An Etymological Dictionary of Astronomy and Astrophysics

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory



Number of Results: 13 Search : approximation

Fr.: 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 Boussinesq

Fr.: 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 naxost

Fr.: 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 xatti

Fr.: 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 payâpey

Fr.: 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-Eddington

Fr.: 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 Newtoni

Fr.: 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.

Newtonian; → approximation.

on-the-spot (OTS) approximation
  نزدینش ِ درجا   
nazdineš-e darjâ


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-parâkaneš


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 dovom

Fr.: 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 Sobolev

Fr.: 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 Stirling

Fr.: 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 Weierstrass

Fr.: 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.