An Etymological Dictionary of Astronomy and Astrophysics
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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.