Light Scattering from Saturn's Rings Calculated by a Markov Chain Formalism.

The theory of Markov chains is used to formulate the radiative transfer problem in a general way by modeling the successive interactions of a photon as a stochastic process. The speed and accuracy of this formalism have been verified for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard doubling routine. The generality of this formalism may thus allow fast, direct solutions to problems previously soluble only by Monte Carlo methods. Observations are presented of phase curves for both rings in four colors for Saturn's 1977 opposition and linear and logarithmic fits are made to the data.