Interplanetary transfers using stable and unstable manifold tubes originating at L1 and L2 in the elliptic restricted three-body problems

The solutions originating at the Lagrangian points L1 and L2 of the restricted three-body problem are used in space flight dynamics to find useful station-keeping orbits as well as convenient low-energy transfers between planets and satellites of the Solar System. The circular restricted three-body problem (CR3BP) provides the simplest model where the Lagrangian points, as well as the related stable and unstable manifold tubes, are defined. Nevertheless, their use for Solar System applications requires to consider hierarchical extensions of the model. The elliptic restricted three-body problem (ER3BP) is the most important extension to consider for space flight dynamics. In this paper we discuss the differences of the manifold tubes of the ER3BP with respect to the CR3BP which have an impact in the transfers between orbits in the manifold tubes related to different planets. We find that there is a threshold value for the eccentricity of the planet, depending on its reduced mass, which changes drastically the distribution of the longitudes of the first pericenter (or apocenter) of the orbits in the manifold tubes leaving or approaching the Lagrangian points L1, L2. For example, such a difference changes the design of the Hohmann transfers between two orbits of the manifold tubes when the planets Mercury or Mars are concerned.