## Abstract

While it is widely known that the Hohmann transfer is the optimal two-bum, coplanar trajectory in terms of Av, it is certainly non-optimal in terms of time of flight (TOF). As a result, the aim of this paper is, using Lambert's Algorithm, to determine those orbital trajectories that require low Av's, but also require small TOFs, with the means of optimization being Evolutionary Algorithms (EAs). Three different heuristics were used in the analysis of this problem: Particle Swarm Optimization (PSO), Differential Evolution (DE), and Covariance Matrix Adapted Evolutionary Strategies (CMA-ES). Two cases were examined, both of which were co-planar orbital transfers, the EA was able to obtain solutions which were marginally more expensive in Av, yet much lower in terms of rendezvous time. For the LEO-LEO co-planar scenario, the trajectory would require an additional 8% more Av; but it would required a rendezvous time that is 6% that of the Hohmann case. For the LEO to GEO co-planar case, the trajectory would require 4% more fuel, but the savings in terms of rendezvous time would be 10%. Two additional cases were analyzed, where the vehicle was performing a non co-planar rendezvous. In the LEO-LEO case, Av expenditure was 1.4242 km/s, and the time of arrival (TOA) was 130 min. A Hohmann transfer with à pure inclination change maneuver would result in a Av cost of 1.4535 km/s, which is 2% higher than the trajectory that the EA identified. In the LEO-GEO case, the Δv expenditure was 7.1779 km/s, with a corresponding TOA of 306 minutes. A Hohmann transfer maneuver coupled with a pure inclination change maneuver for this scenario would yield a Δv of 4.0373 km/s, which is significantly lower in terms of Δv compared to the trajectory the EA found. After a comprehensive algorithm comparison, PSO performed the best in terms of speed and reliability. DE was a close second, with CMA-ES's poor reliability record relegating it ineffective on these trajectory problems.

Original language | English (US) |
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Title of host publication | Spaceflight Mechanics 2006 - Proceedings of the AAS/AIAA Space Flight Mechnaics Meeting |

Pages | 1611-1628 |

Number of pages | 18 |

State | Published - Dec 1 2006 |

Event | Spaceflight Mechanics 2006 - AAS/AIAA Space Flight Mechnaics Meeting - Tampa, FL, United States Duration: Jan 22 2006 → Jan 26 2006 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 124 II |

ISSN (Print) | 0065-3438 |

### Other

Other | Spaceflight Mechanics 2006 - AAS/AIAA Space Flight Mechnaics Meeting |
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Country/Territory | United States |

City | Tampa, FL |

Period | 1/22/06 → 1/26/06 |

## All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science