Instability zones for satellites of asteroids: The example of the (87) Sylvia system

The stability of the (87) Sylvia system and of the neighborhood of its two satellites is investigated. We use numerical integrations considering the non-sphericity of Sylvia, as well as the mutual perturbation of the satellites and the solar perturbation. Two numerical models have been used, which describe respectively the short and long-term evolution of the system. We show that the actual system is in a deeply stable zone, but surrounded by both fast and secular chaotic regions due to mean-motion and evection resonances. We then investigate how tidal and BYORP effects modify the location of the system over time with respect to the instability zones. The conclusion is that the system will cross the evection resonance before 1 Gyr. eralize this study to other known triple systems, investigate possible evolutions of the systems under tidal and BYORP effects, and discuss their distance from instability regions. In particular, it is possible to show how systems in a joint opposing evolution can be destroyed depending on the masses of the satellites and their dissipative parameters.