## Abstract

In the circular restricted three-body problem (CR3BP) the weak stability boundary (WSB) is defined as a boundary set in the phase space between stable and unstable motion relative to the second primary. At a given energy level, the boundaries of such region are provided by the stable manifolds of the central objects of the L_{1} and L_{2} libration points, i.e., the two planar Lyapunov orbits. Besides, the unstable manifolds of libration point orbits (LPOs) around L_{1} and L_{2} have been identified as responsible for the weak or temporary capture around the second primary of the system. These two issues suggest the existence of natural dynamical channels between the Earth's vicinity and the SunEarth libration points L_{1} and L_{2}. Furthermore, it has been shown that the SunEarth L_{2} central unstable manifolds can be linked, through an heteroclinic connection, to the central stable manifolds of the L_{2} point in the EarthMoon three-body problem. This concept has been applied to the design of low energy transfers (LETs) from the Earth to the Moon. In this contribution we consider all the above three issues, i.e., weak stability boundaries, temporary capture and low energy transfers, and we discuss the role played by the invariant manifolds of LPOs in each of them. The study is made in the planar approximation.

Original language | British English |
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Pages (from-to) | 1038-1052 |

Number of pages | 15 |

Journal | Acta Astronautica |

Volume | 67 |

Issue number | 9-10 |

DOIs | |

State | Published - Nov 2010 |

## Keywords

- Circular restricted three-body problem
- Invariant manifolds
- Libration points
- Periodic orbits
- Two-body problem
- Weak stability boundary