### Abstract

In this paper, we develop the low energy trajectory design of a spacecraft from the Earth to the Moon in the context of the Planar Restricted Four Body Problem, which may be approximately modeled by coupling two Planar Restricted Three Body Problems, i.e., the Sun-(Earth+Moon)-Spacecraft and the Earth-Moon-Spacecraft systems. The principal idea lies in the so-called tube dynamics, which may patch invariant manifolds of the two PR3BPs to obtain the required lunar capture trajectories. We first model the S-E-M-S/C system by the coupled Planar Restricted Circular Three Body Problem (PRC3BP) and we also analyze the case, in particular, where the E-M-S/C system is modeled by the Planar Restricted Elliptic Three Body Problem (PRE3BP), since the E-M system has the nonnegligible eccentricity. Finally, we develop the low energy lunar capture trajectory in the coupled PRC3B-PRE3BP in comparison with the case of the coupled PRC3BP.

Original language | English |
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Title of host publication | AIAA SPACE 2013 Conference and Exposition |

Publication status | Published - 2013 |

Event | AIAA SPACE 2013 Conference and Exposition - San Diego, CA Duration: 2013 Sep 10 → 2013 Sep 12 |

### Other

Other | AIAA SPACE 2013 Conference and Exposition |
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City | San Diego, CA |

Period | 13/9/10 → 13/9/12 |

### Fingerprint

### ASJC Scopus subject areas

- Space and Planetary Science
- Aerospace Engineering

### Cite this

*AIAA SPACE 2013 Conference and Exposition*

**Lunar capture trajectories in the four-body problem.** / Onozaki, K.; Yoshimura, Hiroaki.

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

*AIAA SPACE 2013 Conference and Exposition.*AIAA SPACE 2013 Conference and Exposition, San Diego, CA, 13/9/10.

}

TY - GEN

T1 - Lunar capture trajectories in the four-body problem

AU - Onozaki, K.

AU - Yoshimura, Hiroaki

PY - 2013

Y1 - 2013

N2 - In this paper, we develop the low energy trajectory design of a spacecraft from the Earth to the Moon in the context of the Planar Restricted Four Body Problem, which may be approximately modeled by coupling two Planar Restricted Three Body Problems, i.e., the Sun-(Earth+Moon)-Spacecraft and the Earth-Moon-Spacecraft systems. The principal idea lies in the so-called tube dynamics, which may patch invariant manifolds of the two PR3BPs to obtain the required lunar capture trajectories. We first model the S-E-M-S/C system by the coupled Planar Restricted Circular Three Body Problem (PRC3BP) and we also analyze the case, in particular, where the E-M-S/C system is modeled by the Planar Restricted Elliptic Three Body Problem (PRE3BP), since the E-M system has the nonnegligible eccentricity. Finally, we develop the low energy lunar capture trajectory in the coupled PRC3B-PRE3BP in comparison with the case of the coupled PRC3BP.

AB - In this paper, we develop the low energy trajectory design of a spacecraft from the Earth to the Moon in the context of the Planar Restricted Four Body Problem, which may be approximately modeled by coupling two Planar Restricted Three Body Problems, i.e., the Sun-(Earth+Moon)-Spacecraft and the Earth-Moon-Spacecraft systems. The principal idea lies in the so-called tube dynamics, which may patch invariant manifolds of the two PR3BPs to obtain the required lunar capture trajectories. We first model the S-E-M-S/C system by the coupled Planar Restricted Circular Three Body Problem (PRC3BP) and we also analyze the case, in particular, where the E-M-S/C system is modeled by the Planar Restricted Elliptic Three Body Problem (PRE3BP), since the E-M system has the nonnegligible eccentricity. Finally, we develop the low energy lunar capture trajectory in the coupled PRC3B-PRE3BP in comparison with the case of the coupled PRC3BP.

UR - http://www.scopus.com/inward/record.url?scp=84884844033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884844033&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84884844033

SN - 9781624102394

BT - AIAA SPACE 2013 Conference and Exposition

ER -