### Abstract

The classic treatment of rendezvous mechanics, or other problems involving the relative motion of two spacecraft, assumes a circular reference orbit, allowing a relatively simple closed-form description of the motion. This paper develops a solution for an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, and gives matrix elements up to second order in eccentricity for both Cartesian and cylindrical coordinates. An example application is given for the proposed LISA (Laser Interferometer Space Antenna) gravity wave experiment.

Original language | English (US) |
---|---|

Pages (from-to) | 2075-2085 |

Number of pages | 11 |

Journal | Advances in the Astronautical Sciences |

Volume | 97 PART 2 |

State | Published - Dec 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Advances in the Astronautical Sciences*,

*97 PART 2*, 2075-2085.

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*Advances in the Astronautical Sciences*, vol. 97 PART 2, pp. 2075-2085.

**Relative motion of satellites in elliptical orbits.** / Melton, Robert Graham.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Relative motion of satellites in elliptical orbits

AU - Melton, Robert Graham

PY - 1997/12/1

Y1 - 1997/12/1

N2 - The classic treatment of rendezvous mechanics, or other problems involving the relative motion of two spacecraft, assumes a circular reference orbit, allowing a relatively simple closed-form description of the motion. This paper develops a solution for an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, and gives matrix elements up to second order in eccentricity for both Cartesian and cylindrical coordinates. An example application is given for the proposed LISA (Laser Interferometer Space Antenna) gravity wave experiment.

AB - The classic treatment of rendezvous mechanics, or other problems involving the relative motion of two spacecraft, assumes a circular reference orbit, allowing a relatively simple closed-form description of the motion. This paper develops a solution for an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, and gives matrix elements up to second order in eccentricity for both Cartesian and cylindrical coordinates. An example application is given for the proposed LISA (Laser Interferometer Space Antenna) gravity wave experiment.

UR - http://www.scopus.com/inward/record.url?scp=3343000304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3343000304&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3343000304

VL - 97 PART 2

SP - 2075

EP - 2085

JO - Advances in the Astronautical Sciences

JF - Advances in the Astronautical Sciences

SN - 1081-6003

ER -