Numerical investigation on the Hill’s type lunar problem with homogeneous potential. (English) Zbl 1526.70013
Summary: 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 the potential exponent \(\alpha \geq 2\), the basin boundaries are smooth. On the other hand, in the subcritical case, with \(\alpha < 1\) the boundaries between the different types of basins exhibit fractal properties.
MSC:
| 70F15 | Celestial mechanics |
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
Keywords:
orbit classification; chaotic scattering; bounded trajectory; escaping trajectory; collisional trajectory; Lagrange point no-returnSoftware:
MathematicaReferences:
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