### Abstract

This paper discusses a semi-analytical approach that can be used to approximate the relative motion of spacecraft around nominal periodic Distant Retrograde Orbits (DROs) in the vicinity of Mars’ largest moon, Phobos. Numerical analysis reveals that in the Circular Restricted Three-Body Problem (CR3BP) rotating reference frame, Mars-Phobos DROs can be represented analytically in a moderately accurate way by two terms of their Fourier series representations due to the fact that the mass of Phobos is much smaller than the mass of Mars. Additionally, assuming that the relative distance between spacecraft is sufficiently small, the equations of motions can be further simplified and semi-analytically solved to obtain an accurate representation of the relative motion in the vicinity of Phobos. It is found that the equations exhibit a secular behavior, which can be accurately described by the Hill-Clohessy-Wiltshire (HCW) equations, and a short-term cyclic behavior which is attributed to the gravitational attraction of Phobos that the HCW equations cannot represent.

Original language | English (US) |
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Title of host publication | AAS/AIAA Astrodynamics Specialist Conference, 2018 |

Editors | Puneet Singla, Ryan M. Weisman, Belinda G. Marchand, Brandon A. Jones |

Publisher | Univelt Inc. |

Pages | 829-845 |

Number of pages | 17 |

ISBN (Print) | 9780877036579 |

Publication status | Published - Jan 1 2018 |

Event | AAS/AIAA Astrodynamics Specialist Conference, 2018 - Snowbird, United States Duration: Aug 19 2018 → Aug 23 2018 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 167 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | AAS/AIAA Astrodynamics Specialist Conference, 2018 |
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Country | United States |

City | Snowbird |

Period | 8/19/18 → 8/23/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*AAS/AIAA Astrodynamics Specialist Conference, 2018*(pp. 829-845). (Advances in the Astronautical Sciences; Vol. 167). Univelt Inc..