### Abstract

We consider periodic orbits in the circular restricted three-body problem, where the third (small) body is a solar
sail. In particular, we consider orbits about equilibrium points in the Earth-sun rotating frame, which are high above
the ecliptic plane, in contrast to the classical "halo" orbits about the collinear equilibria. It is found that due to coupling in the equations of motion, periodic orbits about 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. It is found that there is much freedom in specifying the position and period/amplitude of the
orbit of the sail, high above the ecliptic and looking down on the Earth.Aparticular use of such solutions is presented,
namely, the year-round constant imaging of, and communication with, the poles. We find that these orbits present a significant improvement on the position of the sail when viewed from the Earth, compared to a sail placed at
equilibrium.

Original language | English |
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Pages (from-to) | 687-693 |

Number of pages | 6 |

Journal | Journal of Guidance, Control and Dynamics |

Volume | 30 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

### Keywords

- astrodynamics
- solar sails
- propulsion systems
- eliptic plane
- design engineering

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## Cite this

Waters, T., & McInnes, C. R. (2007). Periodic orbits above the ecliptic plane in the solar sail restricted 3-body problem.

*Journal of Guidance, Control and Dynamics*,*30*(3), 687-693. https://doi.org/10.2514/1.26232