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The Eddington approximation is a relatively-easy-to-work-with description of electromagnetic radiation's variation by direction (anisotropy, departure from isotropic), used in modeling stellar structure. Assuming isotropy could make modeling even simpler, but would fail to (realistically?) transfer energy toward the surface where it is emitted as starlight. The Eddington approximation assumes there is a general transfer of energy outward from the middle of the star ("up"), and models the intensity of radiation in each direction such as to do that, by specifically modelling slightly more energy transfer in "upward" (outward) directions than in "downward" (inward). It does this by using separate equations for energy transferred in any upward direction versus any downward: using separate equations adds complication, yet is tractable than more realistic approaches. It is one of the approximations developed to make the modeling of stars practical and can be considered an example of a two-stream approximation. I believe the Eddington approximation represents a simplified model yielding the net effect of the slow outward diffusion of inherent in the photons' random walks. The method has been refined over time, and variants have been developed that trade away some of the simplicity for more realism.