Open AccessStability of the Lagrangian point L 4 in the spatial restricted three‐body problem – application to exoplanetary systems
Author(s) -
Schwarz R.,
Bazsó Á.,
Érdi B.,
Funk B.
Publication year - 2012
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2012.21986.x
Subject(s) - physics , eccentricity (behavior) , lagrangian point , stability (learning theory) , trojan , three body problem , celestial mechanics , mass ratio , orbit (dynamics) , plane (geometry) , circular orbit , point (geometry) , binary number , libration (molecule) , classical mechanics , geometry , astrophysics , mathematics , astronomy , arithmetic , engineering , machine learning , political science , computer science , law , aerospace engineering
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.