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

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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 the potential exponent \(\alpha \ge 2\), 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.

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Authors and Affiliations

  1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, Guangdong, China

    Yanxia Deng

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

    Slim Ibrahim

  3. Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece

    Euaggelos E. Zotos

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  1. Yanxia Deng
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  2. Slim Ibrahim
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  3. Euaggelos E. Zotos
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Correspondence to Euaggelos E. Zotos.

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Deng, Y., Ibrahim, S. & Zotos, E.E. Numerical investigation on the Hill’s type lunar problem with homogeneous potential. Meccanica 56, 2183–2195 (2021). https://doi.org/10.1007/s11012-021-01386-4

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  • DOI: https://doi.org/10.1007/s11012-021-01386-4

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