The Mean Moment of Inertia for Irregularly Shaped Phobos and Its Application to the Constraint for the Two-Layer Interior Structure for the Martian Moon

Abstract

The interior structure of Phobos has been the subject of debate in recent years, with the moment of inertia being a determining factor. To study this structure, we modeled Phobos with a two-layer structure and calculated its mean density and moment of inertia using updated gravity coefficients of degree-2 and forced libration amplitudes. By minimizing the misfit between modeled and derived moment of inertia, and observed and modeled mean density, we determined the frequency distribution for estimated parameters, including the core radius rc, core density ρc, and density ρm of the outer layer. Our results indicate that the optimized core radius is around 8.2 km for our models, along with a core density compromise of approximately 2500 kg·m−3, and an outer layer density of around 1400 kg·m−3. These values have remarkable sensitivity to the misfit function, implying a higher density likely inside Phobos compared to the outer layer. Given that the large core density was associated with ice content, it suggested that the fractional ice content in the outer layer is approximately 11% with a rock density of 2200 kg·m−3, while the content in the core is lower at 2.4% with a rock density of 3000 kg·m−3. The methodology introduced in this study can be further used to study the interior structure of irregularly shaped asteroids.