The thermal emission and temperatures of the main rings of Saturn depend on the energy the ring particles absorb, reflect and scatter and/or on their Bond albedo, emissivity, thermal inertia, rotation rate and porosity. However, the energy that each particle absorbs also depends on the amount of energy (e.g., solar energy) that reaches its surface and this latter on the local optical depth, that controls the mutual eclipsing between neighbouring particles and, in general, all shadowing effects on the rings. On the other hand, thermal models of the rings of Saturn based on the energy balance equation strongly depend on a function that described how the non-shadowed area of ring particles changes with solar elevation. Experimental and analytical shadowing functions have been proposed by [6] and [1], respectively. In this work, we propose shadowing functions based on the creation of 3D arrays of spherical particles that simulate specific regions of the main rings of Saturn. The methods implemented to obtain these shadowing functions follow the next general steps:
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