### Abstract

This paper introduces new families of Sun-centered non-Keplerian orbits

(NKOs) that are constrained to a three-dimensional surface such as a cylinder or

sphere. As such, they are an extension to the well-known families of two dimensional NKOs. For both the cylindrical and spherical types of orbits, the

equations of motion are derived in an appropriate reference frame, constraints

are introduced to confine the orbit to a cylindrical or spherical surface and further constraints allow the definition of the set of feasible orbits. Additionally, the phase spaces of the orbits are explored and a numerical analysis is developed to find periodic orbits within the set of feasible orbits. The richness of the problem is further enhanced by considering both an inverse square acceleration law (mimicking solar electric propulsion) and a solar sail acceleration law to keep the spacecraft on the cylindrical or spherical surface. These new families of NKOs generate a wealth of new orbits with a range of interesting applications ranging from solar physics to astronomy and planetary observation.

(NKOs) that are constrained to a three-dimensional surface such as a cylinder or

sphere. As such, they are an extension to the well-known families of two dimensional NKOs. For both the cylindrical and spherical types of orbits, the

equations of motion are derived in an appropriate reference frame, constraints

are introduced to confine the orbit to a cylindrical or spherical surface and further constraints allow the definition of the set of feasible orbits. Additionally, the phase spaces of the orbits are explored and a numerical analysis is developed to find periodic orbits within the set of feasible orbits. The richness of the problem is further enhanced by considering both an inverse square acceleration law (mimicking solar electric propulsion) and a solar sail acceleration law to keep the spacecraft on the cylindrical or spherical surface. These new families of NKOs generate a wealth of new orbits with a range of interesting applications ranging from solar physics to astronomy and planetary observation.

Original language | English |
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Pages | AAS 13-871 |

Number of pages | 20 |

Publication status | Published - 11 Aug 2013 |

Event | AAS/AIAA Astrodynamics Specialist Conference 2013 - Hilton Head, South Carolina, United States Duration: 11 Aug 2013 → 15 Aug 2013 |

### Conference

Conference | AAS/AIAA Astrodynamics Specialist Conference 2013 |
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Country | United States |

City | Hilton Head, South Carolina |

Period | 11/08/13 → 15/08/13 |

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### Keywords

- orbital dynamics
- non-Keplerian orbits
- solar sailing
- solar electric propulsion

### Cite this

Heiligers, J., & McInnes, C. (2013).

*Cylindrically and spherically constrained families of non-Keplerian orbits*. AAS 13-871. Paper presented at AAS/AIAA Astrodynamics Specialist Conference 2013, Hilton Head, South Carolina, United States.