Double lunar swing-by orbits revisited

The double lunar swing-by orbits are a special kind of orbits in the Earth-Moon system. These orbits repeatedly pass through the vicinity of the Moon and change their shapes due to the Moon’s gravity. In the synodic frame of the circular restricted three-body problem consisting of the Earth and the Moon, these orbits are periodic, with two close approaches to the Moon in every orbit period. In this paper, these orbits are revisited. It is found that these orbits belong to the symmetric horseshoe periodic families which bifurcate from the planar Lyapunov family around the collinear libration point L3. Usually, the double lunar swing-by orbits have k=i+j loops, where i is the number of the inner loops and j is the number of outer loops. The genealogy of these orbits with different i and j is studied in this paper. That is, how these double lunar swing-by orbits are organized in the symmetric horseshoe periodic families is explored. In addition, the 2n lunar swing-by orbits (n?2) with 2n close approaches to the Moon in one orbit period are also studied.