This study is aimed at demonstrating the numerical convergency of spectral polynomial approximations to the radiative transfer equation in spherical media. To this end, T-N method is employed as a representative of classical polynomial approximations to the corresponding pseudo-slab problem of spherical media radiative transfer equation. The method is used to calculate the albedo and density for isotropic scattering in a homogeneous spherical medium. Spherical harmonics or P-N method is also applied to the same problem for comparison purposes. Benchmark results of both methods for an absorbing and scattering spherical medium transfer problem are reported. The results contribute remarkable improvements to the previously reported data in the literature. More importantly, on contrary to some literature works, numerical divergence of spherical harmonics method in spherical media transfer problems is illustrated to be unsound provided that arbitrary precision arithmetic is available when considering higher order approximations.