Open AccessStability of Jupiter Trojans investigated using frequency map analysis: the MATROS project
Author(s) -
Marzari F.,
Tricarico P.,
Scholl H.
Publication year - 2003
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 - 10.1046/j.1365-2966.2003.07051.x
Subject(s) - physics , trojan , orbit (dynamics) , libration (molecule) , jupiter (rocket family) , lagrangian point , stability (learning theory) , eccentricity (behavior) , asteroid , lyapunov exponent , amplitude , classical mechanics , mathematical analysis , space exploration , astronomy , geometry , quantum mechanics , mathematics , point (geometry) , nonlinear system , machine learning , computer science , law , political science , engineering , aerospace engineering
Using the frequency map analysis (FMA) method we investigate the stability properties of Trojan‐type orbits in the proximity of the L 4 and L 5 Lagrangian points of Jupiter. This study is part of the MATROS project. The orbits of about 2 × 10 4 virtual Trojans with random initial conditions have been computed numerically and for each body the diffusion rate in frequency space has been determined by spectral analysis. The diffusion portraits show where stable orbits are located in the space of proper elements for different values of inclination. For low inclined orbits we reproduce the stability region outlined by Levison, Shoemaker & Shoemaker and, due to our fast sampling capability, we find additional resonant features in the libration amplitude versus proper eccentricity space. At higher inclinations, the stability region gradually shrinks and it disappears for inclinations of about 40°. The maximal Lyapunov characteristic exponent is computed for a limited number of Trojan orbits in our sample and the predictions concerning the chaotic behaviour of each orbit are compared with those given by the FMA method. A good agreement is obtained and the value of the Lyapunov exponent may be used to tune the results of the FMA analysis. A synthetic secular theory for the proper frequencies of Jupiter Trojans is obtained by numerically fitting the outcome of the frequency map analysis.