### Abstract

This paper is devoted to the study of the stability of the Lagrangian point L _{4} in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61° of the test particle. At moderate inclinations (~10° to ~50°), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385 - with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio-eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61°. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits.

Original language | English |
---|---|

Pages (from-to) | 397-402 |

Number of pages | 6 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 427 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 21 2012 |

### Fingerprint

### Keywords

- Celestial mechanics
- Methods: numerical
- Planetary systems

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

_{4}in the spatial restricted three-body problem - application to exoplanetary systems.

*Monthly Notices of the Royal Astronomical Society*,

*427*(1), 397-402. https://doi.org/10.1111/j.1365-2966.2012.21986.x

**Stability of the Lagrangian point L _{4} in the spatial restricted three-body problem - application to exoplanetary systems.** / Schwarz, R.; Bazsó, Á; Érdi, B.; Funk, B.

Research output: Contribution to journal › Article

_{4}in the spatial restricted three-body problem - application to exoplanetary systems',

*Monthly Notices of the Royal Astronomical Society*, vol. 427, no. 1, pp. 397-402. https://doi.org/10.1111/j.1365-2966.2012.21986.x

_{4}in the spatial restricted three-body problem - application to exoplanetary systems. Monthly Notices of the Royal Astronomical Society. 2012 Nov 21;427(1):397-402. https://doi.org/10.1111/j.1365-2966.2012.21986.x

}

TY - JOUR

T1 - Stability of the Lagrangian point L 4 in the spatial restricted three-body problem - application to exoplanetary systems

AU - Schwarz, R.

AU - Bazsó, Á

AU - Érdi, B.

AU - Funk, B.

PY - 2012/11/21

Y1 - 2012/11/21

N2 - This paper is devoted to the study of the stability of the Lagrangian point L 4 in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61° of the test particle. At moderate inclinations (~10° to ~50°), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385 - with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio-eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61°. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits.

AB - This paper is devoted to the study of the stability of the Lagrangian point L 4 in the spatial restricted three-body problem and to the possibility of inclined Trojan-like objects in exoplanetary systems (single and binary star systems). The stability is investigated by numerical methods, computing stability maps in different parameter planes. In the case of circular motion of the primary bodies, it is shown that there are stable orbits up to an inclination i = 61° of the test particle. At moderate inclinations (~10° to ~50°), we find that the stability limit in the mass ratio of the primaries extends well beyond the linear stability value of 0.0385 - with stable orbits existing even for extreme mass ratios of 0.048. In the case of elliptic motion of the primaries, the stable region in the mass ratio-eccentricity plane shrinks as the inclination increases, with no stable orbits being found for inclinations in excess of i = 61°. Both in the circular and elliptic cases, the structure of the stability regions is closely connected with secondary resonances between the librational frequencies. As an application, the results are applied to 35 known exoplanetary systems showing which of them may possess Trojan-like objects in inclined orbits.

KW - Celestial mechanics

KW - Methods: numerical

KW - Planetary systems

UR - http://www.scopus.com/inward/record.url?scp=84868543843&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868543843&partnerID=8YFLogxK

U2 - 10.1111/j.1365-2966.2012.21986.x

DO - 10.1111/j.1365-2966.2012.21986.x

M3 - Article

AN - SCOPUS:84868543843

VL - 427

SP - 397

EP - 402

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 1

ER -