A new class of periodic solutions of the three-dimensional restricted problem
W. H. Jefferys · The Astronomical Journal · 1966
The existence of a class of inclined periodic solutions of the restricted three-body problem is shown. These orbits form a continuous sequence with eccentricity as the parameter, and a discrete sequence with mean motion as the parameter. They exist only for special values of the inclination and are related to certain phenomena already known. The orbits are shown to exist if the ratio of the mean motion of the massless point to that of Jupiter is sufficiently small or sufficiently large, although the exact size is not specified and this ratio may be close to unity. The orbits are obtained by analytic continuation of periodic orbits for the case where Jupiter's mass is zero.