An analytic ID spherical time dependent solution for the spectrum of a sphere radiating into a surrounding semi-infinite material of arbitrary opacity but uniform material temperature is presented. Two solutions are presented. One is for the frequency dependent or multi-group diffusion equation and the other is for the transport equation. The solution is exact for non-participating media. It is also valid for participating media in the prompt or early phase where the gradient of the matter temperature in the surrounding medium is near zero. A companion paper presents a comparison between the analytic and numerical solutions for several realistic opacities. The solution should prove useful for benchmarking multi-group diffusion and transport codes.
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