Stability of Jupiter Trojans investigated using frequency map analysis: the MATROS project

Using the frequency map analysis (FMA) method we investigate the stability properties of Trojan-type orbits in the proximity of the L4 and L5 Lagrangian points of Jupiter. This study is part of the MATROS project. The orbits of about 2 × 104 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