A Monte Carlo approach to scattering off surfaces of triaxial ellipsoids

We developed a Monte Carlo procedure to calculate the scattering properties of ellipsoidal bodies. Although originally intended for application to Saturn's ring A, the technique can also be applied to surfaces of asteroids modeled as triaxial ellipsoids. A simple coordinate transformation allows the Monte Carlo approach to be quick and efficient. By modifying the well-known acceptance-rejection technique to reflect the dependence of surface albedo on the angle of incidence, we can apply this technique to any surface scattering function. The backscattered brightness and the phase curve at small phase angles can be calculated to a high degree of accuracy in a small amount of computing time. The technique is shown to be accurate for problems that have analytic solutions. Light curve amplitudes of biaxial ellipsoids as a function of the axial ratio are plotted for several scattering laws. The application of this technique to a direct integration approach is also considered.