Asteroids, or more formally, Small Solar System Bodies, offer a wealth of scientific knowledge and, increasingly, economic potential. Regrettably, because of their small size and the fact that the largest groups of asteroids in the solar system are situated tens of millions of kilometers from Earth, ground based observations yield limited data, mostly confined to surface characteristics. To date, space missions traveling to asteroids, or other SSSBs, have also been principally focused upon collecting data from the surface, or within approximately 2m thereof. More penetrative interior survey methods exist in terrestrial application, but methods like seismology and core drilling would require specific equipment and direct landing on the asteroid. Muography potentially presents a means of going in-between these two extremes of the study of asteroid interiors. High energy galactic cosmic ray primaries constantly, and randomly, impact all objects in the solar system, generating secondary showers of particles when they interact with stationary matter. Of primary interest to this project, unsurprisingly, are muons. These particles have a considerable mass, are generally very energetic (>200 MeV), and exist in positive or negative species with a charge magnitude equal to that of 1 electron. These factors contribute to a very low energy loss through conventional mechanisms like ionization,bremsstrahlung, or pair production, making muons very penetrative. Their high energy, highly penetrative nature, and relative abundance as GCR secondaries present an opportunity to perform radiography of the inside of rocks of very large dimensions. Prettyman et al, who have performed initial analyses of the space-bourne tomographic methodology itself, estimate that the interior of asteroids up to 1km in diameter may be surveyed with this technique. This thesis details the project of a feasibility study for a small-scale hodoscopic detector of the type that could be flown with a somewhat standardized satellite bus no larger than the commonly-used ”small” or ”micro” satellite categories for use in just such muography.