Regularization of the Circular Restricted Three Body Problem on Surfaces of Constant Curvature

We consider a restricted three body problem on surfaces of constant curvature. As in the classical Newtonian case the collision singularities occur when the position particle with infinitesimal mass coincides with the position of one of the primaries. We prove that the singularities due to collision can be locally (each one separately) and globally (both as the same time) regularized through the construction of Levi-Civita and Birkhoff type transformations respectively. As an application we study some general properties of the Hill’s regions and we present some ejection–collision orbits for the symmetrical problem.