Equilibrium dynamics of the restricted 3-body problem with prolate primaries

Abstract

In this paper, the equilibrium dynamics of the circular restricted (2+1)-body problem with two elongated main bodies is investigated. More precisely, the influence of the mass parameter and the non-sphericity parameter on the position and stability of the libration points of this characteristic configuration is studied through numerical and semi-analytical methods. In addition, the effect of these two parameters of the system on the fractality of the basins of convergence is also investigated, for this, two quantitative indicators are used: the boundary basin entropy and the uncertainty dimension. It is shown that when the two objects have the same value of the non-sphericity parameter, the appearance of new collinear and non-collinear libration points takes place. Compared to the classical circular restricted three-body problem, our numerical study reveals that when both primaries are prolate, some of the collinear libration points may be stable.

Keywords

• Restricted three-body problem
• Equilibrium points
• Stability analysis