# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 13 Search : approximation
 approximation   نزدینش   nazdinešFr.: approximation   1) General: A guess or estimate; nearness in space, position, degree. 2) Math., Physics: Result that is not quite exact, but is within the limits of accuracy required for a given purpose.Approximation, verbal noun of → approximate.Nazdineš, verbal noun of nazdinidan, → approximate. Boussinesq approximation   نزدینش ِ بوسینسک   nazdineš-e BoussinesqFr.: approximation de Boussinesq   A simplification in the equations of → hydrodynamics that treats the density as constant except in the → buoyancy term. This approximation is motivated by the fact that when pressure and temperature differences in a flow are small, then it follows from the thermodynamic → equation of state that a change in the density is also small.Named after Joseph Valentin Boussinesq (1842-1929), a French physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat; → approximation. first approximation   نزدین ِ نخست   nazdin-e naxostFr.: première approximation   1) Generally, an expression to indicate that a comment or result is only approximate. 2) Math.: In calculus, limiting a differential equation to its → first derivative, for example: ex≅ 1 + x. Also called → linear approximation.→ first; → approximation. linear approximation   نزدینش ِ خطی   nazdineš-e xattiFr.: approximation linéaire   Taking the first term in the Taylor series as an approximation to a mathematical function at a given point. → first approximation.→ linear; → approximation. method of successive approximations   روش ِ نزدینش‌های ِ پیاپی   raveš-e nazdinešhâ-ye payâpeyFr.: méthode d'approximations successives   The solution of an equation or by proceeding from an initial approximation to a series of repeated trial solutions, each depending upon the immediately preceding approximation, in such a manner that the discrepancy between the newest estimated solution and the true solution is systematically reduced.→ method; → successive; → approximation. Milne-Eddington approximation   نزدینش ِ میلن-ادینگتون   nazdineš-e Milne-EddingtonFr.: approximation de Milne-Eddington   The approximation of a stellar atmosphere with a plane parallel grey atmosphere in radiative equilibrium. It is assumed that a spectral is formed in such a way that the ratio of the line absorption coefficient to the continuous absorption coefficient is constant with depth.→ Milne Universe; Arthur Stanley Eddington (1882-1944), prominent British astrophysicist; → approximation. Newtonian approximation   نزدینش ِ نیوتنی   nazdineš-e NewtoniFr.: approximation newtonienne   A particular solution of the → general relativity when the → gravitational mass is small. The → space-time is then approximated to the → Minkowski's and this leads to → Newtonian mechanics. on-the-spot (OTS) approximation   نزدینش ِ درجا   nazdineš-e darjâFr.:   An approximation in the treatment of photoionized → H II regions, whereby secondary ionizing photons are absorbed immediately very close to their site of emission. The secondary photons, produced by → radiative recombinations directly to the → ground states, are thus ignored with respect to the ionizing photons emitted by the → exciting star. The OTS approximation requires that the ionized gas be sufficiently dense so that secondary ionizing photons are very likely absorbed within the H II region.→ on; → spot; → approximation.Nazdineš, → approximation; dar "in," from Mid.Pers. andar, → intra-. quasi-single-scattering approximation   نزدینش ِ چونان-تک‌پراکنش   nazdineš-e cunân-tak-parâkanešFr.:   A model of radiative transfer that ignores forward scattering of photons; assuming forward-scattered light as un-scattered.→ quasi-; → single; → scattering; → approximation. second approximation   نزدینش ِ دوم   nazdineš-e dovomFr.: deuxième approximation   Math: In calculus, limiting an equation to its → second derivative, for example: ex≅ 1 + x + x2/2. Also called linear approximation. → first approximation.→ second; → approximation. Sobolev approximation   نزدینش ِ سوبولف   nazdineš-e SobolevFr.: approximation de Sobolev   A method allowing for a simplified solution to the → radiative transfer equation at frequencies of spectral lines in media moving with a high velocity gradient. This method assumes that the macroscopic velocity gradients are more important than local random variations of thermal line width: dv/dr > vth/l, where dv/dr is the velocity gradient, vth is the thermal broadening of the line, and l the length scale. The Sobolev approximation is only valid if the conditions of the gas do not change over the → Sobolev length. Under the Sobolev approximation, each point in the medium is isolated from other points, and the → radiative transfer problem becomes a local one and therefore much easier to solve.Named after the Russian astronomer Viktor Viktorovich Sobolev, Moving Envelopes of Stars [in Russian], Leningr. Gos. Univ., Leningrad (1947) [translated by S. Gaposchkin, Harvard Univ. Press, Cambridge, Mass. (1960)]; → approximation. Stirling's approximation   نزدینش ِ استرلینگ   nazdineš-e StirlingFr.: approximation de Stirling   A mathematical formula yielding an approximate value for → factorial n, when n is large: n! ≅ (2πn)1/2nne-n, where e is the base of → natural logarithm.Named after James Stirling (1692-1770), a Scottish mathematician; → approximation. Weierstrass approximation theorem   فربین ِ نزدینش ِ وایرشتراس   farbin-e nazdineš-e WeierstrassFr.: théorème d'approximation de Weierstrass   If a function φ(x) is continuous on a closed interval [a,b], then for every ε > 0 there exists a polynomial P(x) such that |f(x) - P(x)| <ε, for every x in the interval.After German mathematician Karl Wilhelm Theodor Weierstrass (1815-1897); → approximation; → theorem.