Transient radiative cooling of a solid or liquid sphere in space, surrounded by a radiatively participating vapor cloud, is considered. A quasi-steady assumption is applied to the radiation transfer in the medium, with the unsteadiness being retained at the inner spherical boundary. The problem is solved by applying the third-order (P3) spherical harmonics approximation to the radiative transfer equation for the participating cloud, and a finite difference scheme for transient conduction in the sphere. In general, the presence of a participating medium decreases the cooling rate of the sphere, and cooling curves are presented to show this effect. Effective emissivity of the surface in the presence of a surrounding medium is evaluated, and an approximate explicit equation is given.

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