On the restricted three body problem with oblate primaries

We present a study of the Lagrangian triangular equilibria in the planar restricted three body problem where the primaries are oblate homogeneous spheroids steadily rotating around their axis of symmetry and whose equatorial planes coincide throughout their motion. Our work differs from previous studies in the fact that the oblateness parameters J (1) and J (2) are not necessarily small but they belong to the largest range where the model is physically valid. In particular, imposing the stability of the primaries’ circular motion, we deduce that J (1) and J (2) belong to a bounded domain. This permits an analytical proof on the existence and uniqueness of a Lagrangian equilibrium (modulo a reflection symmetry). Linear stability is studied numerically. We find that the critical mass ratios μ cr of the primaries forms a smooth surface in the parameter space and observe that μ cr decreases as oblate parameters increase. We also prove that for non-critical mass ratios, equilibria locations, stability properties, and any elementary periodic solution whose period is not a multiple of 2 π of the restricted problem persist in the full three-body problem with two oblate bodies and on small mass point.