The restricted three body problem revisited

The restricted three body problem deals with the Lyapunov stability of the Lagrangian configuration of a system of three bodies in vertices of an equilateral triangle. Two of the bodies (Sun and Jupiter) rotate along circular orbits and the third body (asteroid) has small mass. The stability follows from the KAM theory, under certain semi-algebraic genericity condition. I will present some calculations related with the latter condition.