An analysis of the Sun-Earth-Asteroid systems based on the two-centre problem

We propose a new analysis of the two--centre problem particularly suited to be used as a basis to study the dynamics of Sun--Earth--Asteroid systems. Our method, based on a tricky choice of initial coordinates, allows us to evaluate the risk of collisions between the Asteroid and Earth. Moreover, it seems to be fitted to prove the existence of chains of transition tori in the planar Sun--Earth--Asteroid systems.