An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

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.

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.

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: e^x≅ 1 + x. Also called → linear approximation.

→ first; → approximation.

Taking the first term in the Taylor series as an approximation to a mathematical function at a given point. → first approximation.

→ linear; → approximation.

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.

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.

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.

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-.

A model of radiative transfer that ignores forward scattering of photons; assuming forward-scattered light as un-scattered.

→ quasi-; → single; → scattering; → approximation.

Math: In calculus, limiting an equation to its → second derivative, for example: e^x≅ 1 + x + x²/2. Also called linear approximation. → first approximation.

→ second; → approximation.

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 > v_th/l, where dv/dr is the velocity gradient, v_th 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.

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.

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.