The internal radiation of a planetary atmosphere

We show how to find the spherical harmonics moments of the radiation at any point within a homogeneous layer embedded in an inhomogeneous planetary atmosphere given only the moments at the boundaries of the layer. The result is used to determine the heating rate within a cloud in a realistic model atmosphere. It is also used to estimate the visibility of the ground from various points in the cloud as a function of view angle. The strength of the method is that the multiple scattering problem for the full atmosphere need be solved only, independently of the proposed applications.