Numerical investigation of the break-down threshold for a restricted three-body problem

Transition to chaos in the planar, circular, restricted three body problem is investigated. In particular, a model Hamiltonian suitable for the description of the motion of the asteroid Ceres is introduced. The break-down threshold of invariant surfaces (nearby the position of Ceres in phase space) is computed by means of different numerical methods, which allow to detect the transition from regular to chaotic motion. The experiments show that in the proximity of the location of the asteroid, invariant surfaces cease to exist for a mass ratio (between the perturbing body, Jupiter and the primary, the Sun) between 0.002 and 0.004. We remind that the real value of the above mass ratio is about 0.001 as derived from astronomical observations.