealand *Limbs, in archery, the upper and lower working parts of the bow; see recurve bow * Bresso Airfield, Bresso, Italy (ICAO code) *Limbu script (ISO 15924 code) See also * Limb darkening Limb darkening is an optical e ...
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Stellar Atmosphere
The stellar atmosphere is the outer region of the volume of a star, lying above the stellar core, radiation zone and convection zone. Overview The stellar atmosphere is divided into several regions of distinct character: * The photosphere, which is the atmosphere's lowest and coolest layer, is normally its only visible part. Light escaping from the surface of the star stems from this region and passes through the higher layers. The Sun's photosphere has a temperature in the 5,770  K to 5,780 K range. Starspots, cool regions of disrupted magnetic field lie on the photosphere. * Above the photosphere lies the chromosphere. This part of the atmosphere first cools down and then starts to heat up to about 10 times the temperature of the photosphere. * Above the chromosphere lies the transition region, where the temperature increases rapidly on a distance of only around 100 km. * The outermost part of the stellar atmosphere is the corona, a tenuous plasma which has ...
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