### Abstract

This paper presents a novel approach to the design of Low-Thrust trajectories, based on a first order approximated analytical solution of Gauss planetary equations. This analytical solution is shown to have a better accuracy than a second-order explicit numerical integrator and at a lower computational cost. Hence, it can be employed for the fast propagation of perturbed Keplerian motion when moderate accuracy is required. The analytical solution was integrated in a direct transcription method based on a decomposition of the trajectory into direct finite perturbative elements (DFPET). DFPET were applied to the solution of two-point boundary transfer problems.

Furthermore the paper presents an example of the use of DFPET for the solution of a multiobjective trajectory optimisation problem in which both the total ∆V and transfer time are minimized with respect to departure and arrival dates. Two transfer problems were used as test cases: a direct transfer from Earth to Mars and a spiral from a low Earth orbit to the International Space Station.

Furthermore the paper presents an example of the use of DFPET for the solution of a multiobjective trajectory optimisation problem in which both the total ∆V and transfer time are minimized with respect to departure and arrival dates. Two transfer problems were used as test cases: a direct transfer from Earth to Mars and a spiral from a low Earth orbit to the International Space Station.

Original language | English |
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Pages (from-to) | 108-120 |

Journal | Acta Astronautica |

Volume | 72 |

Publication status | Published - 1 Mar 2012 |

### Keywords

- low-thrust propulsion
- trajectory design
- analytic solutions
- perturbation theory
- multiobjective optimization

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## Cite this

Zuiani, F., Vasile, M., Avanzini, G., & Palmas, A. (2012). Direct transcription of low-thrust trajectories with finite trajectory elements.

*Acta Astronautica*,*72*, 108-120.