Abstract
The project aims to study the dynamical evolution of a family of asteroids formed from a fully differentiated parent body, considering family members with different physical properties consistent with what is expected from the break up of a body formed by a metallic nucleus surrounded by a rocky mantle. Initially, we study the effects of variations in density, bond albedo, and thermal inertia in the semi-major axis drift caused by the Yarkovsky effect. The Yarkovsky effect is a non-conservative force caused by the thermal re-radiation of the solar radiation by an irregular body. In Solar System bodies, it is known to cause changes in the orbital motions (Peterson, 1976), eventually bringing asteroids into transport routes to near-Earth space, such as some mean motion resonances. We expressed the equations of variation of the semi-major axis directly in terms of physical properties (such as the mean motion, frequency of rotation, conductivity, thermal parameter, specific heat, obliquity and bond albedo). This development was based on the original formalism for the Yarkovsky effect (i.e., Bottke et al., 2006 and references therein). The derivation of above equations allowed us to closely study the variation of the semi-major axis individually for each physical parameter, clearly showing that the changes in semi-major axis for silicate bodies is twice or three times greater than for metal bodies. The next step was to calculate the orbital elements of a synthetic family after the break-up. That was accomplished assuming that the catastrophic disruption energy is given by the formalism described by Stewart and Leinhardt (2009) and assuming an isotropic distribution of velocities for the fragments of the nucleus and the mantle. Finally, the orbital evolution of the fragments is implemented using a simpletic integrator, and the result compared with the distribution of real asteroid families.
