### Abstract

Perturbation solutions are obtained in spherical coordinates for the spacecraft relative motion problem in the case of a slightly eccentric chief orbit. The use of spherical coordinates eliminates many of the secular terms in the Cartesian coordinate solution and extends the range of validity of these solutions to larger intrack separations. Both the chief eccentricity and the normalized separation are treated as order ϵ. Finally, the third order solution is used in the "double transformation" to improve the accuracy of the "approximate double transformation" Cartesian solution and as an alternative method to obtain the proposed third order spherical solution.

Original language | English (US) |
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Title of host publication | Spaceflight Mechanics 2016 |

Publisher | Univelt Inc. |

Pages | 3455-3474 |

Number of pages | 20 |

Volume | 158 |

ISBN (Print) | 9780877036333 |

State | Published - 2016 |

Event | 26th AAS/AIAA Space Flight Mechanics Meeting, 2016 - Napa, United States Duration: Feb 14 2016 → Feb 18 2016 |

### Other

Other | 26th AAS/AIAA Space Flight Mechanics Meeting, 2016 |
---|---|

Country | United States |

City | Napa |

Period | 2/14/16 → 2/18/16 |

### Fingerprint

### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2016*(Vol. 158, pp. 3455-3474). Univelt Inc..

**Spherical coordinate perturbation solutions to relative motion equations : Application to double transformation spherical solution.** / Butcher, Eric; Lovell, T. Alan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Spaceflight Mechanics 2016.*vol. 158, Univelt Inc., pp. 3455-3474, 26th AAS/AIAA Space Flight Mechanics Meeting, 2016, Napa, United States, 2/14/16.

}

TY - GEN

T1 - Spherical coordinate perturbation solutions to relative motion equations

T2 - Application to double transformation spherical solution

AU - Butcher, Eric

AU - Lovell, T. Alan

PY - 2016

Y1 - 2016

N2 - Perturbation solutions are obtained in spherical coordinates for the spacecraft relative motion problem in the case of a slightly eccentric chief orbit. The use of spherical coordinates eliminates many of the secular terms in the Cartesian coordinate solution and extends the range of validity of these solutions to larger intrack separations. Both the chief eccentricity and the normalized separation are treated as order ϵ. Finally, the third order solution is used in the "double transformation" to improve the accuracy of the "approximate double transformation" Cartesian solution and as an alternative method to obtain the proposed third order spherical solution.

AB - Perturbation solutions are obtained in spherical coordinates for the spacecraft relative motion problem in the case of a slightly eccentric chief orbit. The use of spherical coordinates eliminates many of the secular terms in the Cartesian coordinate solution and extends the range of validity of these solutions to larger intrack separations. Both the chief eccentricity and the normalized separation are treated as order ϵ. Finally, the third order solution is used in the "double transformation" to improve the accuracy of the "approximate double transformation" Cartesian solution and as an alternative method to obtain the proposed third order spherical solution.

UR - http://www.scopus.com/inward/record.url?scp=85007341040&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007341040&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85007341040

SN - 9780877036333

VL - 158

SP - 3455

EP - 3474

BT - Spaceflight Mechanics 2016

PB - Univelt Inc.

ER -