Asteroid families are formed as the result of collisions. Fragments of the collision are ejected with terminal ejection velocities of the order of the escape velocity from the parent body. After the family formation, the fragments orbits evolve in space because of gravitational and non-gravitational effects, such as the Yarkovsky effect2. Disentangling the contribution to the current orbital position of family members caused by the initial ejection velocity field and the subsequent orbital evolution is not always an easy task15,16. The Yarkovsky effect strengths depend on parameters, such as the asteroid density and thermal conductivity, that are not always known with high precision. Age estimates may therefore be affected by large errors, depending on which values of the
Yarkovsky affecting parameters are chosen13. Among the more than 100 asteroid families currently known, some interact with linear and non-linear secular resonances. Linear secular resonances occurs when there is a commensurability between the precession frequency of the longitude of the pericenter (g) or of the longitude of node (s) of an asteroid and a planet, or a massive asteroid14. The linear secular resonance most effective in increasing an asteroid eccentricity is the ν6 secular resonance, that corresponds to a commensurability between the precession frequency g of an asteroid and Saturn.
Non-linear secular resonances involve commensurabilities of higher order, and can often be expressed as combinations of linear secular resonances3,4. This is the case, for instance, of the zk=k(g-g6)+s-s6 resonances. Asteroid families that have a large portion of their members in secular resonant states are of particular interest in dynamical astronomy. Conserved quantities of secular dynamics can be used to set independent constraints on the magnitude of the original ejection velocity field16,5,6,7. For the case of the ν6 secular resonance, objects in anti-aligned librating states (or in paradoxal libration, according to other authors12), can be prevented to achieve high values of eccentricity, and remain stable in unstable region, as is the case for members of the Tina family6. Finally, by increasing the value of inclination of family members, and, indirectly, of the vW component of the observed ejection velocity field, nodal secular resonances with massive asteroids or dwarf planets, such as the s-sC secular resonance with Ceres, can cause vW to become more and more leptokurtic, i.e., more peaked and with larger tails than that of a Gaussian distribution8. By simulating fictitious asteroid families and by requiring that the current value of the Pearson kurtosis of vW,, γ2(vW), be attained, independent constraints on the value of families ages can be obtained for families affected by these kinds of resonances9,10,11,1. In this talk we will briefly revise some recent results on asteroid families affected by secular resonances, and discuss the use of the γ2(vW) parameter to set independent constraints on families ages9,10,11,1.