### Abstract

Original language | English |
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Number of pages | 11 |

Publication status | Published - Jul 2008 |

Event | 2nd Conference on Nonlinear Science and Complexity - Porto, Portugal Duration: 28 Jul 2008 → 31 Jul 2008 |

### Conference

Conference | 2nd Conference on Nonlinear Science and Complexity |
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City | Porto, Portugal |

Period | 28/07/08 → 31/07/08 |

### Fingerprint

### Keywords

- periodic orbits
- solar sail
- elliptic three body problem

### Cite this

*New periodic orbits in the solar sail restricted three body problem*. Paper presented at 2nd Conference on Nonlinear Science and Complexity, Porto, Portugal, .

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**New periodic orbits in the solar sail restricted three body problem.** / Biggs, J.D.; McInnes, C.; Waters, Thomas.

Research output: Contribution to conference › Paper

TY - CONF

T1 - New periodic orbits in the solar sail restricted three body problem

AU - Biggs, J.D.

AU - McInnes, C.

AU - Waters, Thomas

PY - 2008/7

Y1 - 2008/7

N2 - In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the Elliptic Restricted Three Body Problem (ERTBP). A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e = 0 and continuing to the required eccentricity of e = 0:0167. The stability of these periodic orbits is investigated.

AB - In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the Elliptic Restricted Three Body Problem (ERTBP). A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e = 0 and continuing to the required eccentricity of e = 0:0167. The stability of these periodic orbits is investigated.

KW - periodic orbits

KW - solar sail

KW - elliptic three body problem

M3 - Paper

ER -