On motions around the collinear libration points in the elliptic restricted three-body problem

Motions around the collinear libration points in the elliptic restricted three-body problem are studied. Literal expansions of the Lissajous orbits and the halo orbits are obtained. These expansions depend on two amplitude parameters and the orbital eccentricity of the two primaries. Numerical simulations are done to check the validity of these literal series and to compare them with the results in the circular restricted three-body problem. According to the properties of these literal expansions, three kinds of symmetric periodic orbits around the collinear libration points are discussed. Finally, applications of these results in the Earth–Moon system and the Sun–Earth+Moon system are discussed.