We consider the planar circular restricted three-body problem for small values of the mass ratio μ. Unperturbed problem (i.e. the two-body problem in the rotating frame) has singular perturbations, related with the body with mass μ, near the body and near a family of stationary points. Here we select the first approximations of the system near these singularities and propose the changes of coordinates which transform the first approximations into unperturbed systems.

Mathematical problems and theory of numerical methods