|
Chapman Function
300px, Graph of ch(x, z) A Chapman function describes the integration of atmospheric absorption along a slant path on a spherical earth, relative to the vertical case. It applies to any quantity with a concentration decreasing exponentially with increasing altitude. To a first approximation, valid at small zenith angles, the Chapman function for optical absorption is equal to :\sec(z),\ where ''z'' is the zenith angle and sec denotes the secant function. The Chapman function is named after Sydney Chapman, who introduced the function in 1931. Definition In an isothermal model of the atmosphere, the density \varrho(h) varies exponentially with altitude h according to the Barometric formula: :\varrho(h) = \varrho_0 \exp\left(- \frac h H \right), where \varrho_0 denotes the density at sea level (h=0) and H the so-called scale height. The total amount of matter traversed by a vertical ray starting at altitude h towards infinity is given by the integrated density ("column depth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chapman Function
300px, Graph of ch(x, z) A Chapman function describes the integration of atmospheric absorption along a slant path on a spherical earth, relative to the vertical case. It applies to any quantity with a concentration decreasing exponentially with increasing altitude. To a first approximation, valid at small zenith angles, the Chapman function for optical absorption is equal to :\sec(z),\ where ''z'' is the zenith angle and sec denotes the secant function. The Chapman function is named after Sydney Chapman, who introduced the function in 1931. Definition In an isothermal model of the atmosphere, the density \varrho(h) varies exponentially with altitude h according to the Barometric formula: :\varrho(h) = \varrho_0 \exp\left(- \frac h H \right), where \varrho_0 denotes the density at sea level (h=0) and H the so-called scale height. The total amount of matter traversed by a vertical ray starting at altitude h towards infinity is given by the integrated density ("column depth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barometric Formula
The barometric formula, sometimes called the ''exponential atmosphere'' or ''isothermal atmosphere'', is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals per meter in first 1000 meters above sea level. Pressure equations There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero: P = P_b \left frac\right The second equation is used when standard temperature lapse rate equals zero: P = P_b \exp \left frac\right/math> where: *P_b = reference pressure ( Pa) *T_b = reference temperature ( K) *L_b = temperature lapse rate (K/m) in ISA *h = height at which pressure is calculated (m) *h_b = height of reference level ''b'' (meters; e.g., ''hb'' = 11 000 m) *R^* = universal gas constant: 8.3144598 J/(mol·K) *g_0 = gravitational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ionosphere
The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an important role in atmospheric electricity and forms the inner edge of the magnetosphere. It has practical importance because, among other functions, it influences radio propagation to distant places on Earth. History of discovery As early as 1839, the German mathematician and physicist Carl Friedrich Gauss postulated that an electrically conducting region of the atmosphere could account for observed variations of Earth's magnetic field. Sixty years later, Guglielmo Marconi received the first trans-Atlantic radio signal on December 12, 1901, in St. John's, Newfoundland (now in Canada) using a kite-supported antenna for reception. The transmitting station in Poldhu, Cornwall, used a spark-gap transmitter to produce a signal with a freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atmospheric Physics
Within the atmospheric sciences, atmospheric physics is the application of physics to the study of the atmosphere. Atmospheric physicists attempt to model Earth's atmosphere and the atmospheres of the other planets using fluid flow equations, chemical models, radiation budget, and energy transfer processes in the atmosphere (as well as how these tie into boundary systems such as the oceans). In order to model weather systems, atmospheric physicists employ elements of scattering theory, wave propagation models, cloud physics, statistical mechanics and spatial statistics which are highly mathematical and related to physics. It has close links to meteorology and climatology and also covers the design and construction of instruments for studying the atmosphere and the interpretation of the data they provide, including remote sensing instruments. At the dawn of the space age and the introduction of sounding rockets, aeronomy became a subdiscipline concerning the upper layers of the atmo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Air Mass (astronomy)
In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere ( Green 1992). It is formulated as the integral of air density along the light ray. As it penetrates the atmosphere, light is attenuated by scattering and absorption; the thicker atmosphere through which it passes, the greater the attenuation. Consequently, celestial bodies when nearer the horizon appear less bright than when nearer the zenith. This attenuation, known as atmospheric extinction, is described quantitatively by the Beer–Lambert law. "Air mass" normally indicates ''relative air mass'', the ratio of absolute air masses (as defined above) at oblique incidence relative to that at zenith. So, by definition, the relative air mass at the zenith is 1. Air mass increases as the angle between the source and the zenith increases, reaching a value of approximately 38 at the horizon. Air mass can be less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when the Helmholtz equation is solved in spherical coordinates. Applications of Bessel functions The Bessel function is a generalizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth Radius
Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denoted ''a'') to a minimum of nearly (polar radius, denoted ''b''). A ''nominal Earth radius'' is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value. A globally-average value is usually considered to be with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the ''mean radius'' (R) of three radii measured at two equator points and a pole; the ''authalic radius'', which is the radius of a sphere with the same surface area (R); and the ''volumetric radius'', which is the radius of a sphere having the same volume as the ellipsoid (R). All three ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Height
In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter ''H'', is a distance (vertical or radial) over which a physical quantity decreases by a factor of e (the base of natural logarithms, approximately 2.718). Scale height used in a simple atmospheric pressure model For planetary atmospheres, scale height is the increase in altitude for which the atmospheric pressure decreases by a factor of ''e''. The scale height remains constant for a particular temperature. It can be calculated by :H = \frac or equivalently :H = \frac where: * ''k'' = Boltzmann constant = 1.38 x 10−23 J·K−1 * ''R'' = gas constant * ''T'' = mean atmospheric temperature in kelvins = 250 K for Earth * ''m'' = mean mass of a molecule (units kg) * ''M'' = mean mass of one mol of atmospheric particles = 0.029 kg/mol for Earth * ''g'' = acceleration due to gravity at the current location (m/s2) The pressure (force per unit area) at a given alt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1931
Events January * January 2 – South Dakota native Ernest Lawrence invents the cyclotron, used to accelerate particles to study nuclear physics. * January 4 – German pilot Elly Beinhorn begins her flight to Africa. * January 22 – Sir Isaac Isaacs is sworn in as the first Australian-born Governor-General of Australia. * January 25 – Mohandas Gandhi is again released from imprisonment in India. * January 27 – Pierre Laval forms a government in France. February * February 4 – Soviet leader Joseph Stalin gives a speech calling for rapid industrialization, arguing that only strong industrialized countries will win wars, while "weak" nations are "beaten". Stalin states: "We are fifty or a hundred years behind the advanced countries. We must make good this distance in ten years. Either we do it, or they will crush us." The first five-year plan in the Soviet Union is intensified, for the industrialization and collectivization of agriculture. * February 10 – Official ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absorption (electromagnetic Radiation)
In physics, absorption of electromagnetic radiation is how matter (typically electrons bound in atoms) takes up a photon's energy — and so transforms electromagnetic energy into internal energy of the absorber (for example, thermal energy). A notable effect is attenuation, or the gradual reduction of the intensity of light waves as they propagate through a medium. Although the absorption of waves does not usually depend on their intensity (linear absorption), in certain conditions (optics) the medium's transparency changes by a factor that varies as a function of wave intensity, and saturable absorption (or nonlinear absorption) occurs. Quantifying absorption Many approaches can potentially quantify radiation absorption, with key examples following. * The absorption coefficient along with some closely related derived quantities * The attenuation coefficient (NB used infrequently with meaning synonymous with "absorption coefficient") * The Molar attenuation coefficient (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sydney Chapman (astronomer)
Sydney Chapman (29 January 1888 – 16 June 1970) was a British mathematician and geophysicist. His work on the kinetic theory of gases, solar-terrestrial physics, and the Earth's ozone layer has inspired a broad range of research over many decades. Education and early life Chapman was born in Eccles, near Salford in England and began his advanced studies at a technical institute, now the University of Salford, in 1902. In 1904 at age 16, Chapman entered the University of Manchester. He competed for a scholarship to the university offered by his home county, and was the last student selected. Chapman later reflected, "I sometimes wonder what would have happened if I'd hit one place lower." He initially studied engineering in the department headed by Osborne Reynolds. Chapman was taught mathematics by Horace Lamb, the Beyer professor of mathematics, and J. E. Littlewood, who came from Cambridge in Chapman's final year at Manchester. Although he graduated with an engineerin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secant Function
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis. The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend the sine and cosi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
