Modeling the Dielectric Properties of Minerals from Crystals to Bulk Powders for Improved Interpretation of Asteroid Radar Observations

Planetary radar has provided a growing number of data sets on the inner planets and near-Earth and main belt asteroid populations in the solar system. Physical interpretation of radar data for inference of surface properties requires constraints on the constitutive parameters of the material making up a given surface. In this study, the complex permittivity of seven minerals as a function of frequency and porosity is measured using the coaxial transmission line method to determine the mixing equation that best describes the relationship between the real part of the complex permittivity of single mineral crystals and granular mineral powders. We find the Looyenga-Landau-Lifshitz and Bruggeman symmetric mixing equations to describe our experimental results with the highest accuracy. The variation in the real part of the permittivity of solid mineral crystals between different minerals is shown to depend on the grain density and the chemical composition of the minerals. These mixing relationships are incorporated into an asteroid radar model and used to calculate the porosity in the near-surface of seven asteroids visited by robotic spacecraft using Earth-based radar observations. The results of the asteroid radar model support the presence of significant porosity in the boulders on the surface of asteroid 101955 Bennu. This research highlights the ability of radar to measure the porosity on asteroid surfaces and provides theoretical and experimental justification for the inversion of permittivity to bulk density assumed by the asteroid radar model. Plain Language Summary Radar observations of planets, the Moon, and asteroids provide information about the upper surface, within a few tens of centimeters to meters, such as the electrical properties of this material. In this study, these electrical properties are measured in the laboratory for seven mineral samples under environmental conditions expected for planetary surfaces. Several well-known mixing equations are tested for their accuracy in modeling the change in the measured electrical properties with the change in the porosity, or amount of empty space, in the samples. We incorporate two of these mixing equations into an asteroid radar model that converts the measured electrical properties of radar-observed asteroids to the density of the surface material. Our model predicts low surface density for seven asteroids observed by Earth-based radar telescopes, such as Arecibo Observatory. Space missions such as the National Aeronautics and Space Administration's OSIRIS-REx and the Japanese Aerospace Exploration Agency's Hayabusa2 missions visiting asteroids will provide ground-truth observations of these asteroids' surface properties, such as density, for validating our models. The density of the surfaces of asteroids provides information about the possible structure and evolutionary history of asteroids, and the early solar system.