On the stability of Martian Trojans

Numerical integrations have been performed for several dozen Mars Trojan test particles in a self-consistent model of the solar system. The integration period exceeds 4 Myr. We study primarily the dependence of the stability of the motion on the particles' orbital inclination. The variational equations for the particles' orbits were also solved to study the chaoticity of the trajectories. Several interesting results emerge: (a) long-term stability for the particles appears possible only in well-defined 'inclination windows' 15 deg less than or equal to i less than or equal to 30 deg and 32 deg less than or equal to i less than or equal to 44 deg with respect to Jupiter's orbit. (b) The decisive perturbing and destabilizing influences seem to be simple secular resonances caused by Jupiter and/or Mars. These are tentatively identified. (c) The variational equation solutions do not indicate chaoticity before the actual destabilization occurs, so that the instability is a threshold phenomenon rather than due to sensitive dependence on initial conditions.