### Abstract

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits above the L2 point. We start by generating a reference trajectory about the libration points. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Because of the instability of the collinear libration points, orbit control is needed for a spacecraft to remian in the vicinity of these points. The reference trajectory is then tracked using a linear Quadratic Regulator (LQR). Finally, simulations are given to validate the control strategy. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon.

Original language | English |
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Pages | IAC-09.C1.2.4 |

Number of pages | 7 |

Publication status | Published - 12 Oct 2009 |

Event | 60th International Astronautical Congress - Daejeon, Korea Duration: 12 Oct 2009 → 16 Oct 2009 |

### Conference

Conference | 60th International Astronautical Congress |
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City | Daejeon, Korea |

Period | 12/10/09 → 16/10/09 |

### Keywords

- Solar sail propulsion
- periodic orbits
- displaced orbits
- Earth-Moon system
- libration points
- Linear Quadratic Regulator

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## Cite this

Simo, J., & McInnes, C. R. (2009).

*Analysis and control of displaced periodic orbits in the Earth-Moon system*. IAC-09.C1.2.4. Paper presented at 60th International Astronautical Congress, Daejeon, Korea, .