### Abstract

The N-body problem is defined and its equations of motion are presented. A new time transformation based on two-body problem series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the N-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the N-body problem is also introduced. These analytic solutions are used to investigate periodic and non-periodic trajectories in the restricted three-body problem and are shown to be capable of describing complete, N-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

Original language | English (US) |
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Title of host publication | Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences |

Subtitle of host publication | Proceedings of the AAS/AIAA Space Flight Mechanics Meeting |

Pages | 1317-1330 |

Number of pages | 14 |

Volume | 136 |

State | Published - Dec 1 2010 |

Event | AAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States Duration: Feb 14 2010 → Feb 17 2010 |

### Other

Other | AAS/AIAA Space Flight Mechanics Meeting |
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Country | United States |

City | San Diego, CA |

Period | 2/14/10 → 2/17/10 |

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### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting*(Vol. 136, pp. 1317-1330)

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*Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting.*vol. 136, pp. 1317-1330, AAS/AIAA Space Flight Mechanics Meeting, San Diego, CA, United States, 2/14/10.

**Approximate time-dependent solutions of the N-body problem.** / Benavides, Julio César; Spencer, David Bradley.

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

TY - GEN

T1 - Approximate time-dependent solutions of the N-body problem

AU - Benavides, Julio César

AU - Spencer, David Bradley

PY - 2010/12/1

Y1 - 2010/12/1

N2 - The N-body problem is defined and its equations of motion are presented. A new time transformation based on two-body problem series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the N-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the N-body problem is also introduced. These analytic solutions are used to investigate periodic and non-periodic trajectories in the restricted three-body problem and are shown to be capable of describing complete, N-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

AB - The N-body problem is defined and its equations of motion are presented. A new time transformation based on two-body problem series solutions is introduced and used to develop a time-dependent, analytic, first-order solution of the N-body problem. A process of deriving higher-order, time-dependent, analytic solutions of the N-body problem is also introduced. These analytic solutions are used to investigate periodic and non-periodic trajectories in the restricted three-body problem and are shown to be capable of describing complete, N-body trajectories with good accuracy and with far fewer function evaluations than are required by numerical integration.

UR - http://www.scopus.com/inward/record.url?scp=80053424815&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053424815&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780877035602

VL - 136

SP - 1317

EP - 1330

BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences

ER -