Two mechanisms of natural transport in the Solar System q Yuan Ren a,⇑ , Josep J. Masdemont a , Gerard Gómez b , Elena Fantino a a IEEC & Departament de Matemàtica Aplicada I, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain b IEEC & Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain article info Article history: Received 20 October 2010 Received in revised form 25 February 2011 Accepted 23 June 2011 Available online 2 July 2011 Keywords: Natural transport Poincaré section Three-body problem Lobe dynamics abstract In this paper, two natural transport mechanisms in Solar System are considered. The first is a short-time transport, and is based on the existence of ‘‘pseudo-heteroclinic’’ connections between libration point orbits of pairs of Sun–planet planar circular restricted three-body problems (PCR3BP). The stable and unstable manifolds associated with the libration point orbits of different Sun–planet PCR3BP systems are computed. Then the intersections between the inner and the outer manifolds of all the consecutive planets in the Solar Sys- tem are explored. The second mechanism, which is common and qualitatively well under- stood in two-degrees of freedom Hamiltonian systems, corresponds to a long-time transport, and is the result of the strongly chaotic motion of the minor body in the PCR3BP. In this contribution, we present an analysis of the natural transport in the Solar System based on these two mechanisms. In particular, we discuss the key properties of the natural transport, such as the possibility of transfering between two specified celestial bodies, the type of transport and the time of flight. The final objective is to provide a deeper dynamical insight into the exchange mechanisms of natural material in the Solar System. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction In this paper, we study two mass transport mechanisms in the Solar System: a short-time transport and a long-time transport. The reference dynamical models for the study are the planar circular restricted three body problem (PCR3BP) and the model consisting in two uncoupled PCR3BPs. The short-time transport is based on the existence of orbits which shadow pseudo-heteroclinic connections between libration point orbits of two uncoupled Sun–planet PCR3BPs, such that the two involved planets are in consecutive orbits in the Solar System. The basic ideas of this approach follow those introduced in [1] for the design of the so called low-energy transfers from the Earth to the Moon by means of connecting invariant manifold trajectories of a Lyapunov orbit around the L 2 equilibrium point of the Sun–Earth PCR3BP and invariant manifold trajectories of a Lyapunov orbit around the L 2 point of the Earth–Moon PCR3BP. Analogous ideas where used by Toppputo et al. in [2] for the study of low-energy interplanetary transfers. Similarly, the intersection between an unstable manifold of an equilibrium point (L 1 or L 2 ) in one Sun-planet sys- tem and the stable manifold of an equilibrium point in another Sun–planet system might explain the transport of natural material between the two planets. The expression pseudo-heteroclinic refers to the non-dynamical nature of the relationship 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.06.030 q E. Fantino and Y. Ren have been supported by the Marie Curie Actions Research and Training Network AstroNet MCRTN-CT-2006-035151. G. Gómez and J.J. Masdemont have been partially supported by the grants MTM2006-05849/Consolider, MTM2009-06973 and 2009SGR859. The authors also acknowledge the use of EIXAM, the UPC Applied Math cluster system for research computing (see http://www.ma1.upc.edu/eixam/), and in particular Pau Roldan for providing technical support in the use of the cluster. ⇑ Corresponding author. E-mail addresses: yuan.ren@upc.edu (Y. Ren), josep@barquins.upc.edu (J.J. Masdemont), gerard@maia.ub.es (G. Gómez), elena.fantino@upc.edu (E. Fantino). Commun Nonlinear Sci Numer Simulat 17 (2012) 844–853 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns