Saturn Trojans: Stability Regions in the Phase Space

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Abstract
We use the frequency map analysis method to identify for Trojan orbits of Saturn the regions in the proper orbital element phase space characterized by higher stability. We find that Trojan orbits with proper eccentricity around 0.05, libration amplitude of about 80°, and inclination lower than 15° show a slow diffusion in the proper frequency of the longitude of perihelion ω, which indicates long-term stability. Numerical integration of some of these stable orbits indicates a half-life of about 2.5 Gyr. Orbits with inclination of about 20° are destabilized by a secular resonance with the forcing term 2g6-g5. At higher inclinations Saturn Trojan orbits are unstable on a short timescale (a few×105 yr). Applying the frequency map analysis to the numbered Jupiter Trojans, we find that the size of the stability region is much larger for Jupiter Trojans than for Saturn Trojans. Moreover, the diffusion rate is significantly lower, suggesting that the dynamical lifetimes of Jupiter Trojans are considerably longer. The frequency analysis method allows us to separate the proper and forced components of the eccentricity of Trojans. A semianalytical model for secular motion of Saturn Trojans is presented