On periodic flybys of the moon

This paper considers the plane circular restricted three-body problem for small . Symmetric periodic solutions of the second species (passing near the body of mass ) and their distance from the center of the body of mass are studied by constructing perturbations of arc-solutions (solutions with consecutive collisions) existing for =0. Orbits which also pass near the body of mass 1- are studied in detail. The results are applied to finding periodic orbits in the Earth-Moon system and in the Sun-Jupiter system.Russian version: Preprint No. 91 (1978) of Inst. Appl. Math.; present English translation was made by L. M. Perko and W. C. Schulz (February 1979).