By means of extensive three-dimensional contact dynamics simulations, we analyse the strength properties and microstructure of a granular asteroid, modelled as a self-gravitating cohesive granular aggregate composed of spherical particles, and subjected to di-ametrical compression tests. We show that, for a broad range of system parameters (shear rate, cohesive forces, asteroid diameter), the behaviour can be described by a modified inertial number that incorporates interparticle cohesion and gravitational forces.