The origins of the Martian moons — Phobos and Deimos — are currently unknown. Origins hypotheses suggest that they are either (1) captured objects from the outer solar system, (2) re-accreted debris from an ancient giant impact, or (3) left over from Mars’ formation. A common means of classifying extraterrestrial bodies (i.e. meteorites) is through a measurement of relative elemental abundances. However, sample return from Phobos and Deimos would be both costly and risky, while optical spectroscopy does not provide sufficient information for this type of compositional analysis. A robust and sensitive technique for obtaining elemental composition of small bodies exposed to radiation is the collection and analysis of sputtered secondary ions using ion mass spectrometry (IMS). Frequently used for laboratory characterization, as well as characterization of ions in space, IMS can achieve excellent signal to noise ratios due to low backgrounds and high detection sensitivities. In order to better understand the potential for IMS to determine the composition of Phobos and Deimos, we carried out a series of Monte Carlo simulations using the SDTrimSP program to estimate the total sputtering yields under both solar wind and Mars magnetosphere irradiation conditions. Experimental secondary-ion measurements were used to determine the element-specific relative ion yields and velocity distributions of ejected ions. After correcting the total yields by the relative secondary ion abundances, estimated sputtered-ion fluxes and measured velocities were then used in Monte Carlo particle tracing simulations to estimate the spatially-resolved secondary-ion densities around Phobos and Deimos. We demonstrate that sufficient secondary ions are sputtered to allow for rapid detection and compositional characterization of Phobos and Deimos, and provide quantitative prediction of the sputtered secondary-ion fluxes from these bodies in preparation for future measurement (e.g. by the JAXA MMX mission). The figure (left) gives the solar-wind sputtered Mg+ density around an 11km diameter airless body subject to the ambient IMF, and (right) analysis of how the sputtered ion ratios can be used to determine the most likely origin for these bodies.