tokens: to have natural transport from one planet to the next one in the sequence of bicircular problems, and a particle could drift away from one planet to reach a neighbourhood of the following planet. After that, for transport between neighbourhoods of the libration points of the same Sun–planet problem, it is enough to consider an RTBP (Sun+planet+infinitesimal particle), in which case the existence of heteroclinic connections between libration point orbits around L 1 and L 2 is well known. These connections would allow a particle to continue its journey towards the innermost Solar system. See Fig. 5 . Figure 5. Scheme of the chain of connections between two consecutive restricted bicircular Sun–Jupiter–planet (BR4BP ip ) problems, and two consecutive restricted Sun–planet ( P ip ) problems (RTBP ip ). For the computation of the connections, we proceed as follows. Consider two consecutive bicircular problems BR4BP ip and BR4BP ip + 1 corresponding to the planets ip and ip + 1. We are interested in transits from the outer to the inner Solar system. In all the bicircular problems, OL 1 is an inner orbit than the orbit of the planet with respect to the Sun, and OL 2 is an outer orbit (see Fig. 4 ). Then, the suitable connections are those involving the invariant manifolds of and . It is well known that the invariant manifolds associated with the equilibrium points L 1 and L 2 in the RTBP have two branches: one goes inwards, while the other one goes outwards, at least for times not too big. The invariant manifolds of the dynamical substitutes have the same behaviour. According to this, we denote by the branch of the invariant manifold that goes outwards, and by the branch of the invariant manifold that goes inwards. See Fig. 6 . Figure 6. Projection in configuration space (rotating coordinates) of branches of the invariant manifold (outer corona) and (inner corona). The dynamical substitute is the periodic orbit between the two branches. See the text for further details and also Fig. 8 . Therefore, in order to find connections, in the BR4BP ip , we compute the (linear approximation of the) parametrization of the stable manifold (see equation 7 ) and we follow the branch , and in the BR4BP ip + 1 , we compute the (linear approximation of the) parametrization of the unstable manifold (again see equation 7 ) and we follow the branch . To study if there exist connections, we also fix a section Σ R = {( x , y ); x 2 + y 2 = R 2 }, where R is an intermediate value between the radii of the orbits of the planets of the two bicircular problems, a ip and a ip + 1 , that is a ip R a ip + 1 (see Fig. 7 ). Figure 7. Projection in configuration space (rotating coordinates) of the dynamical substitutes , , one orbit on the invariant manifolds and , and the section Σ R for . The main objectives are: first, to determine if both manifolds reach the section Σ, and, secondly, to study which is the minimum distance between the sets and . That is, we want to see if both
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