A Caltech Library Service

Radiative transfer in a sphere illuminated by a parallel beam - an integral equation approach

Shia, Run-Lie and Yung, Yuk L. (1986) Radiative transfer in a sphere illuminated by a parallel beam - an integral equation approach. Astrophysical Journal, 301 (2). pp. 554-570. ISSN 0004-637X. doi:10.1086/163923.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. Our analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the inter-connection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems are provided.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle
Shia, Run-Lie0000-0003-1911-3120
Yung, Yuk L.0000-0002-4263-2562
Additional Information:© 1986 American Astronomical Society. Provided by the NASA Astrophysics Data System. Received 1985 February 15; accepted 1985 June 4. We thank K. S. K. Chow, L. W. Esposito, A. J. Friedson, R. M. Goody, and N. D. Sze for helpful discussions. The search for a variational principle for the planetary problem was assigned as one of the research topics in Professor R. M. Goody's class on atmospheric radiation at Harvard in 1972. The length of time it has taken to solve the problem is perhaps a measure of the sagacity of the master and the stupidity of the pupil (Y. L. Y.). The research is supported by NASA grant NSG 7376 under the Planetary Atmospheres Program.
Funding AgencyGrant Number
Subject Keywords:planets: atmospheres - radiative transfer
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences4084
Issue or Number:2
Record Number:CaltechAUTHORS:20140908-150910488
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49357
Deposited By: Tony Diaz
Deposited On:08 Sep 2014 23:40
Last Modified:10 Nov 2021 18:42

Repository Staff Only: item control page