  The first integral characteristic of the two--centres problem is proven to be
an approximate integral (in the sense of N.N.Nekhorossev) to the three--body
problem, at least if the masses are very different and the particles are
constrained on the same plane. The proof uses a new normal form result,
carefully designed around the degeneracies of the problem, and a new study of
the phase portrait of the unperturbed problem. Applications to the prediction
of collisions between the two minor bodies are shown.
