Abstract
We show that a hypersurface of the regularized, spatial circular restricted three-body problem is of contact type whenever the energy level is below the first critical value (the energy level of the first Lagrange point) or if the energy level is slightly above it. A dynamical consequence is that there is no blue sky catastrophe in this energy range.
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Notes
The radius of the Moon-component of the Hill’s region is bounded by the distance of the Moon to \(\ell ^1\).
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Acknowledgements
During this Project, W.C. and G.K. were supported by NRF Grant NRF-2016R1C1B2007662. H.J. was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) (No. 2017R1A5A1015626).
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Communicated by Janko Latschev.
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Cho, W., Jung, H. & Kim, G. The contact geometry of the spatial circular restricted 3-body problem. Abh. Math. Semin. Univ. Hambg. 90, 161–181 (2020). https://doi.org/10.1007/s12188-020-00222-y
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DOI: https://doi.org/10.1007/s12188-020-00222-y