### Abstract

system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624

Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model.

Language | English |
---|---|

Pages | 191-219 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 112 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2012 |

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### Keywords

- restricted problems
- stability
- periodic orbits

### Cite this

*Celestial Mechanics and Dynamical Astronomy*,

*112*(2), 191-219. https://doi.org/10.1007/s10569-011-9391-x

}

*Celestial Mechanics and Dynamical Astronomy*, vol. 112, no. 2, pp. 191-219. https://doi.org/10.1007/s10569-011-9391-x

**Low thrust propulsion in a coplanar circular restricted four body problem.** / Ceccaroni, Marta; Biggs, James.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Low thrust propulsion in a coplanar circular restricted four body problem

AU - Ceccaroni, Marta

AU - Biggs, James

PY - 2012/2/1

Y1 - 2012/2/1

N2 - This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraftsystem is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model.

AB - This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraftsystem is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model.

KW - restricted problems

KW - stability

KW - periodic orbits

UR - http://www.scopus.com/inward/record.url?scp=84856515521&partnerID=8YFLogxK

UR - http://www.springerlink.com/content/728265144j86524h/

U2 - 10.1007/s10569-011-9391-x

DO - 10.1007/s10569-011-9391-x

M3 - Article

VL - 112

SP - 191

EP - 219

JO - Celestial Mechanics and Dynamical Astronomy

T2 - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 2

ER -