The dynamic properties of loose sands under low stresses have been poorly investigated because of the higher order of magnitude of stress levels in terrestrial geotechnical structures. However, low densities and low stresses prevail in the sandy surface deposits of some other rocky planets, making low stress conditions relevant for extra-terrestrial soil mechanics. This is the case of Mars, on the surface of which a seismometer has been placed during the InSight mission. In this context, a dynamic shear rheometer was used to measure the shear modulus and damping ratio of a Martian regolith simulant under very low stresses to improve the interpretation of the InSight dataset on surface materials. This paper also revisits the grain contact stiffness and the overall modulus of a random packing of identical spheres, based on the Hertz-Mindlin contact theory. A micromechanical model accounting for the effects of both grain roughness and slipping in the soil degradation curve is proposed. The results of the model show a good agreement with experimental data, capturing the non-linear transition from low to high-shear strains. The model hence provides a new framework for a better understanding of the behaviour of granular materials in low gravity (extra-terrestrial) conditions.