  The atmospheres of planets (including Earth) and the outer layers of stars
have often been treated in radiative transfer as plane-parallel media, instead
of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give
an exact solution of the radiative transfer specific intensity at all points
and directions in a finite spherical medium having arbitrary radial spectral
distribution of: source (temperature), absorption, emission and anisotropic
scattering. The power and efficiency of the method stems from the spherical
numerical gridding used to discretize the transfer equations prior to matrix
solution: the wanted ray and the rays which scatter into it both have the same
physico-geometric structure. Very good agreement is found with an isotropic
astrophysical benchmark (Avrett & Loeser, 1984). We introduce a specimen
arbitrary forward-back-side phase scattering function for future comparisons.
Our method directly and exactly addresses spherical symmetry with anisotropic
scattering, and could be used to study the Earth's climate, nuclear power
(neutron diffusion) and the astrophysics of stars and planets.
