A semi-analytical model for coorbital motion

Abstract

ABSTRACT A globally valid analytically averaged Hamiltonian model for the coorbital motion is hard to construct because the analytical expansions of the disturbing function usually diverge in the quasi-satellite domain that is close to collision singularity. In this paper, an analytically averaged model for the coorbital motion is proposed in case of the circular restricted three-body problem, which can describe properly the transitions that occur at small eccentricities and inclinations, such as the transition between the horseshoe orbit and the quasi-satellite orbit. With the help of the numerical averaging method, numerical experiments are carried out to show the validity and accuracy of the analytically averaged model. The averaged model proposed here can be easily extended to more complicated cases such as the elliptic three-body problem or the planetary three-body problem.