Numerical investigation on the Hill's type lunar problem with homogeneous potential

Abstract

We consider the planar Hill's lunar problem with a homogeneous gravitational potential. The investigation of the system is twofold. First, the starting conditions of the trajectories are classified into three classes, that is bounded, escaping, and collisional. Second, we study the no-return property of the Lagrange point $L_2$ and we observe that the escaping trajectories are scattered exponentially. Moreover, it is seen that in the supercritical case, with $\alpha \ge 2$, the basin boundaries are smooth. On the other hand, in the subcritical case, with $\alpha <2$ the boundaries between the different types of basins exhibit fractal properties.

12 pages, 10 figures

References in corpus (3)

• Basin entropy: a new tool to analyze uncertainty in dynamical systems
• Investigating the planar circular restricted three-body problem with strong gravitational field
• Global existence and singularity of the Hill's type lunar problem with strong potential

Cited by in corpus (1)

• Global existence and singularity of the Hill's type lunar problem with strong potential