Periodic solutions of the restricted three-body problem for a small mass ratio

A plane circular restricted three body problem is considered for small values of the ratio of the masses μ of the main bodies. All the limit problems as μ → 0: the two-body problem, Hill's problem, the intermediate Hénon problem and the basic limit problem, are found using a Power Geometry. In each of them, solutions are isolated which are the limits of the periodic solutions of the restricted problem as μ → 0 and the limits of the families of periodic solutions (which are called generating families). Using the generating families in the case of small μ > 0, the families are studied which are started as the reverse (family h) and forward (family i) circular orbits of infinitesimal radius around the body of greater mass. It is shown that, as μ increases, there is a small change in the structure of family h but family i undergoes infinitely many self-bifurcations with the formation of an infinite number of closed subfamilies, each of which only exists in a certain range of values of μ. A theory of the formation of horseshoe-shaped orbits and orbits in the form of “tadpoles” is given, and the structure of the basic families containing periodic solution with these orbits is indicated.