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M.H.M. Morais, C.D. Murray (QMW, London)
We present some mechanisms that can lead to instability of initially small eccentricity Trojan-type orbits associated with planetary satellites.
Dermott & Murray (1981) showed that in the context of the hierarchical restricted three-body problem (M\gg m), stable small eccentricity coorbital motion associated with the mass m, occurs within a region of relative width in semi-major axis as=0.74 \epsilon (where \epsilon is the dimensionless Hill's radius). However, for large eccentricities, the size of the stable coorbital region shrinks as as=4 (\epsilon/e)1/2 \epsilon (Namouni 1999).
The perturbations from other nearby bodies can cause increases in both eccentricity and semi-major axis, leading to ejection from the coorbital region via collisions with the parent body or a nearby perturber. We show that mean motion resonances among saturnian satellites can cause chaotic diffusion of both the eccentricity and the semi-major axis of their associated Trojan orbits. Moreover, we show that secular resonances inside the coorbital regions of some uranian and saturnian satellites can induce significant increases in the eccentricity of Trojan objects.
A better insight into the complicated dynamics exhibited by Trojan objects when they are being subject to perturbations is fundamental to be able to assess the likelihood of finding real examples of these configurations.
\vspace{1.5cm} \noindent Dermott & Murray (1981). Icarus 48, 1-11.
\noindent Namouni (1999). Icarus 137, 293-314.