## Abstract

We identify displaced periodic orbits in the circular restricted three-body problem, where the third (small) body is a solar sail. In particular, we consider solar sail orbits in the Earth-Sun system which are high above the ecliptic plane. It is shown that periodic orbits about surfaces of artificial equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the solar sail elliptical restricted three-body problem. A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e=0 and continuing to the required eccentricity of e=0.0167. The stability of these periodic orbits is investigated.

Original language | English |
---|---|

Title of host publication | Nonlinear Science and Complexity |

Editors | J. A. Tenreiro Machado, Alberto C. J. Luo, Ramiro S. Barbosa, Manuel F. Silva, Lino B. Figueiredo |

Publisher | Springer Netherlands |

Pages | 131-138 |

Number of pages | 8 |

ISBN (Electronic) | 9789048198849 |

ISBN (Print) | 9789048198832 |

DOIs | |

Publication status | Published - 2011 |

## Keywords

- Displaced periodic orbits
- Restricted three body problem
- Solar sail