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

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 proper...

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Bibliographic Details
Published in:Meccanica (Milan) 2021-09, Vol.56 (9), p.2183-2195
Main Authors: Deng, Yanxia, Ibrahim, Slim, Zotos, Euaggelos E.
Format: Article
Language:English
Subjects:
Automotive Engineering
Boundaries
Civil Engineering
Classical Mechanics
Engineering
Lagrangian equilibrium points
Mechanical Engineering
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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 α ≥ 2 , the basin boundaries are smooth. On the other hand, in the subcritical case, with α < 1 the boundaries between the different types of basins exhibit fractal properties.
ISSN:0025-6455
1572-9648
DOI:10.1007/s11012-021-01386-4