A Computational Approach to Chandrasekhar's Planetary Problem

摘要

Chandrasekhar's planetary problem is reformulated using an initial-value approach. The problem concerns the diffuse reflection of radiation from a finite atmosphere with a reflecting surface at the bottom. In the direct problem, the angular distribution of multiple-scattered radiation is computationally obtained as the solution of an initial-value problem for ordinary differential equations for S, a generalization of the Chandrasekhar scattering function for an inhomogeneous atmosphere. In the inverse planetary problem, the properties of the atmosphere and the surface are to be estimated, given the angular distribution of scattered radiation. The quasilinearization technique for nonlinear multipoint boundary-value problems provides an effective method for obtaining a computational solution to the inverse problem. A FORTRAN program for both the direct and inverse problems is presented in the Appendix. (Author)