Abstract
I present the first complete analytical solution to finding the specular point on a spherical surface, known as the Alhazen-Ptolemy problem, for the cases where either the observer of the light source may be approximated as infinitely distant, and where they must both be treated as finitely distant. I also present Vulcan, a new orbital integration code which offers the benefits of modernization to existing orbital integration algorithms: efficient parallelization, advanced memory management, and concurrent output. Lastly, I present my work compiling the Titan data from Cassini’s Visible Infrared Mapping Spectrometer (VIMS) instrument to create a set of composite maps which summarize the dataset for future work.