A cartographic study of the phase space of the elliptic restricted three body problem. Application to the Sun–Jupiter–Asteroid system

Abstract

This work deals with numerical investigations of the phase space of the planar elliptic restricted three body model. The Sun–Jupiter–Asteroid system is considered and the fast Lyapunov indicator (FLI) is used as a tool to examine various types of orbits on which the infinitesimal mass can undergo. The FLI is computed on given grids of initial conditions regularly spaced in the domain 1.5AU⩽a⩽6AU and 0⩽e⩽0.5 and for various choices of initial angles: the argument of perihelion ω and mean anomaly M. On the obtained charts the stability regions, the chaotic zones and the geography of resonances are clearly displayed. Moreover, the ‘V’ shaped layers associated with the mean motion resonances of low order with its chaotic zones due to separatrix splitting and libration regions are clearly distinguished. Their size is discussed as a function of the resonance order and the parameters entering into the perturbing function. The results are discussed and compared with analytical studies concerning the subject.